Final answer:
To solve for h(c) = 42 for the function h(c)=8c²−41c, first set the equation equal to 42 and rearrange it to 8c²−41c−42 = 0. Then use the quadratic formula with a=8, b=-41, and c=-42 to find the values of c.
Step-by-step explanation:
To solve for h(c) when h(c) = 42 given the function h(c) = 8c² − 41c, we first need to set the function equal to 42:
8c² − 41c = 42
Now, we need to bring all terms to one side to form a quadratic equation:
8c² − 41c − 42 = 0
This equation is in the standard form at² + bt + c = 0. To solve it, we can use the quadratic formula, which is:
x = −b ± ∛(b² − 4ac) / (2a)
Comparatively, in our equation, a = 8, b = −41, and c = −42. Plugging these values into the quadratic formula gives us:
c = −41 ± ∛((−41)² − 4(8)(−42)) / (2×8)
After calculating the values under the square root and the entire expression, we find the two possible solutions for c. The student should use a calculator to find the numerical solutions to the equation. These solutions are the values of c where h(c) equals 42.