Question

in a chemistry lab, the temperature of a solution, f(s), in degrees celsius, is modeled by f(s)=sqrt3{(s + 5)^2}, where s is the grams of a certain substance. how many grams of the substance must be in the solution to make the temperature of the solution 9°celsius? a 9 b 19 c 22 d 32

Explanation:

Step1: Set up the equation

We are given the function $f(s)=\sqrt[3]{(s + 5)^2}$ and we want to find $s$ when $f(s)=9$. So we set up the equation $\sqrt[3]{(s + 5)^2}=9$.

Step2: Cube both sides

Cubing both sides of the equation $\sqrt[3]{(s + 5)^2}=9$ gives us $(s + 5)^2=9^3$. Since $9^3=729$, the equation becomes $(s + 5)^2=729$.

Step3: Take square - root of both sides

Taking the square - root of both sides, we get $s + 5=\pm\sqrt{729}=\pm27$.

Step4: Solve for s

Case 1: If $s + 5 = 27$, then $s=27 - 5=22$.
Case 2: If $s + 5=-27$, then $s=-27 - 5=-32$. But in the context of the amount of a substance (grams), we usually consider non - negative values for $s$. So we take $s = 22$.

Answer:

C. 22