Which expression is equivalent to ^4 square root

Mathematics

1 answer:

Nesterboy [21]3 years ago

7 0

$\bf \sqrt[4]{\cfrac{24x^6y}{128x^4y^5}}\implies \cfrac{\sqrt[4]{4x^6y}}{\sqrt[4]{128x^4y^5}}\quad 
\begin{cases}
24=2\cdot 2\cdot 2\cdot 3\\
128=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\\
x^6=x^{4+2}\\
\qquad x^4x^2\\
y^5=y^{4+1}\\
\qquad y^4y^1
\end{cases}$

$\bf \cfrac{\sqrt[4]{\underline{2\cdot 2\cdot 2}\cdot 3\cdot \underline{x^4} x^2\underline{y}}}{\sqrt[4]{\underline{2\cdot 2\cdot 2}\cdot 2\cdot 2\cdot 2\cdot 2\cdot \underline{x^4} y^4\underline{y^1}}}
\implies
\cfrac{\sqrt[4]{3x^2}}{\sqrt[4]{2^4y^4}}\implies \cfrac{\sqrt[4]{3x^2}}{2y}$

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The Saxena family plans to install a light to illuminate part of their rectangular yard. Nikki and Dylan each proposed a differe

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Options:

a. Nikki's proposed placement will light a greater area than Dylan's placement.

b. Dylan's proposed placement will light a greater area than Nikki's placement.

c. Both proposed placements will light the same sized area.

d. Nikki's proposed placement will light more than half the yard.

e. Dylan's proposed placement will light more than half the yard.

f. Dylan's proposed placement will light exactly half of the yard.

g. Nikki's proposed placement will light less than half of the yard.

Answer:

C) Both proposed placements will light the same sized area.

F) Dylan's proposed placement will light exactly half of the yard.

Step-by-step explanation:

The area of a triangle is (base x height) / 2, and both lights illuminate the same base and height = (60 x 38) / 2 = 1,140 sq ft

Both Dylan's and Nikki's proposed placement will lit exactly half of the yard. The yard's total area = 60 x 38 = 2,280 sq ft, which is twice the area lit by the lights.