Answer:
see explanation
Step-by-step explanation:
Given y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
(1)
To find k use the condition x = 5, y = 10, thus
k = yx = 10 × 5 = 50
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(2)
y = [tex]\frac{k}{x}[/tex]
To find k use the condition y = 8, x = 10
k = yx = 8 × 10 = 80
y = [tex]\frac{80}{x}[/tex] ← equation of variation
when y = 4, then
4 = [tex]\frac{80}{x}[/tex] ( multiply both sides by x )
4x = 80 ( divide both sides by 4 )
x = 20
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(3)
y = [tex]\frac{k}{x}[/tex]
To find k use the condition y = - 5, x = 20
k = yx = - 5 × 20 = - 100
y = [tex]\frac{-100}{x}[/tex] ← equation of variation
when y = - 4, then
- 4 = [tex]\frac{-100}{x}[/tex] ( multiply both sides by x )
- 4x = - 100 ( divide both sides by - 4 )
x = 25
