The volume of a spherical balloon is increasing at the rate of 25cm^3/min, how fast is the radius increasing when the radius is equal to 20 cm?

So the radius is increasing at .

This is approximately 0.00497 cm/min that the radius is increasing.  

Step-by-step explanation:

The volume and radius are both things that are changing with respect to time.

So their derivatives will definitely not be 0.

Let's differentiate:

I had to use constant multiple rule and chain rule.

We are given and .

We want to find .

Let's plug in first:

Multiply both sides by 3:

Divide both sides by :

So the radius is increasing at .

This is approximately 0.00497 cm/min that the radius is increasing.  

1/64pi cm/min or 0.00497 cm/min

Step-by-step explanation:

dV/dr = 4pi×r²

At r = 20, dV/dr = 1600pi

dr/dt = dr/dV × dV/dt

dr/dt = 1/1600pi × 25

dr/dt = 1/64pi cm/min

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.