Question

Check my work please will give medals if you tell if this is right or not!!!

Let f(x)=x+5 and g(x)=x^2. find (g o f) (4)
A. 9 <--- my answer
B. 81
C. 20
D. 1
2. police can estimate the speed of a vehicle before the brakes are applied using the formula 0.75d=s^2/30.25, where s is the speed in miles per hour and d is the length of the vehicle's skid marks. what was the approximate speed of a vehicle that left skid marks measuring 140 feet?
A. about 10 miles per hour <-- my answer
B. about 75 miles per hour
C. about 15 miles per hour
D. about 56 miles per hour,

Answer 1

1. The answer is letter B. 81
Since f(x)=(x+5) and g(x)=x^2,
First substitute 4 into f which is
f(4)=4+5=9.
then g(f(4))=g(9).
9^2=81

2.The answer is D. about 56 miles per hour
75d=s^2/30.25
given: d= 140
so 0.75*140=s^2/30.25
s^2=105*30.25=3176.25
= +/- sqrt 3176.25
s=56.358
=56 miles per hour.

Answer 2

Since f(x)=(x+5) and g(x)=x^2, (g circle f)(x) means g(f(x)) which is composition. This tells us to substitute f(x) into g wherever there is an x. Here we want g(f(4)). First substitute 4 into f. THat is f(4)=4+5=9. THe we want g(f(4))=g(9). SUbstitute 9 into g which would be 9^2=81. The answer is 81. If .75d=s^2/30.25 and we know d is the length of the skid mark which here is 140, we substitute 140 in for d. 0.75*140=s^2/30.25 Multiply both sides by 30.25. s^2=105*30.25=3176.25 Take the square root of both sides and we get +/- sqrt 3176.25 But we only want the positive answer since we are talking speed. So s=56.358 which is about 56 miles per hour.