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Sloan [31]
3 years ago
6

One brand of coffee is packaged in cylinders where the height is equal to the radius, r. The volume of the package, in cubic cen

timeters, can be found using the function V(r) = πr3. The number of ounces of coffee in the cylinder depends on the volume of the cylinder, V, in cubic centimeters. This can be modeled by the function C(V) = 3.2V.
Mathematics
1 answer:
igor_vitrenko [27]3 years ago
7 0

Answer:

<h2>C(V(r)) = 3.2πr3</h2>

Step-by-step explanation:

This problem is a composition of function defined by C(V(r)), now we have the functions V(r)= \pi r^{3} and C(V)=3.2V, where the first depends on the radius, and the second dependes on the volume, that means, to find the number of ounce of coffe, we need to determine the volume of the cylinder, that's why we have to replace the volume function inside the ounces function,

C(V(r))=3.2(\pi r^{3} )

Therefore, the right answer is the last choice.

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We begin with an unknown initial investment value, which we will call P. This value is what we are solving for.

The amount in the account on January 1st, 2015 before Carol withdraws $1000 is found by the compound interest formula A = P(1+r/n)^(nt) ; where A is the amount in the account after interest, r is the interest rate, t is time (in years), and n is the number of compounding periods per year.

In this problem, the interest compounds annually, so we can simplify the formula to A = P(1+r)^t. We can plug in our values for r and t. r is equal to .025, because that is equal to 2.5%. t is equal to one, so we can just write A = P(1.025).

We then must withdraw 1000 from this amount, and allow it to gain interest for one more year.

The principle in the account at the beginning of 2015 after the withdrawal is equal to 1.025P - 1000. We can plug this into the compound interest formula again, as well as the amount in the account at the beginning of 2016.

23,517.6 = (1.025P - 1000)(1 + .025)^1
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