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pm\(^2\) + qm + 1 = (m - 1) Q(x) + 2, where Q(x) = remainder. p(1)\(^2\) + q(1) + 1 = 2 p + q + 1 = 2 p + q = 1.....(i) pm\(^2\) + qm + 1 = (m - 1)Q(x) + 4 p(-1)\(^2\) + q(-1) + 1 = 4 p - q + 1 = 4 p - q = 3....(ii) p + q = 1, p - q = 3 Using elimination method, add eqn i and ii 2p = 4, p = 2 from eqn ii p - q = 3 2 - q = 3 -q = 3 - 2 = 1 q = - 1 Therefore, p = 2 and q = -1 q = 2

Area of a sector = \(\frac{\theta}{360}\) x \(\pi\)r\(^2\) Area of a sector = \(\frac{50}{360}\) x 3.142 x 3.5 x 3.5 = \(\frac{50 \times 3.142\times 3.5 \times 3.5}{360}\) = \(\frac{1924.475}{360}\) ≈ 5.346cm\(^2\)

Using Pythagora's rule for △PSM Hyp\(^2\) = Opp\(^2\) + Adj\(^2\) 5\(^2\) = Opp\(^2\) + 4\(^2\) → Opp\(^2\) = 25 - 16 → Opp = \sqrt9 = 3 base SR = 18 + 3 = 21 base PQ = 18 side PS = 5 side QR = 4 perimeter of the trapezium PQRS = 21 + 18 + 5 + 4 = 48cm

diagonal of a square(x) = y\sqrt2 y in terms of x → y = \(\frac{x}{\sqrt2}\)

V = \(\pi r^2 h\) = 123.2 x 1000 = \(\frac{22}{7}\) x 28 x 28 x h = 123200 = 88 x 28h = 2464h ∴ h = \(\frac{123200}{2464}\) = 50cm N.B: 1 litre = 1 dm3 = 1000cm3

cos 30 = \(\frac{adj}{hyp}\) cross multiply: adj = cos 30 X 5 = 5 \(\frac{\sqrt3}{2}\)

If X represent the total number of students where the bus holds a right angle; 90º \(\frac{90}{360}\times X=100\)(students traveling by bus) \(X=\frac{100\times 360}{90}=400\)

\(\Delta t = \frac{gh}{c} = \frac{1260 \times 10}{4200}\) = 3.0o

Taking moment about P, 2 x d = 0.5 x (50 - 30) 2x = 10 x = 5 cm

The horizontal (eastward) component of the 10N force is = 10 cos60 → 10 x 0.5 = 5N. The equilibrant force needed to stop the body moving eastward must act in exactly the opposite direction. Therefore, the needed force is 5N in the direction of West

30^\circC + 273 = 303K 57^\circC + 273 = 330K ∆T = 330K - 303K → 27K

In optics, parabolic mirrors are used to gather light in reflecting telescopes and solar furnaces, and project a beam of light in flashlights, searchlights, stage spotlights, and car headlights.

When a solid is heated, the particles are given more energy and start to vibrate faster. At a certain temperature, the particles vibrate so much that their ordered structure breaks down. At this point the solid melts into liquid.

Zinc oxide doesn't react to hydrogen gas because the reaction is not spontaneous.

from Cr2- to CrO42- involves 8 electrons to give oxidation state of Cr is +6