The volume of a cantaloupe is given by Upper V equals four thirds pi font size decreased by 5 r cubed . The radius is growing at the rate of 0.7 cm divided by week, at a time when the radius is 7.5 cm. How fast is the volume changing at that moment?

dV/dt = 494.8 cm^3 per week

the volume is changing at 494.8 cm^3 per week at that moment;

Completed question:

The volume of a cantaloupe is given by V = (4/3)πr^3 . The radius is growing at the rate of 0.7 cm/week, at a time when the radius is 7.5 cm. How fast is the volume changing at that moment?

Step-by-step explanation:

Given:

V = (4/3)πr^3

Radius r = 7.5 cm

dr/dt = 0.7cm/week

How fast is the volume changing at that moment;

dV/dt = d((4/3)πr^3)/dt

dV/dt = (4πr^2)dr/dt

Substituting the given values;

dV/dt = (4π×7.5^2)×0.7

dV/dt = 494.8 cm^3 per week

the volume is changing at 494.8 cm^3 per week at that moment;

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b