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

d ≈ 6.41

Step-by-step explanation:

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

F = ← k is the constant of proportion

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

8 = = ( multiply both sides by 36 )

288 = k

F = ← equation of proportion

When F = 7 , then

7 = ( multiply both sides by d² )

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

d² = ( take the square root of both sides )

d = ± ≈ ± 6.41

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

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

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

Therefore,

when F = 7, d = 6.41

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!