lunnar2003
30.10.2020 •
Mathematics
Are these two quantities inversely proportional? a.) The time it takes to drive 100 miles and the average driving speed b.) The lengths of sides of a rectangle if the perimeter is fixed c.) The lengths of sides of a rectangle if the are is fixed
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Ответ:
A, B & C are inversely proportional.
Step-by-step explanation:
For two quantities like x and y to be inversely proportional, they are to be written as;
y ∝ 1/x
This means that if x increases, then y decreases and if x decreases, then y increases.
A) The time it takes to drive 100 miles and the average driving speed.
Now, formula for time in motion is;
Time = Distance/speed
Let's denote time as t and speed as v.
Thus;
t = 100/v
From this relationship, it's clear that when v increases, then t decreases and vice versa. Thus it is inversely proportional.
B) The lengths of sides of a rectangle if the perimeter is fixed.
Perimeter of a rectangle is given as;
P = 2(L + W)
Where L is length and W is width.
Now, if the perimeter is fixed, it means an increase in the length will lead to a decrease in the width and vice versa. Thus, it is inversely proportional
C) The lengths of sides of a rectangle if the area is fixed.
If the sides are x & y.
Then;
A = xy
A/x = y
This means that;
1/x ∝ y.
Thus, the sides will be inversely proportional.
Ответ: