Question

F is inversely proportional to d 2 . When F = 8 , d = 6 Work out d (positive value rounded to 2 DP) when F = 7

Answer 1

Answer:

d ≈ 6.41

Step-by-step explanation:

Given that F is inversely proportional to d² then the equation relating them is

F = $\frac{k}{d^2}$ ← k is the constant of proportion

To find k use the condition when F = 8, d = 6 , then

8 = $\frac{k}{6^2}$ = $\frac{k}{36}$ ( multiply both sides by 36 )

288 = k

F = $\frac{288}{d^2}$ ← equation of proportion

When F = 7 , then

7 = $\frac{288}{d^2}$ ( multiply both sides by d² )

d² × 7 = 288 ( divide both sides by 7 )

d² = $\frac{288}{7}$ ( take the square root of both sides )

d = ± $\sqrt{\frac{288}{7} }$ ≈ ± 6.41

The positive value of d is 6.41 ( to 2 dec. places )

Answer 2

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

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$d=\sqrt{\frac{288}{7}},\:d=-\sqrt{\frac{288}{7}}$

but, we need to take the positive value of d, so

$d=\sqrt{\frac{288}{7}}$

$d=6.41$

Therefore,

when F = 7, d = 6.41