Independent Assessment
1: Direction: Solve for the constant of variation:
1. If a varies jointly as b and c, and a=13, when b=39, and c=3.
2. If P varies directly as Q and inversely as R, and P=30, when Q=15 and R=4.
3. If I varies jointly as the square of L and the square of M, and J=12, when L=12 and M=3.
4. If D varies jointly as the square of E and F, and D=210, when E=32 and F=70.
5. If y varies directly as x and inversely as the square of z, and y=40, when x=10 and y=3
1: Direction: Solve for the constant of variation:
1. If a varies jointly as b and c, and a=13, when b=39, and c=3.
2. If P varies directly as Q and inversely as R, and P=30, when Q=15 and R=4.
3. If I varies jointly as the square of L and the square of M, and J=12, when L=12 and M=3.
4. If D varies jointly as the square of E and F, and D=210, when E=32 and F=70.
5. If y varies directly as x and inversely as the square of z, and y=40, when x=10 and y=3
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✍️ANSWER:
1. K = 1/9
A = kbc
Then,
13 = k(39)(3)
So,
K = 1/9 ( proportionality constant)
Equation is
A= BC/9
2. k = 8
Solve for constant variation(k):
P = kQ/R
30 = k(15)/4 do a cross multiplication
15k(1) = 30(4)
15k = 120 divide both side by 15
k = 8
3. J=kL²M²
12=k(12)²(3)²
12=1296k
12/1296=1296k/1296
k = 1/108
4. D=kE²F²
210=k(32)²(70)²
210=5017600k
210/5017600=5017600k/5017600
k=3/71680
5. y=kx/z²
40=k(10)/(3)²
10k=360
10k/10=360/10
k=36
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