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3 years ago

Solve for x: 5^3x+2=1/25

Mathematics

2 answers:

krek1111 [17]3 years ago

6 0

X
=
−
4
9
3
1
2
5
x=−
3125

49

grigory [225]3 years ago

5 0

If you meant 5^(3x+2)=1/25
5^(3x+2)=5^-2
Cross the bases off
3x+2=-2
3x=-4
x=-4/3

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<u>Maximization With Derivatives</u>

Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.

We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.

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$\displaystyle x=\frac{\frac{1}{2}-3y}{4}$

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Substituting x

$\displaystyle A=\frac{\frac{1}{2}-3y}{4}.y$

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Differentiating with respect to y

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Equate to 0

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Compute the second derivative

$\displaystyle A''=-\frac{3}{2}.$

Since it's always negative, the point is a maximum

Thus, the maximum area is

$\displaystyle A=\frac{1}{12}\cdot \frac{1}{16}=\frac{1}{192}$

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