A car leaves Seattle heading east The speed of the car in mp

A car leaves Seattle heading east. The speed of the car in mph after m minutes is given by the function C(m) = 70m^2/10 + m2 .

(a) Find a function m = f(s) that converts seconds s into minutes m. Write out the formula for the new function C(f(s)); what does this function calculate?

(b) Find a function m = g(h) that converts hours h into minutes m. Write out the formula for the new function C(g(h)); what does this function calculate?

Solution

C(m) = 70m^2/(10 + m2)

a)

C(m) = 70m^2/(10 + m^2) where m is minutes

m =f(s);

m= s/60

Now C(f(s) is found by plugging m= f(s) =60/s

C(f(s)) = 70(s/60)^2/( 10 +(s/60)^2)

= 70s^2/( 36000 +s^2) .The function calculates speed of car after s seconds.

b) m =g(h); m= h*60 =60h

Plug m= 60h in C(m) ;

we get C(g(h)) = 70(60h)^2/( 10 + (60h)^2 )

= 70*3600h^2/( 10 + 3600h^2)

=252000h^2/( 10 + 3600h^2)

This function calculates speed after h hours