For question 39 & 40, we need to use the below equation to complete the sentence
[tex] l=m\sqrt{n} [/tex]
Question 39:
When ' n ' increase, the [tex] \sqrt{n} [/tex] will also increase and that multiplied with constant ' m ', the l will also increase.
Solution for question 39:
As [tex] n [/tex] increases and [tex] m [/tex] stays constant , [tex] l [/tex] increases
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Question 40:
Solving the equation for m, we get
[tex] l = m\sqrt{n} \\ \\ m=\frac{l}{\sqrt{n}} [/tex]
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 [tex] l [/tex] increase and [tex] n [/tex] stays constant, [tex] m [/tex] increases
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For question 41 & 42, we need to use the below equation to complete the sentence
[tex] r=s^2/t^2 [/tex]
Question 41:
When [tex] s [/tex] is triped, the equation will be...
[tex] r=(3s)^2/t^2=\frac{3^{2}s^{2}}{t^2} =9s^2/t^2 [/tex]
Solution for question 41:
If [tex] s [/tex] is tripled and [tex] t [/tex] stays constant, [tex] r [/tex] is multiplied by 9
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Question 42:
When t is doubled, the equation will be...
[tex] 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} [/tex]
Solution for 42:
If [tex] t [/tex] doubled and [tex] s [/tex] stays constant, [tex] r [/tex] is multiplied by 1/4 or 0.25
