Correct Answer: B. 5cm

Correct Answer: C. T =R - \(\frac{15P^3}{Q}\)

Correct Answer: A. x = 5[(s − 2) ÷ t] - 3/5y

Correct Answer: C. \(-\frac{\sqrt{2}}{2}\)

Correct Answer: C. p=10, q=- 7

Explanation

If the body is in equilibrium then

F + R = N

3i - 12j + 7i + 5j = pi + qj

10i - 7j = pi + qj

p = 10, q = -7

Explanation

(a)

In the diagram above, \(\theta = y\) (vertically opposite angles)

\(\alpha = 180° - 110° = 70°\) (angles on a straight line)

Thus, \(\beta = \theta + \alpha\) (sum of interior opp. angles)

\(\beta = y + 70° ..... (1)\)

\(x + r + \beta = 180° ..... (2)\)

But 2x = r = y

Hence, \(x + 2x + (2x + 70) = 5x + 70 = 180\)

\(5x = 180 - 70 = 110\)

\(x = 22°\)

(b) Let Nx represent the donation collected by the girls. Then, the donation collected by the boys = N(x + 600).

Also, let y represent the average collection, \(x_{g}\), of the girls. Then the average collection, \(x_{b}\), of the boys = N(y + 100).

Thus, \(x_{g} = \frac{x}{12} = y\)

\(x = 12y ... (1)\)

\(x_{b} = \frac{x + 600}{10} = y + 100\)

\(x + 600 = 10(y + 100) .... (2)\)

Substitute 12y for x in (2) :

\(12y + 600 = 10y + 1000\)

\(12y - 10y = 1000 - 600 \)

\(2y = 400 \implies y = 200\)

From (1), \(x = 12y\)

\(\therefore x = 12 \times 200 = N2,400\).

Thus, the girls collected N2,400

The boys collected N2,400 + N600 = N3000

Total = N(2,400 + 3,000) = N5,400

(a)

In the diagram above, \(\theta = y\) (vertically opposite angles)

\(\alpha = 180° - 110° = 70°\) (angles on a straight line)

Thus, \(\beta = \theta + \alpha\) (sum of interior opp. angles)

\(\beta = y + 70° ..... (1)\)

\(x + r + \beta = 180° ..... (2)\)

But 2x = r = y

Hence, \(x + 2x + (2x + 70) = 5x + 70 = 180\)

\(5x = 180 - 70 = 110\)

\(x = 22°\)

(b) Let Nx represent the donation collected by the girls. Then, the donation collected by the boys = N(x + 600).

Also, let y represent the average collection, \(x_{g}\), of the girls. Then the average collection, \(x_{b}\), of the boys = N(y + 100).

Thus, \(x_{g} = \frac{x}{12} = y\)

\(x = 12y ... (1)\)

\(x_{b} = \frac{x + 600}{10} = y + 100\)

\(x + 600 = 10(y + 100) .... (2)\)

Substitute 12y for x in (2) :

\(12y + 600 = 10y + 1000\)

\(12y - 10y = 1000 - 600 \)

\(2y = 400 \implies y = 200\)

From (1), \(x = 12y\)

\(\therefore x = 12 \times 200 = N2,400\).

Thus, the girls collected N2,400

The boys collected N2,400 + N600 = N3000

Total = N(2,400 + 3,000) = N5,400

Correct Answer: A. 4

Correct Answer: A. 10

Explanation

\((x + \frac{2}{x^2})^5\)

n = 5, r = 4, p = x and q = \(\frac{2}{x^2}\)

5C\(_4\)x\(^4\) (\(\frac{2}{x^2}\))1 = 5C\(_4\) \(\frac{2x^4}{x^2}\)

5C\(_4\) 2x\(^2\) = \(\frac{5!}{[5-4]!4!}\) * 2x\(^2\)

\(\frac{5*4!}{4!} * 2x^2\) = 5 * 2x\(^2\) = 10x\(^2\)

The coefficient is 10.

Correct Answer: A. x ≤ 0, y ≤ 0, 2y + 3x ≤ 6

Correct Answer: B. 11