4 multiple choice 2 points suppose p varies directly with the square root of q. if p = 24 when q = 16, find…
4 multiple choice 2 points suppose p varies directly with the square root of q. if p = 24 when q = 16, find p when q = 25. 28 27 29 30
Answer
Explanation:
Step1: Write the direct - variation equation
Since (p) varies directly with (\sqrt{q}), the equation is (p = k\sqrt{q}), where (k) is the constant of variation. When (p = 24) and (q = 16), substitute into the equation: (24=k\sqrt{16}). Since (\sqrt{16}=4), the equation becomes (24 = 4k). Solve for (k): (k=\frac{24}{4}=6).
Step2: Find (p) when (q = 25)
Substitute (k = 6) and (q = 25) into (p = k\sqrt{q}). (p=6\sqrt{25}). Since (\sqrt{25}=5), then (p=6\times5 = 30).
Answer:
30