Correct Answer: D. 0.299 cms\(^{-1}\)

Explanation

Area of a circle (A) = \(\pi r^2\)

Given

\(\frac{dA}{dt} = 1.5cm^2s^{-1}\)

\(\frac{dr}{dt}\) = ?

A = 2cm\(^2\)

Now

2 = \(\pi r^2\)

= r\(^2 = \frac {2}{\pi}\)

r = \(\sqrt \frac {2}{\pi}\) cm = 0.798cm

\(\frac {dr}{dt} = \frac {dA}{dt} \times \frac {dr}{dt}\)

\(\frac {dA}{dr} = 2\pi r\) (differentiating A = \(\pi r^2)\)

\(\frac {dr}{dA} = \frac {1}{2\pi r}\)

\(\frac {dr}{dt} = 1.5 \times \frac {1}{2\times \pi \times 0.798} = 1.5 \times 0.199\)

\(\frac {dr}{dt} = 0.299cms^{-1}\) (to 3 s.f)

Correct Answer: B. fantasy

Correct Answer: B. N1,360

Correct Answer: D. x = 4 and y = 1

Explanation

3x - 2y = 10 - - x 3

x + 3y = 7 ---x 2

------------------------

9x - 6y = 30

2x + 6y = 14

-------------------------

\(\frac{11x}{11} \frac{44}{11}\)

x = 4

From x + 3y = 7

3y = 7 - 4

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

y = 1

Explanation

Factors that should motivate a producer to supply more of a commodity are:

(i)Price of the commodity.The higher the price, the higher the quantity supplied

(ii)Technology: An improvement in technology which results in the reduction of .cost of production leads to an increase in the quantity of the commodity supplied

(iii) Cost of production: A decrease in the cost of production ensures that a larger quantity will be produced and supplied.

(iv) Government policy:Subsidy given to farmers, in terms of free importation of equipment will affect supply.

(v)Weather: If the weather of a particular area is favourable at a particular period, more agricultural products will be produced and their supply to the market will increase

(vi) Prices of other commodities: The supply of a commodity will be affected if the prices of other commodities rise. An increase in the price of a commodity will encourage more production of other commodities.

Correct Answer: B. timber trees do not grow in pure stands

Correct Answer: C. 40%

Correct Answer: A. 10 gm

Correct Answer: D. gross national product per head

Correct Answer: C. 14\(\sqrt{3}\)

Explanation

\(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)

= \(3\sqrt{4\times3} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)

= \(6\sqrt{3} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)

treating like a fraction, then

= \(\frac{18 + 30 - 6}{\sqrt{3}}\)

= \(\frac{42}{\sqrt{3}}\)

rationalizing

= \(14\sqrt{3}\)