y varies partly as the square of x and partly as the inverse of the square root of x.Write down the expression for y if y = 2 when x = 1 and y = 6 when x = 4
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A.
y = (frac{10x^2}{31} + frac{52}{31sqrt{x}}) -
B.
y = x2 + (frac{1}{sqrt{x}}) -
C.
y = x2 + (frac{1}{x}) -
D.
y = (frac{x^2}{31} + frac{1}{31sqrt{x}})
Correct Answer: Option A
Explanation
y = kx2 + (frac{c}{sqrt{x}})
y = 2when x = 1
2 = k + (frac{c}{1})
k + c = 2
y = 6 when x = 4
6 = 16k + (frac{c}{2})
12 = 32k + c
k + c = 2
32k + c = 12
= 31k + 10
k = (frac{10}{31})
c = 2 – (frac{10}{31})
= (frac{62 – 10}{31})
= (frac{52}{31})
y = (frac{10x^2}{31} + frac{52}{31sqrt{x}})