Question

fill in the blank with the appropriate answer. to determine proper dosing of a medication, doctors use the formula $s = sqrt{\frac{wh}{3000}}$ to determine a patients body surface area (s in square meters), based on their weight (w, in pounds) and height (h, in centimeters). if someones body surface area is 4 square meters and they are 190 cm tall, how much does the person weigh to the nearest pound? pounds

Explanation:

Step1: Square both sides of the formula

Given $s = \sqrt{\frac{wh}{3000}}$, squaring both sides gives $s^{2}=\frac{wh}{3000}$.

Step2: Rearrange the formula to solve for $w$

Multiply both sides by 3000: $3000s^{2}=wh$. Then $w=\frac{3000s^{2}}{h}$.

Step3: Substitute the given values

We know $s = 4$ and $h=190$. Substitute into the formula: $w=\frac{3000\times4^{2}}{190}=\frac{3000\times16}{190}=\frac{48000}{190}\approx252.63$.

Step4: Round to the nearest pound

Rounding 252.63 to the nearest pound gives 253.

Answer:

253