唔識計! 66666

y partly varies directly as x and partly varies directly as X^2. if Y=10 when X = -2 and Y = 115 when X = 5, find
a) the equation of variation: and
b) the value of Y when X = -10.


a)
y = k1x + k2x² where k1 and k2 are proportional constants.

If y = 10, x = -2
10 = k1(-2) + k2(-2)²
-k1 + 2k2 = 5 …… (1)

If y = 115, x = 5
115 = k1(5) + k2(5)²
k1 + 5k2 = 23 …… (2)

(1) + (2):
7k2 = 28
k2 = 4

Put k2 = 4 into (1):
-k1 + 2(4) = 5
k1 = 3

The equation of variation:
y = 3x + 4x²

b)
When x = -10
y = 3(-10) + 4(-10)²
y = -30 + 400
y = 370