Correct Answer: C. Oxyacetylene flame

Correct Answer: A. a common elasticity in different markets

Correct Answer: A. configure firewall.

Correct Answer: D. Waziri

Correct Answer: C. 22

Correct Answer: C. partnership

Correct Answer: B. ashamed and embarrassed

Explanation

(a) 3, x, y, 18.

Note : When given the consecutive terms of an A.P to be \(a, b, c, d\), then

\(\frac{a + c}{2} = b ; \frac{b + d}{2} = c\).

\(\therefore \frac{3 + y}{2} = x \implies 3 + y = 2x .... (1)\)

Also, \(\frac{x + 18}{2} = y \implies x + 18 = 2y ..... (2)\)

From (2), x = 2y - 18. Putting that in (1), we have

\(3 + y = 2(2y - 18) \implies 3 + y = 4y - 36\)

\(3 + 36 = 4y - y \implies 3y = 39\)

\(y = 13\)

\(x = 2y - 18\)

\(x = 2(13) - 18 = 26 - 18 = 8\)

\((x, y) = (8, 13)\).

(b)(i) G.P

\(T_{2} = ar ; T_{3} = ar^{2} ; T_{4} = ar^{3}\)

\(T_{2} + T_{3} = 6T_{4}\)

\(ar + ar^{2} = 6ar^{3}\)

\(6ar^{3} - ar^{2} - ar = 0\)

\(6ar^{3} - 3ar^{2} + 2ar^{2} - ar = 0\)

\(3ar^{2}(2r - 1) + ar(2r - 1) = 0\)

\((3ar^{2} + ar)(2r - 1) = 0\)

\(ar(3r + 1)(2r - 1) = 0\)

\(\implies 3r + 1 = 0 ; 2r - 1 = 0\)

\(r = \frac{-1}{3} ; r = \frac{1}{2}\)

(ii) Since r is positive, then \(r = \frac{1}{2}\).

\(T_{2} = ar = 8 \implies \frac{a}{2} = 8\)

\(a = 16\)

\(\therefore \text{The first 6 terms} = 16, 8, 4, 2, 1, \frac{1}{2}\)

Explanation

(a) Area of sector = \(\frac{\theta}{360} \times \pi r^{2}\)

\(280 = \frac{\theta}{360} \times \frac{22}{7} \times 21 \times 21\)

\(280 = \frac{1386 \theta}{360}\)

\(\theta = \frac{280 \times 360}{1386}\)

\(\theta = 72.72°\)

Perimeter of sector = \(2r + \frac{\theta}{360} \times 2\pi r\)

= \(2(21) + \frac{72.72}{360} \times 2 \times \frac{22}{7} \times 21\)

= \(42 + (0.202 \times 2 \times 66)\)

= \(42 + 26.667\)

= \(68.667 cm\)

\(\approxeq 68.7 cm\)

(b) When the sector is bent to form a cone, its radius becomes the slant height of the cone.

The radius of the base of the cone is obtained from the relation \(r = \frac{R \theta}{360}\),

where r = radius of the base of the cone, R = radius of the sector, θ = angle of the sector.

Therefore, r = \(\frac{21 \times 800}{11 \times 360}\)

= \(\frac{140}{33}\)

If y is the vertical angle of the cone, then \(sin \frac{y}{2} = \frac{r}{l}\)

= \(\frac{140}{33 \times 21}\)

= 0.2020

Hence, required angle = y = 2 x sin\(^{-1}\) (0.2020) = 23\(^o\).

Explanation

(a) Plane polarized waves are:

(i) radio waves

(ii) x-rays.

(iii) infrared radiation etc

(b) Application of plane polarized light

– To reduce glare from reflecting surfaces.

– In sunglasses to reduce the intensity of incident sunlight.

– To determine sugar solution concentration etc.