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1. If x varies direct with y, and x = 27 when y = 6, find x when y = 2.
k =
Equation:
x =
2. If m varies directly with p², and m = 20 when p = 2, find m when p = 5.
k =
Equation:
m =
3. If a varies directly with the square of b, and a = 48 when b = 4, find b when a = 147.
k =
Equation:
b =
4. u is inversely proportional to v. If v = 30, then u = 12. Find u when v is 10.
k =
Equation:
u =
5. y varies inversely with the square root of w. If w = 4, then y = 1.5. Find w when y = 4.
k =
Equation:
w =
1. If x varies direct with y, and x = 27 when y = 6, find x when y = 2.
k =
Equation:
x =
2. If m varies directly with p², and m = 20 when p = 2, find m when p = 5.
k =
Equation:
m =
3. If a varies directly with the square of b, and a = 48 when b = 4, find b when a = 147.
k =
Equation:
b =
4. u is inversely proportional to v. If v = 30, then u = 12. Find u when v is 10.
k =
Equation:
u =
5. y varies inversely with the square root of w. If w = 4, then y = 1.5. Find w when y = 4.
k =
Equation:
w =
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Answer:
If x varies direct with y, and x = 27 when y = 6, find x when y = 2.
k = x/y = 27/6 = 4.5
Equation: x = ky
x = 4.5(2) = 9
If m varies directly with p², and m = 20 when p = 2, find m when p = 5.
k = m/p² = 20/2² = 5
Equation: m = kp²
m = 5(5)² = 125
If a varies directly with the square of b, and a = 48 when b = 4, find b when a = 147.
k = a/b² = 48/4² = 3
Equation: a = kb²
147 = 3b²
b = √(147/3) ≈ 6
u is inversely proportional to v. If v = 30, then u = 12. Find u when v is 10.
k = uv = 12(30) = 360
Equation: u = k/v
u = 360/10 = 36
y varies inversely with the square root of w. If w = 4, then y = 1.5. Find w when y = 4.
k = y√w = 1.5(2) = 3
Equation: y = k/√w
4 = 3/√w
w = (3/4)² = 0.5625