Answer:
Length of the Rectangle is to be considered as the circumference of the resulting cylinder and the width of the rectangle should be considered as the height of the cylinder only then we get the maximum volume of the cylinder which is 47.77[tex]in^3[/tex]
Step-by-step explanation:
The given dimensions are
Width of the rectangle is 6inches.
Length of the rectangle 10inches.
Now we need to choose in what orientation we need to use the length and the width of the rectangle so that it can be rolled into a rectangle and we get the maximum volume of the resulting cylinder.
so lets consider two cases
CASE-1: width of the rectangle is to be rolled as the circumference of the cylinder and length of the rectangle is to used as the height of the cylinder
2*pi*r = 6
r = [tex]\frac{6}{2pi}[/tex]
r = [tex]\frac{3}{pi}[/tex] Inch
and the height = 10inch.
Volume of the resultant cylinder will be
= [tex]pi*r^2*h[/tex]
= [tex]pi*(\frac{3}{pi} )^2*10[/tex]
= [tex]\frac{9}{pi}*10[/tex]
= [tex]\frac{90}{pi}[/tex] = 28.662 [tex]in^3[/tex]
CASE-2: When the length of the rectangle is to used as the circumference of the resultant cylinder and the width of the cylinder is used as the height of the cylinder.
2*pi*r= 10
r = [tex]\frac{5}{pi}[/tex]
and the height of the cylinder is 6 inch
Now the volume of the cylinder will be
Volume= [tex]pi*r^2*h[/tex]
= [tex]pi*(\frac{5}{pi} )^2*6[/tex]
= [tex]\frac{25}{pi}*6[/tex]
= [tex]\frac{150}{pi}[/tex] = 47.77[tex]in^3[/tex]
Clearly we have the second case in which the resulting Cylinder will have the maximum volume.
Therefore the CASE-2 will provide the maximum Volume of 47.77[tex]in^3[/tex] to the resulting cylinder in which the length of the rectangle is to be considered as the circumference of the Cylinder and the width of the rectangle is to be considered as the height of the cylinder.
If x and y are positive integers is x - y always positive explain
Note that x and y are nonzero integers. It means that x and y will always have same sign (both are either positive or negative, since they are nonzero). Hence, xy term is always positive.
Answer:
No, if y happens to be a larger integer than x, then the result will be negative.
Step-by-step explanation:
For example, lets say that x=4 and y=9, so x-y = 4-9 = -5.
But if we were to reverse it and make x=9 and y=4, then x-y = 9-4 = 5.
A cyclist travels 8 miles in 15 minutes.
What is her average speed in mph?
Answer:
0.53 mph
Step-by-step explanation:
A cyclist travels 8 miles in 15 minutes.
So the average speed is
=8/15 mph
=0.53 mph
I WILL GIVE BRAINLIEST. HURRY PLEASE
Answer:
Concept: Linear Algebra
Let us pick -5 and -4 which are one unit apart.We will find the difference by finding the slope: -3-(-11)/-4-(-5)= 8 Next for 2 units apart we will choose 1 and 3We do the same thing: 53-37/3-1= 16/2=8 Next we will pick something 2 units apart. Let's pick 0 and 3 Hence we will do the same: 53-29/3-0= 24/3=8No matter what difference we pick, whether that be one, two or three units, the difference is the same and consistent.Rate brainlist and drop a follow4
5 6 7 8 9 10
11
12 13
The sum of three numbers is 56. If the second number is equal to the first diminished by 4, and the third number is 3
times the first. What are the numbers?
If x represents the first number, then which of the following equations could be used to solve the problem?
x = 3x-4
56=4x4
56=3x-4
56-5x4
a
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Answer:
56-5x4
Step-by-step explanation:
The reason you want to do it that way is because they will cansle eatch other out
in order to receive a b on an essay, the grade must be no lower then 82% and no higher than an 89%.write a compound inequality to represent the range of scores to earn a B on the essay
Answer:
0.82 ≤ x ≤ 0.89
Step-by-step explanation:
hope this helps, pls mark brainliest :D
-x+3=4 plz solve and Explain
Answer:
x=-1
Step-by-step explanation:
-x+3=4
-3 -3
-x=1
multiply by negative one to get rid of negative in front of x
x=-1
Answer:
here we have to bring the +4 into first part then -x in second part then it will be 3-4=x
then solve now -1=x
A school lunch contains 12 cheese sticks. Seventy-five students buy the lunch. What is the total number of cheese sticks served?
Answer:
900 cheese sticks served (thats a lot of cheese)
Step-by-step explanation:
You can multiply to find how much in total
12*75
you’d get 900
Total number of cheese sticks served in 75 school lunches is 900.
Given that a school lunch contains 12 cheese sticks and 75 students buy the lunch,
we have to find the total number of cheese sticks served.
To find the solution,
We can use a simple multiplication formula that says,
The total number of cheese sticks served equals the number of cheese sticks in one lunch multiplied by the number of lunches served.
Therefore,
we can write,
⇒Total number of cheese sticks served = Number of cheese sticks in one lunch x Number of lunches served
As there are 75 students who buy the lunch,
We can find the number of lunches served by dividing the total number of students by the number of students in one lunch.
Since one lunch contains 12 cheese sticks, we can write,
⇒ Number of lunches served = Total number of students / Number of students in one lunch
⇒ Number of lunches served = 75 / 1
⇒ Number of lunches served = 75
Now that we know the number of lunches served,
we can use the multiplication formula to find the total number of cheese sticks served,
⇒ Total number of cheese sticks served = Number of cheese sticks in one lunch x Number of lunches served
⇒ Total number of cheese sticks served = 12 x 75
⇒ Total number of cheese sticks served = 900
Therefore,
The total number of cheese sticks served in 75 school lunches is 900.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ6
I
4)
73,693 I’m lookin to round the number
Answer:
Which place are you rounding with?
If your rounding with ones then the answer will be 73,690
If your rounding with tens then the answer will be 73,700
If your rounding with hundreds then the answer will be 73,600
If your rounding with thousands then the answer will be 74,000
There you go and your welcome!
what is the area of a shaded region in the quarter circle
radius 12
Answer:
I guess that the shaded area is a quarter of a circle of radius 12 units.
Is easy to know that the area, will be equal to the quotient between the area of a circle of radius 12, and 4
We know that the area of a circle of radius R is:
A = pi*R^2
in this case, R = 12
pi = 3.14
Then:
A = 3.14*12^2 = 452.16
And a fourth of that is:
A/4 = (452.16)/4 = 113.04
The area of the shaded region is 113.04 square units
Suppose that a new employee starts working at $7.72 per hour and receives a 4% raise each year. After time t, in years, his hourly wage is given by the equation y=$7.72(1.04)t. Find the amount of time after which he will be earning $10.00 per hour.
Answer:
6.5978 years
Step-by-step explanation:
y=7.72(1.04)^t
10=7.72(1.04)^t
1.04^t=1.2953367875647668
log 1.04^t=log 1.2953367875647668
t log 1.04=log 1.2953367875647668
t=6.5978 years .............
________ Is the largest industry In the world.
O Technology
O Travel and tourism
O Manufacturing
O Education
I believe it’s travel and tourism. Hope this helps!
Answer:
Manufacturing is the largest industry In the world.
please help will give brainliest
Answer:
a² = 144
b² = 25
c² = 169
c = 13
Step-by-step explanation:
• a² = 12×12
= 144
• b² = 5×5
= 25
• a² + b² = c²
= 144 + 25 = 169
• c = _/169
= 13
PLssssss HELPPPPPPP will GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Mr. Mayhood had 4½ pounds of sand in a bucket. He put 2¾ pounds
of sand around his flower bed. How much sand did he have left in the
bucket?
Answer:
For addition 7 1/4. For subtraction 1 3/4. For multiplication 12 2/8. For division 1 7/11.
Step-by-step explanation:
the mean of a,b,c,and d is 9 and the mean of a,b,c,d,e and f is 12. find the mean of e and f
Answer:
mean of e + f = 18
Step-by-step explanation:
(a + b + c + d)/4 = 9 Multiply by 4
a + b + c + d = 9 * 4 = 36
(a + b + c + d + e + f ) / 6 = 12
but a + b + c + d = 36
(36 + e + f)/6 = 12 Multiply by 6
36 + e + f = 72 Subtract 36 from both sides
e + f = 36 Divide by 2 to find the mean.
(e + f)/2 = 36/2
mean of e + f = 18
If another equation is graphed so that the system has no solution, which equation could that be?
y=-2(x-1/2)
y=-1/2(4x+2)
y=-x+1
y=-1/2x+2
Answer:
y=-2(×-1/2)
Step-by-step explanation:
...........
What is the value of b? 10 ( 1 + 3b ) = -20
Answer:
b=-1
Step-by-step explanation:
10(1+3b)=-20
1+3b=-2
3b=-3
b=-1
Answer question in the picture for brainliest and 10 points.
Answer:
D
Step-by-step explanation:
I know because I am smart. Trust me, it is D.
Its D
Step-by-step explanation:
pwease ik
The sum of three consecutive numbers is 72 what is the smallest of the numbers
Answer:
23
Step-by-step explanation:
Suppose,
the first number = x
the second number = x+1
the third number = x+1+1 = x+2
Question wise,
x+x+1+x+2 = 72
3x+3 = 72
3x = 72-3 = 69
x = 69/3 = 23
so the numbers are,
23,(23+1)=24 and (23+2)=25
What is the rise over the run (slope) in this graph? Please write in simplest form.
Answer:
6
Step-by-step explanation: count the numbers from 26 to 32 from 32 to 38 from 38 to 44
Answer:
it would be at 5 i'm pretty sure
write a function G whose graph represents the indicated transformation of the graph f
[tex]f(x) = \frac{2}{3} {x}^{2} + 2[/tex]
vertical stretch by a factor of 3
Answer:
[tex]G(x) = 2x^2+6[/tex].
Step-by-step explanation:
The given function is
[tex]f(x) = \frac 2 3 x^2 +2[/tex]
On vertical stretch by a factor of 3, the new function G(x) is
G(x) = 3 f(x)
So, [tex]G(x) = 3 \times ( \frac 2 3 x^2 +2)= 2x^2+6[/tex]
Hence, the required function is [tex]G(x) = 2x^2+6[/tex].
Which linear inequality is represented by the graph?
A) y>2/3x-2
B) y<2/3x+2
C) y>2/3x+1
D) y<2/3x-1
The answer is C
Answer:
hey you guys
Step-by-step explanation:
For question b, how is the answer is ㏒ₐ2 + 4(n-1)㏒ₐ3?
Please help me.
Answer:
[tex]T_n=(4-n)\text{log}_a(3)+\text{log}_a(2)[/tex]
Step-by-step explanation:
nth term of an A.P. is given by the explicit formula,
[tex]T_n=a+(n-1)d[/tex]
Here, 'a' = First term
n = number of term
d = common difference
For an A.P. given as,
[tex]\text{log}_a(54),\text{log}_a(18),\text{log}_a(6),....[/tex]
First term 'a' of the given A.P. = [tex]\text{log}_a(54),[/tex]
Common difference 'd' = [tex]T_2-T_1[/tex]
= [tex]\text{log}_a(18)-\text{log}_a(54)[/tex]
= [tex]\text{log}_a(\frac{18}{54})[/tex]
= [tex]\text{log}_a(\frac{1}{3})[/tex]
= [tex]-\text{log}_a(3)[/tex]
[tex]T_n=\text{log}_a(54)+(n-1)[-\text{log}_a(3)][/tex]
[tex]=\text{log}_a(54)-(n-1)\text{log}_a(3)[/tex]
[tex]=\text{log}_a(3^3\times 2)-(n-1)\text{log}_a(3)[/tex]
[tex]=\text{log}_a(3^3)+\text{log}_a(2)-(n-1)\text{log}_a(3)[/tex]
[tex]=3\text{log}_a(3)+\text{log}_a(2)-(n-1)\text{log}_a(3)[/tex]
[tex]=3\text{log}_a(3)+\text{log}_a(2)-n\text{log}_a(3)+\text{log}_a(3)[/tex]
[tex]=4\text{log}_a(3)+\text{log}_a(2)-n\text{log}_a(3)[/tex]
[tex]=(4-n)\text{log}_a(3)+\text{log}_a(2)[/tex]
find the amount on #45,000 in 3 years at 10% per annum and also find the compound interest
Answer:
Amt. = 45000 ( 1+ 10/100 ) ^3
Interest = 45000 - Amt.
Step-by-step explanation:
Hope this helped have an amazing day!
The equation modeling the population growth of a small town is P(t)=30000(1.02)^t, where P represents the population, and t represents the years from now. What is the approximate population change that occurs between 2 years from now and 10 years from now.
Answer:
5358
Step-by-step explanation:
The equation modeling the population growth of a small town is given as:
P(t)=30000(1.02)^t
When t = 2
P(2) = 30000(1.02)^2
P(2) = 31212
When t = 10
P(10) = 30000(1.02)^10
P(10) = 36569.8326
The approximate population change that occurs between 2 years from now and 10 years from now is calculated as:
= P(10) - P(2)
= 36569.83259984272 − 31212
= 5357.8325998
Approximately ≈ 5358
Im confusion? Could someone help me out.
Answer:
20cm
Step-by-step explanation:
for the triangle:
Perimeter = 30cm
a + a + a = 30
3a = 30
hence a = 10cm
For the rectangle:
Perimeter = 30cm
a + a + b + b = 30
but a = 10cm
10 + 10 + b + b = 30
20 + 2b = 30
2b = 10
hence b = 5cm
Perimeter of square = b + b + b + b
= 5 + 5 + 5 + 5 = 20cm
(04.05)Marcus painted one-third of his bedroom in fourth-fifths of an hour. At this rate, how long would it take him to paint the entire room?
five-twelfths of an hour
twelve-fifths of an hour
fifteen-fourths of an hour
four-fifteenths of an hour
Answer:
12/5
Step-by-step explanation:
1/3 = 4/5
2/3= 8/5
3/3= 12/5
Identify the initial amount and the growth rate of the following:
Y = 250 (1+0.2)
Answer:
y = 300
Step-by-step explanation:
y = 250 (1+0.2)
First add the 1 and 0.2
y=250(1.2)
multiply 250 with 1.2
y = 300
:)
In some languages, every consonant must be followed by a vowel. How many seven-letter ‟words” can be made from the Hawaiian word MAKAALA if each consonant must be followed by a vowel?
Answer:
One. Kamala.
Step-by-step explanation:
A linear function has an x-intercept of 12 and a slope of StartFraction 3 Over 8 EndFraction. How does this function compare to the linear function that is represented by the table?
x
y
Negative two-thirds
Negative three-fourths
Negative one-sixth
Negative StartFraction 9 Over 16 EndFraction
One-third
Negative StartFraction 3 Over 8 EndFraction
StartFraction 5 Over 6 EndFraction
Negative StartFraction 3 Over 16 EndFraction
It has the same slope and the same y-intercept.
It has the same slope and a different y-intercept.
It has the same y-intercept and a different slope.
It has a different slope and a different y-intercept
Answer:
The correct option is;
It has the same slope and a different y-intercept
Step-by-step explanation:
The data on the table can be presented as follows;
x [tex]{}[/tex] y
-2/3 [tex]{}[/tex] -3/4
-1/6 [tex]{}[/tex] -9/16
1/3 [tex]{}[/tex] -3/8
5/6 [tex]{}[/tex] -3/16
The rate of change of the function, m = (-3/16 - (-3/4))/(5/6 - (-2/3)) = 3/8
The equation of the line given by the data points in point and slope form is given as follows;
y - (-3/16) = 3/8×(x - 5/6)
y = 3·x/8 - 5/16 - 3/16 = 3·x/8 - 1/2
y = 3·x/8 - 1/2
The y intercept is given at when x = 0, therefore, at the y-intercept, y = 3 × 0/8 - 1/2 = -1/2
The y-intercept is (0, -1/2)
The x-intercept occurs at y = 0, therefore, at the x-intercept, we have;
0 = 3·x/8 - 1/2
∴ 3·x/8 = 1/2
x = 4/3
Therefore, the x-intercept is 4/3 and the coordinates of the x-intercept is (4/3, 0)
Given that the x-intercept is different, the y-intercept of the two lines with the same slope are also different
The correct option is therefore that it has the same slope and a different y-intercept;
Answer:
the answer is B
Step-by-step explanation:
Which statement describes the graph of function g?
f(x) = 2x
g(x) = 2x + 3
The graph of g is 3 units to the left of the graph of f.
The graph of g is 3 units below the graph of f.
The graph of g is 3 units above the graph of f.
The graph of g is 3 units to the right of the graph of f.
9514 1404 393
Answer:
The graph of g is 3 units above the graph of f.
Step-by-step explanation:
Adding 3 to each y-value shifts the graph up 3 units.
__
In the case of the straight line given here, it also has the appearance of shifting the graph left. The left-shift, however, is not 3 units. The amount of apparent horizontal shift will depend on the slope of the original line.
Answer:
The answer is above
Step-by-step explanation:
its above because the sign is positive