Question

F is inversely proportional to √g. When f=10, g= 16 Work out f when g=25

Answer 1

f = 8

Step-by-step explanation:

given f is inversely proportional to
`√(g)` , then the equation relating them is

f =
`(k)/(√(g) )` ← k is the constant of proportionality

to find k, substitute f = 10, g = 16 into the equation

10 =
`(k)/(√(16) )` =
`(k)/(4)` ( multiply both sides by 4 )

40 = k

f =
`(40)/(√(g) )` ← equation of proportion

when g = 25 , then

f =
`(40)/(√(25) )` =
`(40)/(5)` = 8

Answer 2

To find the value of f when g is 25, we use the equation F = k/√g, where k is a constant. Given f = 10 when g = 16, we can solve for k and then substitute it into the equation to find the value of f.

Step-by-step explanation:

To find the value of f when g is 25, we can use the fact that F is inversely proportional to the square root of g. In math terms, this can be represented as F = k/√g, where k is a constant.

Given that f = 10 when g = 16, we can plug these values into the equation to solve for k. We have 10 = k/√16. Simplifying, we get 10 = k/4, which means k = 40.

Now, we can substitute k = 40 and g = 25 into the equation to find the value of f. We have: f = 40/√25 = 40/5 = 8. Hence, when g is 25, f equals 8, attained through the derived constant k and the given inverse proportionality relationship.