Evaluate [² as dx Select the better substitution: (A) = x. (B) u = e, or (C) u = -5x². O(A) O(B) O(C) With this substitution, the limits of integration are updated directly as follows: The lower lim

Answers

Answer 1

(A) This substitution is straightforward and simplifies the integral directly.

(B) This substitution is not suitable for this integral since it does not directly relate to the variable x or the integrand x^2. It would not simplify the integral in any meaningful way.

(C) In this case, du = -10x dx, which is not a direct relation to the integrand x^2. It would complicate the integral and make the substitution less efficient.

To evaluate the integral ∫x^2 dx, we can consider the given substitutions and determine which one would be better.

(A) Letting u = x as the substitution:

In this case, du = dx, and the integral becomes ∫u^2 du. This substitution is straightforward and simplifies the integral directly.

(B) Letting u = e as the substitution:

This substitution is not suitable for this integral since it does not directly relate to the variable x or the integrand x^2. It would not simplify the integral in any meaningful way.

(C) Letting u = -5x^2 as the substitution:

In this case, du = -10x dx, which is not a direct relation to the integrand x^2. It would complicate the integral and make the substitution less efficient.

Therefore, the better substitution among the given options is (A) u = x. It simplifies the integral and allows us to directly evaluate ∫x^2 dx as ∫u^2 du.

Regarding the limits of integration, if the original limits were from a to b, then with the substitution u = x, the updated limits would become u = a to u = b. In this case, since no specific limits are given in the question, the limits of integration remain unspecified.

Learn more about integral here:

https://brainly.com/question/31059545

#SPJ11


Related Questions

when alejandro runs the 400 meter dash, his finishing times are normally distributed with a mean of 60 seconds and a standard deviation of 1 second. if alejandro were to run 34 practice trials of the 400 meter dash, how many of those trials would be between 59 and 61 seconds, to the nearest whole number?

Answers

We can say that approximately 23 out of the 34 practice trials would fall between 59 and 61 seconds.

To determine the number of practice trials out of 34 that would fall between 59 and 61 seconds, we can utilize the properties of a normal distribution with the given mean and standard deviation.

Given that Alejandro's finishing times are normally distributed with a mean of 60 seconds and a standard deviation of 1 second, we can represent this distribution as follows:

μ = 60 (mean)

σ = 1 (standard deviation)

To find the proportion of trials that fall between 59 and 61 seconds, we need to calculate the area under the normal curve within this range. Since the normal distribution is symmetrical, we can determine this area by calculating the area under the curve between the mean and the upper and lower limits.

Using a standard normal distribution table or a statistical calculator, we can find the z-scores for the values 59 and 61, based on the mean and standard deviation. The z-score represents the number of standard deviations a data point is away from the mean.

For 59 seconds:

z = (59 - 60) / 1 = -1

For 61 seconds:

z = (61 - 60) / 1 = 1

Next, we find the area under the curve between these z-scores. By referring to a standard normal distribution table or using a calculator, we can determine the area associated with each z-score.

The area to the left of z = -1 is approximately 0.1587.

The area to the left of z = 1 is approximately 0.8413.

To find the area between these two z-scores, we subtract the smaller area from the larger area:

Area between z = -1 and z = 1 = 0.8413 - 0.1587 = 0.6826

This means that approximately 68.26% of the trials will fall between 59 and 61 seconds.

To find the number of trials out of 34 that fall within this range, we multiply the proportion by the total number of trials:

Number of trials between 59 and 61 seconds = 0.6826 * 34 ≈ 23.23

Rounding this to the nearest whole number, we can say that approximately 23 out of the 34 practice trials would fall between 59 and 61 seconds.

for more such question on seconds visit

https://brainly.com/question/25734188

#SPJ8

Problem 14. (1 point) Use the definition of the derivative to find the derivative of: f(x) = 4 Part 1: State the definition of the derivative ^ f'(x) = lim = h0 Part 2: Using the function given, find

Answers

Part 1. The definition of the derivative is f'(x) = lim (h->0) [f(x + h) - f(x)] / h.

Part 2. The derivative of f(x) = 4 is f'(x) = 0.

Part 1: The definition of the derivative is stated as follows:

f'(x) = lim (h->0) [f(x + h) - f(x)] / h

Part 2: Let's find the derivative of f(x) = 4 using the definition.

We have f(x) = 4, which means the function is a constant. In this case, the derivative can be found as follows:

f'(x) = lim (h->0) [f(x + h) - f(x)] / h

Substituting f(x) = 4:

f'(x) = lim (h->0) [4 - 4] / h

Simplifying:

f'(x) = lim (h->0) 0 / h

Since the numerator is 0, the limit evaluates to 0 regardless of the value of h:

f'(x) = 0

Therefore, the derivative of f(x) = 4 is f'(x) = 0.

Learn more about "derivative ":

https://brainly.com/question/23819325

#SPJ11

Use the Wronskian to show that the functions y1 = e^6x and y2 = e^2x are linearly independent. Wronskian = det[] = These functions are linearly independent because the Wronskian isfor all x.

Answers

The functions y1 = e^(6x) and y2 = e^(2x) are linearly independent because the Wronskian, which is the determinant of the matrix formed by their derivatives, is nonzero for all x.

To determine the linear independence of the functions y1 and y2, we can compute their Wronskian, denoted as W(y1, y2), which is defined as:

W(y1, y2) = det([y1, y2; y1', y2']),

where y1' and y2' represent the derivatives of y1 and y2, respectively.

In this case, we have y1 = e^(6x) and y2 = e^(2x). Taking their derivatives, we have y1' = 6e^(6x) and y2' = 2e^(2x).

Substituting these values into the Wronskian formula, we have:

W(y1, y2) = det([e^(6x), e^(2x); 6e^(6x), 2e^(2x)]).

Evaluating the determinant, we get:

W(y1, y2) = 2e^(8x) - 6e^(8x) = -4e^(8x).

Since the Wronskian, -4e^(8x), is nonzero for all x, we can conclude that the functions y1 = e^(6x) and y2 = e^(2x) are linearly independent.

Therefore, the linear independence of these functions is demonstrated by the fact that their Wronskian is nonzero for all x.

Learn more about linearly independent  here:

https://brainly.com/question/12902801

#SPJ11

Find the radius and interval of convergence for each of the following series:
∑n=0[infinity]xnn!
∑n=1[infinity](−1)n+1xnn
∑n=0[infinity]2n(x−3)n
∑n=0[infinity]n!xn

Answers

The radius and interval of convergence for each of the following series:

∑n=0[infinity]xnn! the radius of convergence is 1, and the interval of convergence is (-1, 1).∑n=1[infinity](−1)n+1xnn the radius of convergence is 1, and the interval of convergence is (-1, 1).∑n=0[infinity]2n(x−3)n  the radius of convergence is 1/2, and the interval of convergence is (3 - 1/2, 3 + 1/2), which simplifies to (5/2, 7/2).∑n=0[infinity]n!xn the radius of convergence is 1, and the interval of convergence is (-1, 1).

To find the radius and interval of convergence for each series, we can use the ratio test. Let's analyze each series one by one:

1. Series: ∑(n=0 to infinity) x^n / n!

Ratio Test:

We apply the ratio test by taking the limit as n approaches infinity of the absolute value of the ratio of the (n+1)-th term to the n-th term:

lim(n→∞) |(x^(n+1) / (n+1)!) / (x^n / n!)|

Simplifying and canceling common terms, we get:

lim(n→∞) |x / (n+1)|

The series converges if the limit is less than 1. So we have:

|x / (n+1)| < 1

Taking the absolute value of x, we get:

|x| / (n+1) < 1

|x| < n+1

For the series to converge, the right side of the inequality should be bounded. Hence, we have:

n+1 > 0

n > -1

Therefore, the series converges for all x such that |x| < 1.

Hence, the radius of convergence is 1, and the interval of convergence is (-1, 1).

2. Series: ∑(n=1 to infinity) (-1)^(n+1) * x^n / n

Ratio Test:

We apply the ratio test:

lim(n→∞) |((-1)^(n+2) * x^(n+1) / (n+1)) / ((-1)^(n+1) * x^n / n)|

Simplifying and canceling common terms, we get:

lim(n→∞) |-x / (n+1)|

The series converges if the limit is less than 1. So we have:

|-x / (n+1)| < 1

|x| / (n+1) < 1

|x| < n+1

Again, for the series to converge, the right side of the inequality should be bounded. Hence, we have:

n+1 > 0

n > -1

Therefore, the series converges for all x such that |x| < 1.

Hence, the radius of convergence is 1, and the interval of convergence is (-1, 1).

3. Series: ∑(n=0 to infinity) 2^n * (x-3)^n

Ratio Test:

We apply the ratio test:

lim(n→∞) |2^(n+1) * (x-3)^(n+1) / (2^n * (x-3)^n)|

Simplifying and canceling common terms, we get:

lim(n→∞) |2(x-3)|

The series converges if the limit is less than 1. So we have:

|2(x-3)| < 1

2|x-3| < 1

|x-3| < 1/2

Therefore, the series converges for all x such that |x-3| < 1/2.

Hence, the radius of convergence is 1/2, and the interval of convergence is (3 - 1/2, 3 + 1/2), which simplifies to (5/2, 7/2).

4. Series: ∑(n=0 to infinity) n! * x^n

Ratio Test:

We apply the ratio test:

lim(n→∞) |((n+1)! * x^(n+1)) / (n! * x^n)|

Simplifying and canceling common terms, we get:

lim(n→∞) |(n+1) * x|

The series converges if the limit is less than 1. So we have:

|(n+1) * x| < 1

|x| < 1 / (n+1)

For the series to converge, the right side of the inequality should be bounded. Hence, we have:

n+1 > 0

n > -1

Therefore, the series converges for all x such that |x| < 1.

Hence, the radius of convergence is 1, and the interval of convergence is (-1, 1).

Learn more about the radius of convergence here:

brainly.com/question/2289050

#SPJ11

Find the volume of the solid generated in the following situation.
The region R bounded by the graph of y=6sinx
and the​ x-axis on [0, π] is revolved about the line y=−6.
The volume of the solid generated when R is revolved about the line y=−6
is _______ in cubic units.
​(Type an exact​ answer, using π as​ needed.)

Answers

The volume of the solid generated when the region R, bounded by the graph of y = 6sin(x) and the x-axis on the interval [0, π], is revolved about the line y = -6 is _______ cubic units (exact answer in terms of π).

To find the volume of the solid generated by revolving the region R about the line y = -6, we can use the method of cylindrical shells. The volume of each cylindrical shell is given by the formula:

V = 2π * integral[R] (radius * height) dx

In this case, the radius of each cylindrical shell is the distance from the line y = -6 to the curve y = 6sin(x), which is 12 units. The height of each shell is the infinitesimal change in x, dx. We integrate this expression over the interval [0, π] to cover the entire region R.

Therefore, the volume of the solid is given by:

V = 2π * integral[0 to π] (12 * dx)

Integrating this expression will give us the volume of the solid in terms of π. Evaluating the integral will provide the exact volume of the solid generated by revolving the region R.

Learn more about cylindrical shell here:

https://brainly.com/question/31786086

#SPJ11

1 Find the Taylor Polynomial of degree 2 for The given function centered at the given number a fu)= cos(5x) a : 2T. at

Answers

The Taylor Polynomial of degree 2 for the given function centered at a is as follows: The Taylor polynomial of degree 2 for the given function is given by, P2(x) = 1 - 25(x - 2)²/2.

Given function is fu)= cos(5x)We need to find the Taylor Polynomial of degree 2 for the given function centered at the given number a = 2T. To find the Taylor Polynomial of degree 2, we need to find the first two derivatives of the given function. f(x) = cos(5x)f'(x) = -5sin(5x)f''(x) = -25cos(5x)We substitute a = 2T, f(2T) = cos(10T), f'(2T) = -5sin(10T), f''(2T) = -25cos(10T) Now, we use the Taylor's series formula for degree 2:$$P_{2}(x)=f(a)+f'(a)(x-a)+f''(a)\frac{(x-a)^{2}}{2!}$$$$P_{2}(2T)=f(2T)+f'(2T)(x-2T)+f''(2T)\frac{(x-2T)^{2}}{2!}$$By plugging in the values, we get;$$P_{2}(2T)=cos(10T)-5sin(10T)(x-2T)-25cos(10T)\frac{(x-2T)^{2}}{2}$$$$P_{2}(2T)=1-25(x-2)^{2}/2$$Therefore, the Taylor polynomial of degree 2 for the given function centered at a = 2T is P2(x) = 1 - 25(x - 2)²/2.

Learn more about derivatives here:

https://brainly.com/question/30466081

#SPJ11

1. DETAILS MY NOTES ASK YOUR TEACHER Suppose that f(4) = 2 and f'(4) = -3. Find h'(4). Round your answer to two decimal places. (a) h(x) = = (3x? + - 5ln (f(x)) ? h'(4) = (b) 60f(x) h(x) = 2x + 3 h'(4

Answers

By using differentiation we find the value of h'(4) = 48.5.

To find h'(4), we need to differentiate the function h(x) with respect to x and then evaluate the derivative at x = 4.

(a) [tex]h(x) = 3x² - 5ln(f(x))[/tex]

To find h'(x), we'll differentiate each term separately using the power rule and chain rule:

[tex]h'(x) = 6x - 5 * (1/f(x)) * f'(x)[/tex]

Since we are given that f(4) = 2 and f'(4) = -3, we can substitute these values into the derivative expression:

[tex]h'(4) = 6(4) - 5 * (1/f(4)) * f'(4)[/tex]

= 24 - 5 * (1/2) * (-3)

= 24 + 15/2

= 48.5

Therefore, h'(4) = 48.5.

learn more about differentiation here:

https://brainly.com/question/24062595

#SPJ11

Plsss helpppp hssnsnns

Answers

Answer:

m∠8 = 45°

Step-by-step explanation:

Angles 8 and 9 are vertical angles. Vertical angles are two angles opposite each other when two straight lines intersect each otherThey're congruent and thus equal.Therefore, since m∠9 = 45°, m∠8 also = 45°

the binary string 01001010001101 is afloating-point number expressed using the 14 bit simple model given inyour text. assuming an exponent bias is 15. waht is its decimal equivalent

Answers

The decimal equivalent of the binary string 01001010001101 using the 14-bit simple model with an exponent bias of 15 is 51/32

What is a binary string?

A binary string is a finite sequence of characters or digits that consists of only two possible symbols, typically represented as "0" and "1". These symbols correspond to the binary numeral system, where each digit represents a power of two. Binary strings are commonly used in computer science and digital communication systems to represent and manipulate binary data.

To convert the binary string 01001010001101 to its decimal equivalent using the 14-bit simple model with an exponent bias of 15, we can follow these steps:

Identify the sign bit: The leftmost bit (bit 0) represents the sign of the number. In this case, the sign bit is 0, indicating a positive number.

Determine the exponent: The next 5 bits (bits 1-5) represent the exponent. Convert these bits to decimal and subtract the bias to obtain the actual exponent value. In this case, the exponent bits are 10010. Converting 10010 to decimal gives us 18. Subtracting the bias of 15, the actual exponent is [tex]18 - 15 = 3.[/tex]

Calculate the significand: The remaining 8 bits (bits 6-13) represent the significand or mantissa. To obtain the significant value, we convert these bits to decimal and divide by 2^8 (since there are 8 bits). In this case, the significant bits are 00110011. Converting 00110011 to decimal gives us 51. Dividing 51 by [tex]2^8,[/tex]we get [tex]51/256.[/tex]

Determine the decimal value: To calculate the decimal equivalent, we multiply the significand value by 2 raised to the power of the exponent. In this case, the decimal value is[tex](51/256) * 2^3 = 51/32.[/tex]

Therefore, the decimal equivalent of the binary string 01001010001101 using the 14-bit simple model with an exponent bias of 15 is [tex]51/32.[/tex]

Learn more about binary strings:

https://brainly.com/question/28564491

#SPJ4

The number N of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given: ) 1996 1998 2000 2002 2004 2006 N 44 69 109 141 182 233 (a) Find the average rate of cell phone growth (i) from 2002 to 2006 (ii) from 2002 to 2004 (iii) from 2000 to 2002 In each case, include the units. (6) Estimate the instantaneous rate of growth in 2002 by taking the average of two average rates of change. What are its units? (c) Estimate the instantaneous rate of growth in 2002 by mea- suring the slope of a tangent

Answers

a(i). The average rate of cellphone growth per year is 23 million subscriber per year.

a(ii). The average rate of growth is 20.5 million subscribers

a(iii). The average rate of growth is 16 million subscribers.

b. The instantaneous rate of growth is 21.75 million subscribers

c. The instantaneous rate of growth is 23 million subscribers

What is the average rate of cell phone growth?

(a) The average rate of cell phone growth is calculated by dividing the change in the number of subscribers by the change in time.

(i) From 2002 to 2006, the number of subscribers increased from 141 million to 233 million. This is a change of 92 million subscribers in 4 years. The average rate of growth is therefore 92/4 = 23 million subscribers per year.

(ii) From 2002 to 2004, the number of subscribers increased from 141 million to 182 million. This is a change of 41 million subscribers in 2 years. The average rate of growth is therefore 41/2 = 20.5 million subscribers per year.

(iii) From 2000 to 2002, the number of subscribers increased from 109 million to 141 million. This is a change of 32 million subscribers in 2 years. The average rate of growth is therefore 32/2 = 16 million subscribers per year.

(b) The instantaneous rate of growth in 2002 is estimated by taking the average of the average rates of change from 2002 to 2004 and from 2002 to 2006. This is equal to (20.5 + 23)/2 = 21.75 million subscribers per year.

(c) The instantaneous rate of growth in 2002 is estimated by measuring the slope of the tangent to the graph of the number of subscribers against time at 2002. The slope of the tangent is equal to the change in the number of subscribers divided by the change in time. The change in the number of subscribers is 92 million and the change in time is 4 years. The slope of the tangent is therefore 92/4 = 23 million subscribers per year.

learn more on average rate here;

https://brainly.com/question/8728504

#SPJ1

Find the average cost function if cost and revenue are given by C(x) = 161 + 6.9x and R(x) = 9x -0.02X? The average cost function is C(x) =

Answers

The average cost function is cavgx) = 161/x + 6. the average cost function is calculated by dividing the total cost (c(x)) by the quantity (x). in this case, we have:

c(x) = 161 + 6.9x (total cost)

x (quantity)

to find the average cost function , we divide the total cost by the quantity:

cavgx) = c(x) / x

substituting the given values:

cavgx) = (161 + 6.9x) / x

simplifying the expression, we can rewrite it as:

cavgx) = 161/x + 6.9 9.

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

(1 point) Evaluate the integral when x>0
(1 point) Evaluate the integral when x > 0 Answer: [m(2²+ In (x² + 17x + 60) dx.

Answers

The integral of [tex]ln(x^2 + 17x + 60)[/tex] with respect to x, when x is greater than 0, evaluates to [tex]2x ln(x + 5) - 2x + C[/tex] , where C represents the constant of integration.

To calculate the integral, we can use the substitution method.

Let [tex]u = x^2 + 17x + 60[/tex].

Then, [tex]du/dx = 2x + 17[/tex],

and solving for dx, we have [tex]dx = du/(2x + 17)[/tex].

Substituting these values into the integral, we get:

[tex]\int\limits{ln(x^2 + 17x + 60) } \,dx = \int\limits ln(u) * (du/(2x + 17))[/tex]

Now, we can separate the variables and rewrite the integral as:

=[tex]\int\limits ln(u) * (1/(2x + 17)) du[/tex]

Next, we can focus on the remaining x term in the denominator. We can rewrite it as follows:

=[tex]\int\limits ln(u) * (1/(2(x + 8.5))) du[/tex]

Pulling the constant factor of 1/2 out of the integral, we have:

=[tex](1/2) * \int\limits ln(u) * (1/(x + 8.5)) du[/tex]

Finally, integrating ln(u) with respect to u gives us:

=[tex](1/2) * (u ln(u) - u) + C[/tex]

Substituting back u = x^2 + 17x + 60, we get the final result:

= [tex]2x ln(x + 5) - 2x + C[/tex]

Therefore, the integral of [tex]ln(x^2 + 17x + 60)[/tex]with respect to x, when x is greater than 0, is [tex]2x ln(x + 5) - 2x + C[/tex], where C represents the constant of integration.

Learn more about integration here:

https://brainly.com/question/29073472

#SPJ11

The correct question is:

Evaluate the integral when > 0

[tex]\int\limits{ ln(x^{2} + 17x+60)} \, dx[/tex]

Solve the following differential equations. (1 - x)y' = cosa y, y(-1) = 3 dy dx - xy = x, y(0) = 2

Answers

The particular solution for the given initial condition is: y = 1 + e^(-x^2/2)

To solve the given differential equations, let's take them one by one:

1. (1 - x)y' = cos(x) * y

Rearranging the equation, we have:

y' = (cos(x) * y) / (1 - x)

This is a separable differential equation. We can separate the variables and integrate both sides:

(1 - x) * dy / y = cos(x) * dx

Integrating both sides:

∫(1 - x) * dy / y = ∫cos(x) * dx

ln|y| - x^2/2 = sin(x) + C1

Simplifying and exponentiating:

|y| = e^(sin(x) + x^2/2 + C1)

Considering the absolute value, we can rewrite it as:

y = ±e^(sin(x) + x^2/2 + C1)

Now, we can use the initial condition y(-1) = 3 to determine the constant C1:

y(-1) = ±e^(sin(-1) + (-1)^2/2 + C1) = ±e^(-1 + 1/2 + C1) = ±e^(1/2 + C1)

Since y(-1) = 3, we can set it as:

3 = ±e^(1/2 + C1)

Taking the positive sign, we have:

e^(1/2 + C1) = 3

1/2 + C1 = ln(3)

C1 = ln(3) - 1/2

Therefore, the particular solution for the given initial condition is: y = e^(sin(x) + x^2/2 + ln(3) - 1/2)

2. (dy/dx) - xy = x

This is a linear first-order differential equation. We can solve it using an integrating factor. First, let's rewrite it in standard form:

dy/dx = xy + x

Comparing this with the standard form of a linear first-order differential equation, we have:

P(x) = x

The integrating factor is given by:

μ(x) = e^(∫P(x)dx) = e^(∫x dx) = e^(x^2/2)

Now, multiplying both sides of the equation by the integrating factor:

e^(x^2/2) * dy/dx - xe^(x^2/2) * y = xe^(x^2/2)

Recognizing the left side as the derivative of (e^(x^2/2) * y) with respect to x, we can rewrite the equation as:

d/dx(e^(x^2/2) * y) = xe^(x^2/2)

Integrating both sides:

∫d/dx(e^(x^2/2) * y) dx = ∫xe^(x^2/2) dx

e^(x^2/2) * y = ∫xe^(x^2/2) dx

To find the integral on the right side, we can use a substitution. Let u = x^2/2, then du = x dx. The integral becomes:

∫e^u du = e^u + C2

Substituting back:

e^(x^2/2) * y = e^(x^2/2) + C2

Dividing both sides by e^(x^2/2):

y = 1 + C2 * e^(-x^2/2)

Using the initial condition y(0) = 2, we can find the value of the constant C2:

2 = 1 + C2 * e^(-0^2/2) = 1 + C2

C2 = 2 - 1 = 1

Therefore, the particular solution for the given initial condition is: y = 1 + e^(-x^2/2)

To know more about differential equations, visit the link : https://brainly.com/question/1164377

#SPJ11

help with 5,6,7 please
Find the second derivative d²y dx2
5)y=x2+x A) 2x3/2-1 x3/2 6) f(x) = x3/2-3x1/4+5x-2 8x3/2-1 B( 43/2 314+5- ,ܛ ܝ 1/2 ,A) T 774- xܛ +x1/2© 7) y =2x3/2-6x1/2 A) 1.5x-1/2+1.5x-3/2 C)3x1/2-3x-1/2 8

Answers

To find the second derivative, d²y/dx², we need to differentiate the given function twice with respect to x.

(5) y = x^2 + x

First, let's find the first derivative, dy/dx:

dy/dx = d/dx (x^2 + x)

= 2x + 1

Now, let's find the second derivative, d²y/dx²:

d²y/dx² = d/dx (2x + 1)

= 2

Therefore, the second derivative of y = x^2 + x is d²y/dx² = 2.

(6) f(x) = x^(3/2) - 3x^(1/4) + 5x^(-2)

First, let's find the first derivative, df/dx:

df/dx = d/dx (x^(3/2) - 3x^(1/4) + 5x^(-2))

= (3/2)x^(1/2) - (3/4)x^(-3/4) - 10x^(-3)

Now, let's find the second derivative, d²f/dx²:

d²f/dx² = d/dx ((3/2)x^(1/2) - (3/4)x^(-3/4) - 10x^(-3))

= (3/4)x^(-1/4) + (9/16)x^(-7/4) + 30x^(-4)

Therefore, the second derivative of f(x) = x^(3/2) - 3x^(1/4) + 5x^(-2) is d²f/dx² = (3/4)x^(-1/4) + (9/16)x^(-7/4) + 30x^(-4).

(7) y = 2x^(3/2) - 6x^(1/2)

First, let's find the first derivative, dy/dx:

dy/dx = d/dx (2x^(3/2) - 6x^(1/2))

= 3x^(1/2) - 3x^(-1/2)

Now, let's find the second derivative, d²y/dx²:

d²y/dx² = d/dx (3x^(1/2) - 3x^(-1/2))

= (3/2)x^(-1/2) + (3/4)x^(-3/2)

Therefore, the second derivative of y = 2x^(3/2) - 6x^(1/2) is d²y/dx² = (3/2)x^(-1/2) + (3/4)x^(-3/2).

To know more about derivative refer here:

https://brainly.com/question/28672151#

#SPJ11

How much interest will $1,200 earn over 10 years with 5% compounded interest annually? A. $600
B. $679.98
C> $754.67 D. $1,954.67

Answers

The interest earned can be calculated using the formula for compound interest, which takes into account the principal amount, the interest rate, and the time period. By substituting the given values into the formula, we can determine the amount of interest earned.

The formula for compound interest is given by: A = P(1 + r/n)^(nt) - P,

where A is the total amount accumulated, P is the principal amount, r is the interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years.

In this case, the principal amount (P) is $1,200, the interest rate (r) is 5% (or 0.05 as a decimal), the number of times interest is compounded (n) is 1 (annually), and the number of years (t) is 10.

Plugging these values into the formula, we get:

A = 1200(1 + 0.05/1)^(1*10) - 1200,

A = 1200(1.05)^10 - 1200.

Evaluating the expression, we find:

A ≈ 1795.86 - 1200,

A ≈ 595.86.

Therefore, the interest earned over 10 years is approximately $595.86.

None of the given options (A, B, C, or D) matches the calculated value.

Learn more about compound interest here: brainly.com/question/29639856

#SPJ11

x² 64000 find For the given cost function C(x) = 128√ + a) The cost at the production level 1500 b) The average cost at the production level 1500 c) The marginal cost at the production level 1500 d

Answers

To find the values of the cost function C(x) = 128√x² + 64000, we can substitute the production level x into the function.

a) The cost at the production level 1500:

Substitute x = 1500 into the cost function:

C(1500) = 128√(1500)² + 64000

        = 128√2250000 + 64000

        = 128 * 1500 + 64000

        = 192000 + 64000

        = 256000

Therefore, the cost at the production level 1500 is $256,000.

b) The average cost at the production level 1500:

The average cost is calculated by dividing the total cost by the production level.

Average Cost at x = C(x) / x

Average Cost at 1500 = C(1500) / 1500

Average Cost at 1500 = 256000 / 1500

Average Cost at 1500 ≈ 170.67

Therefore, the average cost at the production level 1500 is approximately $170.67.

c) The marginal cost at the production level 1500:

The marginal cost represents the rate of change of cost with respect to the production level, which can be found by taking the derivative of the cost function.

Marginal Cost at x = dC(x) / dx

Marginal Cost at 1500 = dC(1500) / dx

Differentiating the cost function:

dC(x) / dx = 128 * (1/2) * (2√x²) = 128√x

Substitute x = 1500 into the derivative:

Marginal Cost at 1500 = 128√1500

                     ≈ 128 * 38.73

                     ≈ $4,951.04

Therefore, the marginal cost at the production level 1500 is approximately $4,951.04.

In summary, the cost at the production level 1500 is $256,000, the average cost is approximately $170.67, and the marginal cost is approximately $4,951.04.

Visit here to learn more about marginal cost:

brainly.com/question/14923834

#SPJ11

The point () T T 9, 3'2 in the spherical coordinate system represents the point (3:50) 9, in the cylindrical coordinate system. Select one: True O False

Answers

The statement "The point (9, 3π/2) in the spherical coordinate system represents the point (3, 50) in the cylindrical coordinate system" is False.

In the spherical coordinate system, a point is represented by three coordinates: (ρ, θ, φ), where ρ represents the distance from the origin, θ represents the angle in the xy-plane, and φ represents the angle from the positive z-axis. In the cylindrical coordinate system, a point is represented by three coordinates: (ρ, θ, z), where ρ represents the distance from the z-axis, θ represents the angle in the xy-plane, and z represents the height.

The given points, (9, 3π/2) in the spherical coordinate system and (3, 50) in the cylindrical coordinate system, have different values for the distance coordinate (ρ) and the angle coordinate (θ). Therefore, the statement is false as the two points do not correspond to each other in the different coordinate systems.

Learn more about coordinate system here: brainly.com/question/4726772

#SPJ11

Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) - 4x 7-X f(x) Σ n = 0 Determine the interval of convergence. (Enter your answer)

Answers

The general form of a Taylor series is Σn=0 to ∞ (f^n(0) * x^n) / n!, where f^n(0) represents the nth derivative of f(x) evaluated at x = 0. The interval of convergence is -1 < x < 1.

To find the power series representation of f(x) = 4x^(7-x), we need to compute the derivatives of f(x) and evaluate them at x = 0. After performing the necessary calculations, we obtain the following power series representation:

f(x) = Σn=0 to ∞ (4 * (-1)^n * x^(7-n)) / n!

This power series representation represents the function f(x) as an infinite sum of terms involving powers of x, each multiplied by a coefficient determined by the corresponding derivative of f(x) at x = 0.

The interval of convergence of this power series can be determined using the ratio test. By applying the ratio test to the power series, we can find the values of x for which the series converges. The ratio test states that if the limit of |a_(n+1) / a_n| as n approaches infinity is less than 1, the series converges. In this case, the ratio |(4 * (-1)^(n+1) * x^(6-n)) / ((n+1)x^n)| simplifies to |4 * (-1)^(n+1) * (x / (n+1))|. The series converges when |x / (n+1)| < 1, which leads to the interval of convergence -1 < x < 1.

Therefore, the power series representation for f(x) = 4x^(7-x) centered at x = 0 is given by Σn=0 to ∞ (4 * (-1)^n * x^(7-n)) / n!, and the interval of convergence is -1 < x < 1.

Learn more about power series here:

https://brainly.com/question/29896893

#SPJ11

Let f(t) = (-1)cos (not). = n=1 Find the term with the largest amplitude in the Fourier series of the periodic solution x (t) to ö + 90x = f(t). = Let u (x, t) denote the vertical displacement at time t and position x of an infinitely long string. Suppose that u (x, t) satisfies au at2 a2u 9 ar2 The initial waveform at t = 0 is a horizontal line with vertical displacement 0 (that is u (x,0) = 0), but initial vertical velocity at x is cos (I). Find a formula for u (x, t). u (x, t) = =

Answers

To find the term with the largest amplitude, we need to evaluate the magnitudes of the coefficients cn and select the term with the highest magnitude.

To find the term with the largest amplitude in the Fourier series of the periodic solution x(t) to the equation ω^2 + 90x = f(t), we need to determine the Fourier series representation of f(t) and identify the term with the largest coefficient.

Given that f(t) = (-1)^n*cos(nt), we can express it as a Fourier series using the formula:

f(t) = a0/2 + ∑(ancos(nωt) + bnsin(nωt))

In this case, since the cosine term has a coefficient of (-1)^n, the Fourier series representation will have only cosine terms.

The coefficient of the nth cosine term, an, can be calculated using the formula:

an = (2/T) * ∫[0,T] f(t)*cos(nωt) dt

where T is the period of the function.

In this case, ω^2 + 90x = f(t), so we can rewrite it as ω^2 = f(t) - 90x. We assume that x(t) also has a Fourier series representation:

x(t) = ∑(cncos(nωt) + dnsin(nωt))

By substituting this representation into the equation ω^2 = f(t) - 90x and comparing coefficients of cosine terms, we can determine the coefficients cn.

Learn more about vertical displacement here:

https://brainly.com/question/32064262

#SPJ11

4. Compute each derivative analytically; show work, and state rule(s) used! (a) [x2.23* + cos(x)] (b) d [sin(x) dx x2+1 (c) & [25.11+ x2]

Answers

(a) To compute the derivative o[tex]f f(x) = x^2 + 3x + cos(x)[/tex], we can use the sum rule and the power rule. Taking the derivative term by term, we have:

[tex]f'(x) = 2x + 3 - sin(x)[/tex]

(b) To find the derivative of [tex]g(x) = (sin(x))/(x^2 + 1)[/tex], we can apply the quotient rule. The quotient rule states that for a function of the form f(x)/g(x), the derivative is given by:

[tex]g'(x) = (g(x)f'(x) - f(x)g'(x))/(g(x))^2[/tex]

Using the quotient rule, we differentiate term by term:

[tex]g'(x) = [(cos(x))(x^2 + 1) - (sin(x))(2x)] / (x^2 + 1)^2[/tex]

(c) Differentiating[tex]h(x) = √(25 + x^2)[/tex] with respect to x, we can use the chain rule. The chain rule states that for a composition of functions f(g(x)), the derivative is given by:

[tex]h'(x) = f'(g(x)) * g'(x)[/tex]

[tex]h'(x) = (1/2)(25 + x^2)^(-1/2) * (2x) = x / √(25 + x^2)[/tex]

learn more about:- quotient rule here

https://brainly.com/question/30278964

#SPJ11

6. Find the volume of the sphere below
where r = 5.
5 in

Answers

Answer:

523.33 in³

-----------------------

Use the equation for volume:

V = (4/3)πr³

Substitute 5 for r and 3.14 for π, then calculate:

V = (4/3)(3.14)(5³) V = 523.33 in³

The volume of the sphere when r is 5.5 inches, is 696.90 in³.

We know that the formula to calculate the volume of the sphere is as follows:

V = (4/3)πr³.......(i)

Where V⇒ Volume of sphere

r⇒ Radius of the sphere to its outer circumference

Now, as per the question:

The radius of sphere, R = 5.5 inches

Putting the values in equation (i),

V=(4/3)π(5.5)³

V=696.90 in³

Thus, the volume of the sphere having 5.5 inches radius will be 696.90 in³.

To learn more about the Volume of the sphere:

https://brainly.com/question/10171109

A volume is described as follows: 1. the base is the region bounded by y y = 2.9x2 + 0.4 and x = 2. every cross section perpendicular to the x-axis is a square. €2.92 = 1; Find the volume of this ob

Answers

The volume of the given oblique cylinder is approximately equal to 14.86.

The given region is bounded by the curve y = 2.9x² + 0.4 and the line x = 2.

The shape of each cross-section is a square. We need to find the volume of the given solid.

Let's represent the given region graphically; Volume of the solid can be obtained using the integral of the area of cross-section perpendicular to x-axis. Each cross-section is a square, therefore its area is given by side².

We need to find the length of each side of a square cross-section in terms of x, then the integral of this expression will give us the volume of the solid.

Since each cross-section is a square, the length of the side of a square cross-section perpendicular to the x-axis is same as the length of the side of a square cross-section perpendicular to the y-axis.

Hence the length of each side of the square cross-section is given by the distance between the curve and the line. Therefore; length of side = 2.9x² + 0.4 - 2 = 2.9x² - 1.6

Now, we will integrate the expression of the area of cross-section along the given limits to get the volume of the solid;[tex]$$\begin{aligned} \text{Volume of the solid} &= \int_{0}^{2} length^2 dx\\ &= \int_{0}^{2} (2.9x^2 - 1.6)^2 dx\\ &= \int_{0}^{2} (8.41x^4 - 9.28x^2 + 2.56) dx\\ &= \left[\frac{8.41}{5}x^5 - \frac{9.28}{3}x^3 + 2.56x\right]_0^2\\ &= \frac{8.41}{5}(32) - \frac{9.28}{3}(8) + 2.56(2)\\ &= \boxed{14.86} \end{aligned}$$[/tex]

Hence, the volume of the given oblique cylinder is approximately equal to 14.86.

To know more about volume, visit:

https://brainly.com/question/32307927#

#SPJ11

On a test that has a normal distribution, a score of 48 falls two standard deviations
above the mean, and a score of 28 falls two standard deviations below the mean.
Determine the mean of this test.

Answers

To determine the mean of the test, we can use the information given about the scores falling two standard deviations above and below the mean.

Let's denote the mean of the test as μ and the standard deviation as σ.

We are given:
48 falls two standard deviations above the mean, so 48 = μ + 2σ.
28 falls two standard deviations below the mean, so 28 = μ - 2σ.

To solve for the mean μ, we can set up a system of equations with these two equations:

48 = μ + 2σ
28 = μ - 2σ

Adding the two equations together eliminates the σ term:
48 + 28 = μ + 2σ + μ - 2σ
76 = 2μ

Dividing both sides by 2 gives us the value of the mean μ:
76/2 = 2μ/2
38 = μ

Therefore, the mean of the test is 38.

I hope this helps! :)

Fill in the blanks with perfect squares to
approximate the square root of 72.
sqrt[x] < sqrt72

Answers

To approximate the square root of 72, we can find perfect squares that are close to 72 and compare their square roots. Let's consider the perfect squares 64 and 81.

The square root of 64 is 8, and the square root of 81 is 9. Since 72 lies between these two perfect squares, we can say that sqrt(64) < sqrt(72) < sqrt(81).

Therefore, we can approximate the square root of 72 as a value between 8 and 9. However, we can further refine the approximation by finding the average of 8 and 9:

sqrt(72) ≈ (sqrt(64) + sqrt(81)) / 2 ≈ (8 + 9) / 2 ≈ 8.5

So, we can estimate the square root of 72 as approximately 8.5.

Learn more about root here : brainly.com/question/16932620?

#SPJ11

find the least squares straight line fit
y = a + bx to the given points. Show that the result is reasonable by graphing the line and plotting the data in the
same coordinate system.
(2, 1), (3, 2), (5, 3), (6, 4)

Answers

The least squares straight line fit for the given points (2, 1), (3, 2), (5, 3), and (6, 4) is y = 0.5x + 0.5. The line and the data points can be graphed in the same coordinate system to visually verify the reasonableness of the fit.

To find the least squares straight line fit, we need to minimize the sum of squared residuals between the observed y-values and the predicted y-values on the line. The equation y = a + bx represents a straight line, where a is the y-intercept and b is the slope. Using the least squares method, we can solve for a and b that minimize the sum of squared residuals. Performing the calculations, we find that the least squares solution for this problem is a = 0.5 and b = 0.5. Therefore, the equation of the line that best fits the given data points is y = 0.5x + 0.5. To verify the reasonableness of the fit, we can plot the line y = 0.5x + 0.5 along with the given data points in the same coordinate system. If the line approximately passes through or near the data points, it indicates a reasonable fit. Conversely, if the line deviates significantly from the data points, it suggests a poor fit.

To know more about least squares here: brainly.com/question/30176124

#SPJ11

Given quadrilateral ABCD is a rhombus, find x and m

Answers

The value of x is 5

The measure of m<ADB is 28 degrees

How to determine the value

From the information given, we have that the figure is a rhombus

Note that the interior angles of a rhombus are equivalent to 90 degrees

Then, we can that;

<ABD and <DBC are complementary angles

Also, we can see that the diagonal divide the angles into equal parts.

equate the angles, we have;

6x - 2 = 4x + 8

collect the like terms

6x - 4x = 10

2x = 10

Divide the values by the coefficient, we have;

x = 5

Now, substitute the value, we have;

m< ADB = 4x + 8 = 4(5) + 8 = 20 + 88 = 28 degrees

Learn more about rhombus at: https://brainly.com/question/26154016

#SPJ1




Find the volume generated by rotating about the x-axis the region bounded by the graph of the equation. y= 74+x, x=2, x= 14 The volume is (Simplify your answer. Type an exact answer in terms of .)

Answers

The volume generated by rotating the region bounded by the graph of the equation y = 74 + x, x = 2, and x = 14 about the x-axis in terms of π, is (2180π/3) cubic units.

To find the volume, we divide the region into infinitely thin vertical strips or shells along the x-axis. The height of each shell is given by the function y = 74 + x. The width of each shell is the infinitesimally small change in x.

The formula for the volume of a cylindrical shell is V = 2πrhΔx, where r represents the distance from the x-axis to the shell, h is the height of the shell, and Δx is the width of the shell. In this case, the distance from the x-axis to the shell is x, and the height of the shell is y = 74 + x.

Integrating the volume formula from x = 2 to x = 14 with respect to x gives us the total volume. Evaluating the integral leads to the simplified exact answer of (2180π/3) cubic units.

Learn more about Integrating here:

https://brainly.com/question/31954835

#SPJ11


Compute the difference quotient f(x+h)-f(x)/H for the function f(x)
= -x^2 -4x -1. Simplify your answer as much as possible.
Homework: HW 1.3 Question 22, 1.3.68 > HW Score: 76.09% points O Points: 0 of 1 f(x+h)-f(x) Compute the difference quotient for the function f(x) = -x2 - 4x-1. Simplify your answer as much as possible

Answers

To compute the difference

quotient

for the function f(x) = -x^2 - 4x - 1, we need to find the expression (f(x + h) - f(x))/h and simplify it. The simplified form will represent the

average

rate of change of the function over the interval [x, x + h].

The

difference

quotient is given by (f(x + h) - f(x))/h. Substituting the function f(x) = -x^2 - 4x - 1, we have:

(f(x + h) - f(x))/h = [-(x + h)^2 - 4(x + h) - 1 - (-x^2 - 4x - 1)]/h.

Expanding and simplifying the

numerator

, we get:

[-(x^2 + 2hx + h^2) - 4x - 4h - 1 + x^2 + 4x + 1]/h

= [-x^2 - 2hx - h^2 - 4x - 4h - 1 + x^2 + 4x + 1]/h.

Canceling out

common terms

and simplifying further, we obtain:

[-2hx - h^2 - 4h]/h

= -2x - h - 4.

Thus, the simplified difference quotient for the function f(x) = -x^2 - 4x - 1 is -2x - h - 4.

To learn more about

quotient

click here:

brainly.com/question/16134410

#SPJ11

Computing triple Integrals Evaluate the following triple integral 3,23 II s t syli y+zdc du da 00+ lui de SIS y+zddydz=1 0 0 +

Answers

The value of the triple integral [tex]∫∫∫_S (t^3 y+zy) dV[/tex], where S is the region defined by the inequalities y+z ≤ 1, y ≥ 0, and z ≥ 0, is x.

To evaluate this triple integral, we first need to determine the limits of integration for each variable. Since the inequalities define the region S, we can set up the integral as follows:

[tex]∫∫∫_S (t^3 y+zy) dV = ∫∫∫_S (t^3 y+zy) dydzdu.[/tex]

For the limits of integration, we start with the innermost integral:

[tex]∫_0^u ∫_0^(1-y) ∫_0^(1-y-z) (t^3 y+zy) dzdydu.[/tex]

Next, we evaluate the y integral:

[tex]∫_0^u ∫_0^(1-y) [(t^3/2)y^2+1/2zy^2] |_0^(1-y-z) dydu.[/tex]

After integrating with respect to y, we obtain:

[tex]∫_0^u [(t^3/6)(1-y-z)^3 + (1/6)z(1-y-z)^3 + (1/2)z(1-y-z)^2] |_0^(1-y) du.[/tex]

Finally, we integrate with respect to u:

[tex][(t^3/6)(1-(1-y)^2)^3 + (1/6)(1-y)(1-(1-y)^2)^3 + (1/2)(1-y)(1-(1-y)^2)^2] |_0^u.[/tex]

Simplifying this expression will yield the final answer, denoted by x.

Learn more about triple Integrals  here

brainly.com/question/30404807

#SPJ11

PLEASE HELP ASAP WILL GIVE THUMBS UP
Let L be the line parallel to the line x+1 Y = =2-2 3 and containing the point (2.-5. 1). Determine whether the following points lie on line L. 1. (-1,0.2) 2. (-1. -7,0) 3. (8.9.3) (enter yes in lower

Answers

Out of the three given points, only the point (-1, -7, 0) lies on line L and the other two points (-1, 0, 2) and (8, 9, 3) do not lie on line L. So, option 2 is correct.

To determine whether the given points lie on the line L, we need to check if their coordinates satisfy the equation of the line L, which is parallel to the line "x + y = 2" and passes through the point (2, -5, 1).

The equation of a line parallel to "x + y = 2" can be written as "x + y = k", where k is a constant. To find the value of k, we substitute the coordinates of the point (2, -5, 1) into the equation: "2 + (-5) = k". This gives us k = -3.

Therefore, the equation of line L is "x + y = -3".

Now, let's check whether the given points satisfy this equation:

1. Point (-1, 0, 2):

  (-1) + 0 = -3

  The point does not satisfy the equation, so it does not lie on line L.

2. Point (-1, -7, 0):

  (-1) + (-7) = -3

  The point satisfies the equation, so it lies on line L.

3. Point (8, 9, 3):

  8 + 9 ≠ -3

  The point does not satisfy the equation, so it does not lie on line L.

So, option 2 is correct.

Learn more about line:

https://brainly.com/question/24644930

#SPJ11

Other Questions
Discuss three types of valency We wish to compute 22 +2 ^ dr. 23+422 - 162 - 64 We begin by factoring the denominator of the rational function. We get 23 + 422 - 162 - 64 = (x - a) (x - b)2 for ab. What are a and b? FORMATTING: Mak Question 4, 10.1.10 Part 1 of 2 O Points: 0 of 1 = Homework: Homework 2 Given are parametric equations and a parameter interval for the motion of a particle in the xy-plane. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion. x= 3 + sint, y=cost-1, Ostst Bank A's stock portfolio has a market value of $10 million. The beta of the portfolio is the same as the market portfolio beta. The market return volatility (om) has been estimated at 10 percent. What is the five-day VAR of this portfolio using adverse rate changes in the 99th percentile? Find the linearization L(x) of the function at a.f(x) = cos x, a = 3/2 For the function: y = 3x + 4 A) Identify any transformations this function has (relative to the parent function). B) For each transformation: 1) identify if it has an effect on the derivative II) if it does have an effect, describe it Part BEconomists frequently use the Consumer Price Index (CPI) to measure inflation, thegeneral increase in prices. The CPI measures the monthly change in the prices ofwhat typical Americans buy. If the CPI is positive, it means that prices are going up.If it is negative, it means that prices are going down. Now, review this US economicdata, and type the relevant information in the chart. Organizational Culture: Side Effects Include Harassment and BullyingHydroHealth is suffering from a culture that has allowed for harassment and bullying to occur. You've been brought in to fix the organizational culture at the organization. Can you assist them before it's too late? The forward rate of 55 days is 1.21 USD/EUR while the current EUR. The annual USA rate is 1.13% and Eurozone rate is 1.18%. FIND THE COST OF THE FORWARD ACTION: Find the exact arc length of the curve y=x^(2/3) over the interval, x=8 to x=125 7) a) Sketch the plane curve defined by the given parametric equation. Eliminate the parameter to find a Cartesian equation of the curve. Indicate with an arrow the direction in which the curve is tra Determine the kinds of intermolecular forces that are present in each of the following elements or compounds. CH3COOH, Br2, He Find the value of x, y, and z in the rhombus below.(x+8)(2z+9)(-y+10)107 gdp is not a perfect way to measure economic activity because: multiple select question. goods and services that are not bought and sold in a market are not included in gdp. it ignores activities that occur outside formal markets. it does not measure wage changes. it does not account for the depletion of natural resources. it does not account for changes in product quality. it does not account for productivity changes. it does not provide a gauge of unemployment. it cannot measure the value of leisure time. for the following questions assume that lines appear to be tangent are tangent find the value of x figures are not drawn to scale Explain the difference between the first and second welfare theorems.A.The first welfare theorem discusses a competitive equilibrium with the help of the government; the second welfare theorem discusses a competitive equilibrium without the help of the government.B.The first welfare theorem states that a competitive equilibrium is Pareto-optimal under certain conditions; the second welfare theorem states that a Pareto optimum is a competitive equilibrium under certain conditions.C.The first welfare theorem discusses a competitive equilibrium without the help of the government; the second welfare theorem discusses a competitive equilibrium with the help of the government.D.The first welfare theorem states that a Pareto optimum is a competitive equilibrium under certain conditions; the second welfare theorem states that a competitive equilibrium is Pareto-optimal under certain conditions. Which of the following items would be added to Net income in the operating activities section of the statement of cash flows prepared using the indirect method? (Check all that apply.)Depreciation and amortization expenseDecreases in operating assetsLoss on sale of investing assetGain on sale of investing assetDecreases in operating liabilities Explain, in your own words, the difference between the first moments and the secondmoments about the x and y axis of a sheet of variable density most pieces that come from the classical era consisted of a single movement.question 22 options:true/false An atom has 17 protons and 17 electrons.The atoms charge is