Answer:
The rate of change of radius is 0.0530 ft/sec.
Step-by-step explanation:
Given : Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.
To find : How fast is the radius increasing after 2 minutes?
Solution : 
The volume of the sphere is 
Differentiating w.r.t. r,

We have given, Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.
i.e. 
Integrate w.r.t. t,

Assuming V=0 when  t=0 then C=0
So, 
 
 ![r=\sqrt[3]{\frac{t}{4\pi}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7Bt%7D%7B4%5Cpi%7D%7D)
Now, we apply chain rule
i.e.  

The radius increasing after 2 minutes i.e. at 




Therefore, the rate of change of radius is 0.0530 ft/sec.
 
        
             
        
        
        
The average rate of change is just change in y divided by change in x.
(f(4)-f(-1))/(4--1)
(16-8-4-1-2+4)/5
5/5
1
So the average rate of change is just 1.
        
                    
             
        
        
        
Answer:
35 m
Step-by-step explanation:
 
        
                    
             
        
        
        
Answer:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. ... A dilation stretches or shrinks the original figure. • A description of a dilation includes the scale factor (or ratio) and the center of the dilation