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3 years ago

When I write my expression in rational exponent form, what is the fraction that goes with the base of 10?

Mathematics

1 answer:

blsea [12.9K]3 years ago

6 0

Answer: Choice A

$\sqrt[4]{3^3}$

The fourth root of 3^3

=============================================

Explanation:

The exponent of 1/4 means "fourth root", so,

$3^{1/4} = \sqrt[4]{3}$

The outer exponent 3 can be moved inward like this

$\left(3^{1/4}\right)^3 = 3^{1/4*3} = 3^{3/4}$

Then we can use the rule

$x^{m/n} = \sqrt[n]{x^m}$

This means

$3^{3/4} = \sqrt[4]{3^3}$

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3 years ago

a pyramid whose altitude is 5ft weighs 800lbs. at what distance from its vertex must it be cut by a plane parallel to its base s

slavikrds [6]

A structure which has a square base and four triangular sides meeting at a point is called pyramid.

At distance of 3.97 feet from its vertex , pyramid is cut by plane so that the two solids of equal weight will be formed.

It is assumed that weight of pyramid is proportional to its volume.

So, $w = k V$ , where V is volume of original pyramid and v is volume of small pyramid and k is constant.

Let us consider that at h distance, pyramid is cut from its vertex. So a small pyramid is also formed.

Assume that base area of original pyramid is A and base of small pyramid is a.

Volume of original pyramid is, $V= \frac{1}{3} *A* 5$

So, weight of original pyramid, $W = k *(\frac{1}{3} *A* 5) = 800$

Volume of small pyramid is, $v = \frac{1}{3}* a* h$

So, weight of small pyramid, $w = k*(\frac{1}{3}* a* h)=400$

Since, base and height of small pyramid and original pyramid are in proportion.

So, $\frac{a}{A} = (\frac{h}{5}) ^{2}$

$a = (\frac{h}{5} )^{2}A$

Substituting value of a in equation $k*(\frac{1}{3}* a* h)=400$

So, $k*(\frac{1}{3}* \frac{h^{2} }{25}A * h)=400$

$(k*\frac{1}{3}* A*5)*\frac{1}{5} *\frac{h^{2} }{25} * h)=400$

Since, $(k *\frac{1}{3} *A* 5) = 800$ , substitute in above equation.

So, $800*\frac{h^{3} }{125}=400\\\\h^{3}=\frac{125}{2}\\\\h=\sqrt[\frac{1}{3} ]{62.5}\\\\h=3.97 feet$

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2 years ago

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2+3+7+34+7000+12242534

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Answer:

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Step-by-step explanation:

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3 years ago

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patriot [66]

Answer:

Slope =-1/4

Step-by-step explanation:

y=mx+n

Slope=m=(y2-y1)/(x2-x1)

A(-1,19).... x1 =-1, y1=19

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