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Highest Common Factors

if d is the h...

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if d is the hcf of 160 and 24 then find x and y satisfying d =160x plus 24y. also show that x and y are not unique

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Q. If d is the HCF of 160 and 24, then find x and y satisfying

d = 160 x + 24 y

d

H C F

56

72,

x, y

d = 56 x + 72 y .

Also, show that

x

y

are not unique.

x

y

are differentiable functions of

t

, then show that

\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}}

\frac{d x}{d t} \neq 0

y^{3} - y = 2 x

, then prove that

\frac{d^{2} y}{d x^{2}} = \frac{- 24 y}{(3 y^{2} - 1)^{3}}

. Hence, show that

9 (x^{2} - \frac{1}{27}) \frac{d^{2} y}{d x^{2}} + 9 x \frac{d y}{d x} = y

\int_{0}^{a} f (x) g (x) d x = 2 \int_{0}^{a} f (x) d x

f

g

f (x) = f (a - x)

g (x) + g (a - x) = 4

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