H(x)= 0.002x^2+0.005x-0.029 where x is the speed of the car in miles per hour.
How can I rewrite the function so that x represe the speed in kilometers per hour. [Find H(x/1.6)]
To rewrite the function so that x represents the speed in kilometers per hour, we need to convert the speed from miles per hour to kilometers per hour.
1 mile is equal to 1.6 kilometers, which means 1 mile per hour is equal to 1.6 kilometers per hour.
So, to convert x from miles per hour to kilometers per hour, we divide it by 1.6:
x/1.6
Now, let's substitute x/1.6 into the original function H(x):
H(x/1.6) = 0.002(x/1.6)^2 + 0.005(x/1.6) - 0.029
Simplifying further:
H(x/1.6) = 0.002(x^2/2.56) + 0.005(x/1.6) - 0.029
Using the rule (a/b)^2 = a^2 / b^2:
H(x/1.6) = 0.002(x^2/2.56) + 0.005(x/1.6) - 0.029
H(x/1.6) = (0.002/2.56)x^2 + (0.005/1.6)x - 0.029
Hence, the rewritten function where x represents the speed in kilometers per hour is H(x/1.6) = (0.002/2.56)x^2 + (0.005/1.6)x - 0.029.