A varries directly as B and C.B=4,C=9 and A=6.(a)find the relationship between A,B and C (b)find A when B=3 and C=10 (c) find AC when A=20 and B=15
(a) If A varies directly as B and C, it can be written as an equation in the form A = kBC, where k is the constant of variation.
Plug in the given values: A = 6, B = 4, and C = 9.
6 = k * 4 * 9
Divide both sides by 4 * 9:
6 / (4 * 9) = k
Simplify:
6 / 36 = k
k = 1/6
The relationship between A, B, and C is A = (1/6)BC.
(b) To find A when B = 3 and C = 10, substitute these values into the equation:
A = (1/6) * 3 * 10
Simplify:
A = 5
When B = 3 and C = 10, A = 5.
(c) To find AC when A = 20 and B = 15, substitute these values into the equation:
AC = (1/6) * 20 * 15
Simplify:
AC = 50
When A = 20 and B = 15, AC = 50.