Type the correct answer in each box. Write your answers in decimal form, rounded to the nearest tenth, if necessary. Type the so
1 answer:
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Answer:
See below.
Step-by-step explanation:
First, notice that this is a composition of functions. For instance, let's let and
. Then, the given equation is essentially
. Thus, we can use the chain rule.
Recall the chain rule: . So, let's find the derivative of each function:
We can use the Power Rule here:
Now:
Again, use the Power Rule and Sum Rule
Now, we can put them together:
Answer:
C. 128/3 meters cubed
Step-by-step explanation:
The volume of a cylinder is denoted by: , where r is the radius and h is the height. We know it's equal to 64, so we can set that equal to V:
We know that the sphere and cylinder have the same height and radius. However, the "height" of a sphere is actually the same as its diameter, which is twice its radius. Then, we can replace h in the above equation with 2r:
Now, the volume of a sphere is denoted by: , where r is the radius. From above, we know that
, so we can plug this into the equation:
Thus, the answer is C.