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Scorpion4ik [409]
2 years ago
9

The radius of the base of a cylinder is increasing at a rate of 7 millimeters per hour. The height of the cylinder is fixed at 1

.51, point, 5 millimeters. At a certain instant, the radius is 12 millimeters.
What is the rate of change of the volume of the cylinder at that instant (in cubic millimeters per hour)?
Mathematics
1 answer:
Ilya [14]2 years ago
6 0

Answer:

The rate of change of the volume of the cylinder at that instant = 791.28\ mm^3/hr

Step-by-step explanation:

Given:

Rate of increase of base of radius of base of cylinder = 7 mm/hr

Height of cylinder = 1.5 mm

Radius at a certain instant = 12 mm

To find rate of change of volume of cylinder at that instant.

Solution:

Let r represent radius of base of cylinder at any instant.

Rate of increase of base of radius of base of cylinder can be given as:

\frac{dr}{dt}=7\ mm/hr

Volume of cylinder is given by:

V=\pi\ r^2h

Finding derivative of the Volume with respect to time.

\frac{dV}{dt}=\pi\ h\ 2r\frac{dr}{dt}

Plugging in the values given:

\frac{dV}{dt}=\pi\ (1.5)\ 2(12)(7)

\frac{dV}{dt}=252\pi

Using \pi=3.14

\frac{dV}{dt}=252(3.14)

\frac{dV}{dt}=791.28\ mm^3/hr (Answer)

Thus rate of change of the volume of the cylinder at that instant = 791.28\ mm^3/hr

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Nastasia [14]

The solution of the given equation is (3,6). The correct option is B.(3,6)

<h3>Given equations,</h3>

y=x+3.......(1)\\4x+y=18.....(2)

<h3>How to solve the equations?</h3>

putting the value of y from equation (1) in equation (2) , we get

4x+x+3=18\\5x=18-3\\5x=15\\x=3

substitute the value of x=3 in equation (1) we get,

y=3+3\\y=6

Hence, the solution of given equation is (3,6).

So, the correct option is B.

For more details about the system of equations, follow the link:

brainly.com/question/12895249

4 0
2 years ago
How tall is a tree which is 15 feet shorter than a pole that is 3 times as tall as the tree?
Citrus2011 [14]
<h2>Height of tree is 7.5 feet</h2>

Step-by-step explanation:

Let t be the height of pole.

Given that the tree is 5 feet shorter than a pole.

Height of pole = t + 15

Also given that the pole is 3 times as tall as the tree.

Height of pole = 3t

So we have

              t + 15 = 3t

                 2t = 15

                   t = 7.5 feet

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7 0
3 years ago
If z = 12.8, what is the value of 2(z - 4)? [Type your answer as a number.]
Anna35 [415]
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3 years ago
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Find an explicit formula for the arithmetic sequence -11, -3, 5, 13, ....
Alekssandra [29.7K]

Answer:

<u>b(n) = -11 + (n-1)*8</u>

<u></u>

Step-by-step explanation:

Let n be the sequence number, with n=1 the first number b(1) -11

The sequence changes by +8 each step.

<u><em>b(1)</em></u><em>   -11</em>         + 8 =   -3

<u><em>b(2)</em></u><em>   -3</em>          + 8 =    5

<u><em>b(3)</em></u>   <em> 5 </em>         + 8 =   13

<u><em>b(4)</em></u><em> </em> <em>13</em>

b(1) = -11

b(2) = -3.   or b(1) + 1*8

b(3) =  5,    or b(1) + 2*8

b(4) =  13,   or b(1) + 3*8

We note that each step adds a multiple of 8 to the initial value of -11.  This can be stated as (n-1)*8

The formula for this sequence would be b(n) = b(1) + (n-1)*8

<u>b(n) = -11 + (n-1)*8</u>

Check:  Does n=3 return the value of 5?

b(n) = -11 + (n-1)*8

b(3) = -11 + ((3)-1)*8

b(3) = -11 + (2)*8

b(3) = -11 + 16

b(3) = 5   <u><em>YES</em></u>

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5 0
3 years ago
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