I'm having trouble with this question.
The number of horse-power H required to overcome wind drag on a certain automobile is approximated by: H(x)= 0.002(x)^2 + 0.005(x) - 0.029, [10 is less then/equal to (x) is less then/equal to 100].
Where x is the speed of the car in miles per hour.
Rewrite the power function so that x represents the speed in kilometers per hour. [Find H(x/1.6)]. Identify the type of transformation applied to the graph of the power function.
To rewrite the power function, we need to convert x, which represents the speed in miles per hour, to kilometers per hour.
Since 1 mile is approximately equal to 1.6 kilometers, we can divide x by 1.6 to convert it to kilometers per hour.
The rewritten power function, H(x/1.6), can be written as:
H(x/1.6) = 0.002(x/1.6)^2 + 0.005(x/1.6) - 0.029
This new function represents the power required to overcome wind drag at different speeds in kilometers per hour.
The transformation applied to the graph of the power function is a horizontal compression or shrink by a factor of 1.6.
To rewrite the power function with x representing the speed in kilometers per hour, you need to convert the miles per hour to kilometers per hour.
Since 1 mile is equal to 1.6 kilometers, you can divide x by 1.6 to convert it to kilometers per hour. Therefore, the rewritten power function would be H(x/1.6) = 0.002 * (x/1.6)^2 + 0.005 * (x/1.6) - 0.029.
Now, let's identify the type of transformation that has been applied to the graph of the power function.
In this case, the transformation is a horizontal compression or shrink. By dividing x by 1.6, each x value is being divided by a factor of 1.6, which makes the graph narrower or compressed horizontally. This means that the graph of H(x/1.6) will be narrower compared to the original function H(x).