Answer:
When y = 4, x is equal to 39
Step-by-step explanation:
The given parameters are;
x = a + b + 4
a ∝ 1/y²
b ∝ 1/(1/y) = y
When y = 2, x = 18
When y = 1, x = -3
Therefore, we have;
a·y² = j
a = j/y²
b ∝ 1/(1/y)
∴ b ∝ y
b = k·y
When y = 2, x = 18, we have;
a = j/y² = j/2² = j/4
b = k·y = k·2
x = a + b + 4
∴ 18 = j/4 + k·2 + 4...(1)
When y = 1, x = -3, we have;
a = j/y² = j/1² = j
b = k·y = k·1 = k
x = a + b + 4
∴ -3 = j + k + 4...(2)
Making 'j', the subject of equation (1) and (2) gives;
From equation (1), we have;
18 = j/4 + k·2 + 4
∴ j = (18 - 4 - k·2) × 4 = 56 - 8·k
From equation (2), we have;
-3 = j + k + 4
∴ j = -3 - 4 - k = -7 - k
Equating the two values of 'j', gives;
56 - 8·k = -7 - k
56 + 7 = 8·k - k
63 = 7·k
k = 63/7 = 9
k = 9
From equation (2), we get;
-3 = j + k + 4
k = 9
∴ -3 = j + 9 + 4
j = -3 - 9 - 4 = -16
j = -16
When y = 4, we get;
x = a + b + 4
a = j/y²
b = k·y
∴ x = j/y² + k·y + 4
Plugging in the values of 'j', and 'k' and y = 4, gives;
x = (-16)/y² + 9·y + 4
∴ x = (-16)/4² + 9 × 4 + 4 = 39
x = 39
Therefore;
When y = 4, x = 39.
