P varies directly as Q and inversely as four times the cube root of R.if p=16,Q=8 and R=0.015,find R in terms of P and Q
P = k Q / [4 R^(1/3) ]
4 R^(1/3) = k Q/P
R^(1/3) = k Q / 4P
R = k^3 (Q/P)^3/64
.015 = k^3 (8/16)^3 / 64
.015 = k^3 /(8*64)
k^3/64 = .12
R = 0.12 (Q/P)^3
so, R varies directly as the cube of the ratio of Q and P.
:-)
To find R in terms of P and Q, we will use the given information that P varies directly with Q and inversely with four times the cube root of R.
First, let's write the direct variation equation for P and Q:
P = kQ
Next, let's write the inverse variation equation for P and four times the cube root of R:
P = k / (4 * ∛(R))
Now, we can substitute the given values of P = 16 and Q = 8 into the direct variation equation to find the value of k:
16 = k * 8
16 = 8k
k = 16 / 8
k = 2
Substituting the value of k into the inverse variation equation, we have:
16 = 2 / (4 * ∛(R))
Multiply both sides by 4 and cube both sides to solve for R:
64 = 2 / ∛(R)
Cube both sides:
64^3 = (2 / ∛(R))^3
262144 = 8 / R
Cross multiply:
262144 * R = 8
R = 8 / 262144
R ≈ 0.00003051758
Therefore, R ≈ 0.00003051758 in terms of P and Q.