5 multiple choice 2 points suppose p varies jointly as x and the square root of y. if p = 48 when x = 4 and…

Explanation:

Step1: Write the joint - variation formula

If (p) varies jointly as (x) and (\sqrt{y}), then the formula is (p = kx\sqrt{y}), where (k) is the constant of variation.

Step2: Find the value of (k)

Substitute (p = 48), (x = 4), and (y = 4) into (p=kx\sqrt{y}). We have (48=k\times4\times\sqrt{4}). Since (\sqrt{4}=2), the equation becomes (48 = k\times4\times2). Simplify the right - hand side: (4\times2k=8k). So, (8k = 48), and (k=\frac{48}{8}=6).

Step3: Find (p) when (x = 7) and (y = 25)

Substitute (k = 6), (x = 7), and (y = 25) into (p = kx\sqrt{y}). Since (\sqrt{25}=5), then (p=6\times7\times5). First, (6\times7 = 42), then (42\times5=210).

Answer:

210