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,
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.
Complete Question
You are measuring walnuts for banana-walnut oatmeal and a spinach and walnut salad. You need 3/4 cup of walnuts for the oatmeal and 7/8 cup of walnuts for the salad. You have a 1/8 -cup scoop. Complete the descriptions of two different ways to find how many scoops of walnuts you will need. Enter all non-whole number answers as mixed numbers in simplest form.
Answer:
13 scoops
Step-by-step explanation:
Description 1
Step 1
3/4 cup of walnuts for the oatmeal
7/8 cup of walnuts for the salad
Total cups of walnuts needed for both salad and oatmeal =
3/4 cups + 7/8 cups
(3/4 + 7/8)
(6 + 7/8)
= 13/8 cups of walnuts
= 1 5/8 cups of walnuts
Step 2
You have a 1/8 -cup scoop
The number of cup scoops of walnuts need is calculated as
1 5/8 cups ÷ 1/8 cup scoop
= 13/8 ÷ 1/8
= 13/8 × 8/1
= 13 scoops
Therefore, 13 scoops of walnuts is needed.
Description 2
3/4 cup of walnuts for the oatmeal
7/8 cup of walnuts for the salad
1/8 cup scoop
Therefore,
(3/4 + 7/8) ÷ 1/8
=(13/8) ÷ 1/8
= 13 scoops of walnuts are needed
Answer:
B)16
Step-by-step explanation:
cz radius is the half of diameter.
Answer:
-3.98 (nearest hundredth)
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
Given interval: -2 ≤ x ≤ 2
Substituting the values into the equation: