The grade $\mathrm{x}$ of a hill is a measure of its steepness. For example, if a road rises 10 feet for every 100 feet of horizontal distance, then it has an uphill grac of $x=\frac{10}{100}$, or $10 \%$. The braking (or stopping) distance $D$ for a car traveling at $50 \mathrm{mph}$ on a wet, uphill grade is given by $D(x)=\frac{2500}{30(0.3+x)}$.
Complete parts (a) through (c).
(a) Evaluate $\mathrm{D}(0.01)$ and interpret the result. Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. $\mathrm{D}(0.01) \approx \square \mathrm{ft}$ and it represents the braking distance for a car traveling at $50 \mathrm{mph}$ on a wet $1 \%$ uphill grade. (Round to the nearest whole number as needed.)
B. $D(0.01) \approx \square$ ft. and represents the braking distance for a car traveling at $50 \mathrm{mph}$ on a wet $0.01 \%$ uphill grade. (Round to the nearest whole number as needed.)
Answer
The function D(0.01) evaluates to approximately 269 feet (rounded to the nearest whole number). This represents the braking distance for a car traveling at 50 mph on a wet 1% uphill grade. Therefore, the correct answer is \(\boxed{269}\) feet.
Step 1 ：The grade \(x\) of a hill is a measure of its steepness. For example, if a road rises 10 feet for every 100 feet of horizontal distance, then it has an uphill grade of \(x=\frac{10}{100}\), or 10%. The braking (or stopping) distance \(D\) for a car traveling at 50 mph on a wet, uphill grade is given by \(D(x)=\frac{2500}{30(0.3+x)}\).
Step 2 ：The question asks to evaluate the function D(x) at x=0.01. This function represents the braking distance for a car traveling at 50 mph on a wet, uphill grade. The value of x represents the grade of the hill, so in this case, the hill has a grade of 1% (since 0.01 is equivalent to 1%). Therefore, we need to substitute x=0.01 into the function and calculate the result.
Step 3 ：Substitute x=0.01 into the function: \(D(0.01) = \frac{2500}{30(0.3+0.01)}\).
Step 4 ：Calculate the result: \(D(0.01) = 268.81720430107526\).
Step 5 ：Round the result to the nearest whole number: \(D(0.01) \approx 269\) feet.
Step 6 ：The function D(0.01) evaluates to approximately 269 feet (rounded to the nearest whole number). This represents the braking distance for a car traveling at 50 mph on a wet 1% uphill grade. Therefore, the correct answer is \(\boxed{269}\) feet.
