Correct Answer: A. 251

Explanation

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Correct Answer: D. \(\frac{10x}{(1-x^2)^6}\)

Explanation

\(y = \frac{1} {(1 - x^2)^5} = (1-x^2)^{-5}\)

Let u = \(1 - x^2; y = u ^{-5}\)

\(\frac{du}{ dx}=-2x;\frac{dy}{ du}=-5u^{-6}\)

Using chain rule:

\(\frac{dy}{dx}=\frac{dy}{du}\times\frac{du}{ dx}\)

\(\frac{dy}{dx}=-2x\times-5u^{-6}\)

\(\frac{dy}{dx}=-2x\times-5(1 - x^2)^{-6}\)

\(\therefore\frac{dy}{dx} = 10x(1-x^2)^{-6}=\frac{10x}{(1-x^2)^6}\)

Correct Answer: A. 1

Explanation

\(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0

\(\frac{4(2n + 1) - 6(3x - 1)}{24}\) = 0

-10x + 10 = 0

-10x = -10

x = \(\frac{-10}{-10}\)

x = 1

Explanation

(a) x-axis: 2 cm to 2 units or 1 cm to 1 unit

y-axis: 2 cm to 10 units or 1 cm to 5 units

(b) x = -2, x = 4

(x+2)(x-4) = 0

x\(^2\) -4x + 2x -8 = 0

x\(^2\) -2x - 8 = 0

y = 8 + 2x - x(curve has a max. point)

m = -1,n = 2, r =8

(c) P(-5,-27),Q(3,5)

Gradient = \(\frac{5+27}{3+5}\)

= \(\frac{32}{8}\)

= 4

(d) Range: {x:-2 < x < 4)

Correct Answer: C. \(\frac{4y - x}{y}\)

Explanation

(\(\frac{x -y}{y}\)); \(\frac{3}{1} - \frac{x y}{y}\)

= \(\frac{3y - (x - y)}{y}\)

= \(\frac{3y - x + y}{y}\)

= \(\frac{4y - x}{y}\)

Correct Answer: (d) 1/8, 1/3, 3/7 and 5/9

Explanation

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Explanation

(a) \((p + qx)^{7} = p^{7} + 7p^{6} qx + 21p^{5} (qx)^{2} + 35p^{4} (qx)^{3} + 35p^{3} (qx)^{4} + 21p^{2} (qx)^{5} + 7p(qx)^{6} + (qx)^{7}\)

The coefficient of \(x^{2}\) = \(21p^{5} q^{2}\)

The cofficient of \(x^{3}\) = \(35p^{4} q^{3}\)

\(\therefore 21p^{5} q^{2} = 35p^{4} q^{3}\)

\(\implies 21p = 35q\)

\(q = \frac{21}{35} p = \frac{3}{5} p\).

(b) N180 + N260 + N340 + ...

This sequence is a linear sequence with first term = a = 180, d = 80.

\(S_{16} = ?\)

\(S_{n} = \frac{n}{2} (2a + (n - 1) d)\)

\(S_{16} = \frac{16}{2} (2(180) + (16 - 1) 80\)

= \(8(360 + 1200)\)

= \(8(1560)\)

= \(N12,480\)

He would have contributed N12,480 by the 16th week.

Correct Answer: (c)-1900

Explanation

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Correct Answer: A. 2¹/₂ years

Explanation

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Correct Answer: A. 6.5 units

Explanation

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