Question

Mathew is attending a very loud concert by the discarded. To avoid permanent ear damage he decides to move farther from the stage. Sound intensity is given by the formula I=k/d*d where k is the constant and d is the distance in metres from the listener to the source of the sound. Determine an expression for the decrease in sound intensity if mathew moves x metres farther from the stage

Answer 1

Your formula makes no sense, because I could just cancel the d's and get
l = k

check your typing.
Is there a square root somewhere
I suspect something like:
" intensity is proportional to the square of the distance"

Answer 2

I= k/ d^2

Decreasing distance: I= k/(d-x)^2

now, subtract the two:

k/d^2 - k/(d-x)^2

expand (d-x)^2 to (d-x)(d-x)

now you have k/d^2 - k/(d-x)(d-x)

find common denominators...

once you do that, you will have

k(d-x)^2 / d^2 (d-x)^2 - kd^2 / d^2(d-x)(d-x)

solve it out and you will get 2kdx+kx^2 / d^2(d-x)^2

Answer 3

Mistake: Use (d+x)^2 instead of (d-x)^2

Answer 4

period