Answer:
d ≈ 6.41
Step-by-step explanation:
Given that F is inversely proportional to d² then the equation relating them is
F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of proportion
To find k use the condition when F = 8, d = 6 , then
8 = [tex]\frac{k}{6^2}[/tex] = [tex]\frac{k}{36}[/tex] ( multiply both sides by 36 )
288 = k
F = [tex]\frac{288}{d^2}[/tex] ← equation of proportion
When F = 7 , then
7 = [tex]\frac{288}{d^2}[/tex] ( multiply both sides by d² )
d² × 7 = 288 ( divide both sides by 7 )
d² = [tex]\frac{288}{7}[/tex] ( take the square root of both sides )
d = ± [tex]\sqrt{\frac{288}{7} }[/tex] ≈ ± 6.41
The positive value of d is 6.41 ( to 2 dec. places )
Answer:
when F = 7, d = 6.41
Step-by-step explanation:
We know that when 'y' varies inversely with 'x', we get the equation
y ∝ 1/x
y = k/x
where 'k' is called the constant of proportionality
Given that F is inversely proportional to d.
F ∝ 1/d
F = k /d²
When F = 8, d = 6, we need to find k
k = Fd²
k = 8×(6)²=288
Now, we need to find d when F = 7
so substitute k = 288, F = 7 in the equation
F = k /d²
d² = k/F
d² = 288/7
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]d=\sqrt{\frac{288}{7}},\:d=-\sqrt{\frac{288}{7}}[/tex]
but, we need to take the positive value of d, so
[tex]d=\sqrt{\frac{288}{7}}[/tex]
[tex]d=6.41[/tex]
Therefore,
when F = 7, d = 6.41