The functions q and r are defined as follows g(x) = -2x-2
r(x) = x² – 2
Find the value of r(q(4)).
r(9 (4)) =

98

Step-by-step explanation:

So we have the two functions:

And we want to find the value of r(g(4)).

To do so, first find the value of g(4):

Multiply:

Subtract:

Now, substitute this into r(g(4)):

And substitute this value into r(x):

Square:

Subtract:

Therefore:

D=distance

VS=velocity through steel

VA=velocity through air

ts=time through steel

ta=time through air

Let's just get some equations out there:

D=VS*ts=16500*ts

D=VA*ta=1100*ta

ta=ts+6 (you can reason that it will take longer through air because the speed is slower)

So, D=16500*ts=1100*ta=D so 16500*ts=1100*ta. Substituting ts+6 in for ta we get 16500*ts=1100*(ts+6), so 16500*ts=1100*ts+6600. Subtracting 1100*ts from both sides, we get 15400*ts=6600, so ts=6600/15400=3/7 seconds. So, to find the distance, we need only plug this time back into the equation D=16500*ts=16500*3/7=7071.43 feet.