Correct Answer: A. 5cm

Correct Answer: A. \(2x - 3\)

Explanation

(b)

(c)(i) From the graph, \(9\cos x + 5\sin x = 0 \implies x = 119°\)

(d) Maximum value of y = 10.3.

(b)

(c)(i) From the graph, \(9\cos x + 5\sin x = 0 \implies x = 119°\)

(d) Maximum value of y = 10.3.

Explanation

Beginning of 1st year (March 2011 - February 2012) - N900,000

Depreciation (30%) = \(\frac{30}{100} \times N900,000\)

= N270,000

Price at the end of 1st year = N(900,000 - 270,000)

= N630,000.

Beginning of 2nd year (March 2012 - February 2013) - N630,000

Depreciation (22%) = \(\frac{22}{100} \times N630,000\)

= N138,600

Price at the end of 2nd year = N(630,000 - 138,600)

= N491,400.

Beginning of 3rd year (March 2013 - February 2014) - N491,400

Depreciation (22%) = \(\frac{22}{100} \times N491,400\)

= N108,108

Price at the end of the 3rd year = N(491,400 - 108,108)

= N383,292.

Beginning of 4th year (March 2014 - February 2015) - N383,292

Depreciation (22%) = \(\frac{22}{100} \times N383,292\)

= N84,324.24

Price at the end of the 4th year = N(383,292 - 84,324.24)

= N298,967.76 \(\approxeq\) N299,000 (to the nearest hundred naira).

Correct Answer: D. x² - 3x + 3

Correct Answer: B. 3.5cm

Explanation

diameter = 12cm

radius = \(\frac{12}{2}\)cm = 6cm

area of sector = 66cm²

area of sector = area of cone

66 = \(\pi rl\)

66 = \(\frac{22}{7} \times r \times 6\)

divide both sides by 6

11 = \(\frac{22}{7}r\)

22r = 11 x 7

r = \(\frac{77}{22}\)

= 3.5cm

Explanation

(a) \(u = 5 - x^{2}\)

= \(\int_{1}^{2} \frac{x}{\sqrt{u}} dx\)

\(\frac{\mathrm d u}{\mathrm d x} = -2x\)

\(\mathrm {d} x = \frac{\mathrm d u}{-2x}\)

\(\implies \int_{1}^{2} \frac{x}{\sqrt{u}} \frac{\mathrm d u}{-2x}\)

= \(-\frac{1}{2} \int_{1}^{2} \frac{1}{\sqrt{u}} \mathrm {d} u\)

= \(-\frac{1}{2} \int_{1}^{2} u^{-\frac{1}{2}} \mathrm {d} u\)

= \(-\frac{1}{2} [2u^{1}{2}]|_{1}^{2}\)

= \(-\frac{1}{2} [2\sqrt{5 - x^{2}}]|_{1}^{2}\)

= \(-\frac{1}{2} [2 - 4]\)

= 1.

(b)\(y = px^{2} + qx\)

\(\frac{\mathrm d y}{\mathrm d x} = 2px + q = 6x + 7\)

\(\implies 2p = 6; p = 3\)

\(q = 7\)

Correct Answer: C. \(\frac{3-x}{1-x^2}\)

Explanation

\(\frac{1}{1-x} + \frac{2}{1+x}\\

\frac{1+x+2-2x}{(1-x)(1+x)} = \(\frac{3-x}{1-x^2}\)\)

Explanation

(a)

\((x + 8)^{2} = x^{2} + (x + 7)^{2}\)

\(x^{2} + 16x + 64 = x^{2} + x^{2} + 14x + 49\)

\(x^{2} + 16x + 64 - 2x^{2} - 14x - 49 = 0\)

\(15 + 2x - x^{2} = 0\)

\(x^{2} - 2x - 15 = 0\)

\((x + 3)(x - 5) = 0\)

x = 5m since measurements cannot be negative.

(b) \(Area = length \times breadth\)

Length = (x + 7) = (5 + 7) = 12 m

Breadth = x m = 5 m

\(Area = 12 \times 5 = 60 m^{2}\)

Correct Answer: B. 2000