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sveticcg [70]
3 years ago
7

Jocelyn invested $8,600 in an account paying an interest rate of 3.1% compounded quarterly. Assuming no deposits or withdrawals

are made, how much money, to the nearest hundred dollars, would be in the account after 15 years?
Mathematics
1 answer:
alexandr402 [8]3 years ago
8 0
A = P*(1 +r/n)^(n*t)
A = $8,600*(1 +.031/4)^(4*15)
A ≈ $13,700

About $13,700 will be in Jocelyn's account after 15 years.
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An open box is to be constructed so that the length of the base is 3 times larger than the width of the base. If the cost to con
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Answer:

Step-by-step explanation:

Let assume that the volume = 88 cubic feet

Then:

L = 3w --- (1)volume = l \times w \times h \\ \\ 88 =  (3w)   \times w  \times h \\ \\ 3w^2 h= 88 \\ \\ h = \dfrac{88}{3w^2}--- (2) \\ \\

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C = 4(l \times w) + 2 ( w  \times h) + 2(l \times h) \\ \\ C = 4(3w^2) + 2(w  \times \dfrac{88}{3w^2}) + 2(3w \times \dfrac{88}{3w^2}) \\\\ C = 12w^2 + \dfrac{176}{3w} + \dfrac{176}{w}

Now, to determine the minimum cost:

\dfrac{dC}{dw}= 0  \\ \\ \implies 24 w - \dfrac{176}{3w^2}- \dfrac{176}{w^2}=0 \\ \\ 24 w ^3 = \dfrac{176}{w^2}(\dfrac{1}{3}+1) \\ \\ 24 w ^3 = \dfrac{176(4)}{3} \\ \\ w^3 = \dfrac{88}{3(3)}

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length = 3 ( \dfrac{88}{3(3)})^{1/3} \ feet

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