horsepower H required to overcome wind drag on a certain automobile is approximated by $H ( x ) = 0.002 x ^ { 2 } + 0.005 x - 0.027,10 \leq x \leq 100$ where $x$ is the speed of the car in miles per hour. Find $H \left( \frac { x } { 1.1 } \right)$. Round the numerical values in your answer to five decimal places.
A) $H \left( \frac { x } { 1.1 } \right) = 0.00150 x ^ { 2 } + 0.00455 x - 0.02700$
B) $H \left( \frac { x } { 1.1 } \right) = 0.00150 x ^ { 2 } + 0.00165 x - 0.00455$
C) $H \left( \frac { x } { 1.1 } \right) = 0.00165 x ^ { 2 } + 0.00150 x - 0.02700$
D) $H \left( \frac { x } { 1.1 } \right) = 0.00165 x ^ { 2 } + 0.00455 x - 0.02700$
E) $H \left( \frac { x } { 1.1 } \right) = 0.00455 x ^ { 2 } + 0.00165 x - 0.02700$

Question

Quizplus · Accepted Answer

Plugging in $\frac{x}{1.1}$ for $x$ in the expression for $H(x)$, we get 
\begin{align*}
H\left(\frac{x}{1.1}ight) &= 0.002\left(\frac{x}{1.1}ight)^2+0.005\left(\frac{x}{1.1}ight)-0.027\
&=0.002\cdot\frac{x^2}{1.21}+0.005\cdot\frac{x}{1.1}-0.027\
&=0.00165x^2+0.00455x-0.027
\end{align*}
Therefore, the answer is $\boxed{	extbf{(D)}}$.

Horsepower H Required to Overcome Wind Drag on a Certain H(x)=0.002x2+0.005x−0.027,10≤x≤100H ( x ) = 0.002 x ^ { 2 } + 0.005 x - 0.027,10 \leq x \leq 100H(x)=0.002x2+0.005x−0.027,10≤x≤100

Horsepower H Required to Overcome Wind Drag on a Certain $H ( x ) = 0.002 x ^ { 2 } + 0.005 x - 0.027,10 \leq x \leq 100$