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3 years ago

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Simplify each expression using an exponent rule learned in class.

29%5E%7B4%7D" id="TexFormula1" title="(\frac{y}{x} )^{4}" alt="(\frac{y}{x} )^{4}" align="absmiddle" class="latex-formula">

2 answers:

Maksim231197 [3]3 years ago

3 0

Hey there! I'm happy to help!

If you raise a fraction to an exponent, you apply that exponent to the numerator and the denominator. This would give us $\frac{y^4}{x^4}$ .

Have a wonderful day! :D

Margarita [4]3 years ago

3 0

Since the exponent is outside the fraction, you apply the exponent to both the numerator and denominator.

(y/x)^4 = y^4/x^4

Best of Luck!

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Step-by-step explanation:

We are given the surface area of a box $S(x)=x^2+\frac{240}{x}$ where x is the length of the sides of the base.

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Evaluate S'(x) at each interval to see if it's positive or negative on that interval.

$\begin{array}{cccc}Interval&x-value&S'(x)&Verdict\\(0,2\sqrt[3]{15}) &2&-56&decreasing\\(2\sqrt[3]{15}, \infty)&6&\frac{16}{3}&increasing \end{array}$

An extremum point would be a point where f(x) is defined and f'(x) changes signs.

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To confirm that this is the point of an absolute minimum we need to find the second derivative of the surface area and show that is positive for $x=2\sqrt[3]{15}$ .

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and for $x=2\sqrt[3]{15}$ we get:

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Therefore S(x) has a minimum at $x=2\sqrt[3]{15}$ which is:

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