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eduard
3 years ago
8

1. Emily is allowed to spend 60% of her allowance. The remaining 40% she deposits into her

Mathematics
2 answers:
kkurt [141]3 years ago
4 0
Answer:

5

Explanation:

40x 200
—— ——
40 40
X=5
stellarik [79]3 years ago
4 0

he gets $5.00 for her allowance

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The sum of the first number cubed and the second number is 500 and the product is a maximum.
soldier1979 [14.2K]

We are given the following information:

the sum of the first number cubed and the second number is 500

their product is a maximum

We are looking for the 2 missing numbers.

To answer this, let's represent the two numbers as x and w.

From the given, we can form the following equation:

x^3+w=500

We can then express y as:

w=500-x^3

We can express their product as:

x(500-x^3)=500x-x^4

To find the maximum value of x, let's solve for the derivative of -x^4 + 500 x.

\begin{gathered} f(x)=-x^4+500x \\ f^{\prime}(x)=-4x^3+500 \end{gathered}

Then we solve for the value of x where f'(x) = 0.

\begin{gathered} -4x^3+500=0 \\ -4x^3=-500 \\ x^3=125 \\ x=5 \end{gathered}

Then we use x = 5 to solve for the second number, w.

\begin{gathered} w=500-x^3 \\ w=500-5^3 \\ w=500-125 \\ w=375 \end{gathered}

Therefore, the two numbers are 5 and 375.

3 0
11 months ago
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