variation2

(1) k is a constant of proportionality
SQRT = the square root of
A. a = kb^2, B. a = k/b^2 C. a = kSQRT (b) D. a = k/SQRT (b)
Express k in terms of a and b
A. k =a/b^2 B. k = ab^2 C. k = a/SQRT (b) d. k = a SQRT(b)
We can forget choice C and D because square root of negative number is not allowed.

For A,
k = 1/(-2)^2 = 0.25, k = 1/2^2 = 0.25, k = 16/(-0.5)^2 = 64, k = 16/(0.5)^2 = 64

For B
k = 1(-2)^2 = 4, k = 1(2)^2 = 4, 16(-0.5)^2 = 4, 16(0.5)^2 = 4

Since k = 4 (constant) for four sets of data, (B) is the correct answer

(2) z = ay + b/y^2
a and b are constants of proportionality.
When y =2, z = -1
-1 = a(2) + b/(2)^2
-1 = 2a + b/4
-4 = 8a + b ------------------------- (i)

When y = -1, z = 5
5 = a(-1) + b/(-1)^2
5 = -a + b -------------------------- (ii)
Solve for a and b
Subtract (ii) from (i)
-9 = 9a
a = -1
5 = - (-1) + b
b = 4
So z = -1y + 4/y^2
3 = -1y + 4/y^2
3y^2 = -y^3 + 4
When y = 1, z = -1(1) + 4/(1)^2
z = -1 + 4
z = 3

When z = 3, y = 1 (Answer)

(3)
c = ka^2/b ( k is a constant)
C = k(0.4a)^2/1.6b
C is the new value of c after a decreaes by 60% and b increases by 60%)
C =k(0.16)a^2/1.6b
C = 0.1 ka^2/b
C = 0.1c
New C is one tenth of old c.
If a decreases by 60% and b increases by 60%, c decreases by 90%

c decreases by 90% (Answer)