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3 years ago

the number of hours,h, it takes to wash c numbers of cars at a school fundraiser is inversely proportional to the number of stud

ents,s, needed to wash the cars. Write a equation to represent his relationship

Mathematics

1 answer:

Alex787 [66]3 years ago

3 0

$\bf \qquad \qquad \textit{inverse proportional variation}
\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\stackrel{\textit{\underline{h}ours to wash a car, is inversely proportional to \underline{s}tudents working on it}}{h=\cfrac{k}{s}}$

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Answer:

1) The simplified radical form is $\sqrt{36x^2}=6x$

2) The simplified radical form is $\sqrt{72x^3}=6x\sqrt{2x}$

3) The simplified radical form is $\sqrt{15x^8}=\sqrt{15}x^4$

4) The simplified radical form is $\sqrt{36x^7}=6x^3\sqrt{x}$

Step-by-step explanation:

1) Given expression is $\sqrt{36x^2}$

To find the simplified radical form of the given expression :

$\sqrt{36x^2}$

$=\sqrt{36\times x^2}$

$=\sqrt{36}\times \sqrt{x^2}$

$=\sqrt{6\times 6}\times \sqrt{x\times x}$

$=6\times x$

$\sqrt{36x^2}=6x$

Therefore the simplified radical form is $\sqrt{36x^2}=6x$

2)Given expression is $\sqrt{72x^3}$

To find the simplified radical form of the given expression :

$\sqrt{72x^3}$

$=\sqrt{72\times x^3}$

$=\sqrt{72}\times \sqrt{x^3}$

$=\sqrt{9\times 8}\times \sqrt{x\times x\times x}$

$=\sqrt{9}\times \sqrt{8}\times x\sqrt{x}$

$=3\times 2\sqrt{2}\times x\sqrt{x}$

$\sqrt{72x^3}=6x\sqrt{2x}$

Therefore the simplified radical form is $\sqrt{72x^3}=6x\sqrt{2x}$

3) Given expression is $\sqrt{15x^8}$

To find the simplified radical form of the given expression :

$\sqrt{15x^8}$

$=\sqrt{15\times x^8}$

$=\sqrt{15}\times \sqrt{x^8}$

$=\sqrt{5\times 3}\times \sqrt{x^4\times x^4}$

$=\sqrt{15}\times x^4$

$\sqrt{15x^8}=\sqrt{15}x^4$

Therefore the simplified radical form is $\sqrt{15x^8}=\sqrt{15}x^4$

4) Given expression is $\sqrt{36x^7}$

To find the simplified radical form of the given expression :

$\sqrt{36x^7}$

$=\sqrt{36\times x^7}$

$=\sqrt{36}\times \sqrt{x^7}$

$=\sqrt{6\times 6}\times \sqrt{x^3\times x^3\times x}$

$=6\times x^3\sqrt{x}$

$\sqrt{36x^7}=6x^3\sqrt{x}$

Therefore the simplified radical form is $\sqrt{36x^7}=6x^3\sqrt{x}$

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3 years ago