Horsepower Function

[nycmathguy]

Section 1.7
Question 61

See attachment.

I will leave part (a) for last.

Part (b)

Do I simply replace x with (x/1.6)?

H(x/1.6) = 0.00004636(x/1.6)^3

I say the transformation is a vertical shrink.

Note: x/1.6 is the same as x(1/1.6). This is why I decided that a vertical shrink is the transformation.

 

[MathLover1]

yes it is
H(x/1.6) = 0.00004636(x/1.6)^3

you can simplify
H(x/1.6) = 0.00004636x^3/(1.6)^3
H(x/1.6) = 0.00004636x^3/(4.096)
H(x/1.6) = (0.00004636/4.096)x^3
H(x/1.6) = 0.000011318359375x^3

 

[nycmathguy]

yes it is
H(x/1.6) = 0.00004636(x/1.6)^3

you can simplify
H(x/1.6) = 0.00004636x^3/(1.6)^3
H(x/1.6) = 0.00004636x^3/(4.096)
H(x/1.6) = (0.00004636/4.096)x^3
H(x/1.6) = 0.000011318359375x^3

Great. Cool. I will show the graph when time allows.

 

[MathLover1]

H(x) = 0.00004636x^3

H(x/1.6) = 0.00004636x^3/(1.6)^3

 

[nycmathguy]

H(x) = 0.00004636x^3

H(x/1.6) = 0.00004636x^3/(1.6)^3

Thank you. Now I don't have to show the graph. More graphs will be posted on Sunday, if time allows. I am also taking off Tuesday evening. I am exhausted. I am in the process of moving from Queens to Brooklyn. I will explain more via PM service.