Question

I need help with #39-42, please explain.

Answer 1

For question 39 & 40, we need to use the below equation to complete the sentence

$l=m\sqrt{n}$

Question 39:

When ' n ' increase, the $\sqrt{n}$ will also increase and that multiplied with constant ' m ', the l will also increase.

Solution for question 39:

As $n$ increases and $m$ stays constant , $l$ increases

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Question 40:

Solving the equation for m, we get

$l = m\sqrt{n} \\ \\ m=\frac{l}{\sqrt{n}}$

When ' l ' increases, the numerator increase, the denominator stays constant because 'n' stays constant, for this condition, the fraction increases.

Solution for question 40:

As $l$ increase and $n$ stays constant, $m$ increases

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For question 41 & 42, we need to use the below equation to complete the sentence

$r=s^2/t^2$

Question 41:

When $s$ is triped, the equation will be...

$r=(3s)^2/t^2=\frac{3^{2}s^{2}}{t^2} =9s^2/t^2$

Solution for question 41:

If $s$ is tripled and $t$ stays constant, $r$ is multiplied by 9

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Question 42:

When t is doubled, the equation will be...

$r=s^2/(2t)^2=\frac{s^2}{2^2 \cdot t^2}=\frac{s^2}{4t^2}\\ \\ r=0.25s^2/t^2 \; \; (or) \; \; \frac{1}{4} \cdot \frac{s^2}{t^2}$

Solution for 42:

If $t$ doubled and $s$ stays constant, $r$ is multiplied by 1/4 or 0.25