Correct Answer: B. 104.05m

Explanation

From the diagram above; Tan\(\theta = \frac{opp}{adj}\)

tan50° = \(\frac{124}{d}\)

d = \(\frac{124}{tan50}\)

therefore, d = 104.05m

Correct Answer: C. -3

Explanation

Using the remainder theorem, the remainder when a polynomial \(ax^{2} + bx + c\) is divided by \((x - a)\) is equal to \(f(a)\).

\(2x^{3} + 3x^{2} + qx - 1\) divided by \((x + 2)\), the remainder = \(f(-2)\)

\(\implies f(-2) = f(1)\)

\(f(-2) = 2(-2^{3}) + 3(-2^{2}) + q(-2) - 1 = -16 + 12 - 2q - 1 = -5 - 2q\)

\(f(1) = 2(1^{3}) + 3(1^{2}) + q(1) - 1 = 2 + 3 + q - 1 = 4 + q\)

\(4 + q = -5 -2q \implies 4 + 5 = -2q - q = -3q\)

\(q = -3\)

Correct Answer: A. \(\frac{3}{2}\) or \(1\)

Explanation

\((2t - 3s)(t - s) = 0 \implies (2t - 3s) = \text{0 or} (t - s) = 0\)

\(2t - 3s = 0 \implies 2t = 3s \therefore \frac{t}{s} = \frac{3}{2}\)

\(t - s = 0 \implies t = s \therefore \frac{t}{s} = 1\)

\(\frac{t}{s} = \frac{3}{2} or 1\)

Correct Answer: C. 4.7

Correct Answer: A. 2

Correct Answer: A. 3

Explanation

No. of times = \(\frac{\text{Total distance}}{\text{Circumference of circle}}\)

= \(\frac{\text{Total distance}}{\pi d}\)

= \(\frac{1000m}{\frac{22}{7} \times 100m}\)

= \(\frac{1000 \times 7}{2200} = 3.187\)

= 3(approx.) nearest whole no.

Correct Answer: A. #15,300

Correct Answer: A. \(\frac{-1}{2}, 8\)

Explanation

U1 = x - 4

U2 = x + 2

U3 = 3x + 1

\(\frac{u_2}{u_1} = \frac{u_3}{u_2}\)

\(\frac{x+2}{x-4} = \frac{3x+1}{x+2}\)

(x+2)(x+2) = (x-4)(3x+1)

x\(^2\) + 4x + 4 = 3x2 - 11x - 4

collecting like terms

2x\(^2\) - 15x - 8 =0

2x\(^2\) + x - 16x - 8 = 0

x(2x + 1) - 8(2x + 1) = 0

(x-8)(2x+1) = 0

x = (\(\frac{-1}{2}, 8\))

Explanation

\(y = x^{3} + 2x ... (1)\)

Let an increment in x = \(\Delta x\) and an increment in y = \(\Delta y\).

Then, \(y + \Delta y = (x + \Delta x)^{3} + 2(x + \Delta x)\)

\(y + \Delta y = x^{3} + 3x^{2} \Delta x + 3x (\Delta x)^{2} + (\Delta x)^{3} + 2x + 2 \Delta x ... (2)\)

\((2) - (1) : \Delta y = 3x^{2} \Delta x + 3x (\Delta x)^{2} + (\Delta x)^{3} + 2 \Delta x\)

\(\frac{\Delta y}{\Delta x} = 3x^{2} + 3x \Delta x + (\Delta x)^{2} + 2\)

\(\frac{\mathrm d y}{\mathrm d x} = \lim \limits_ {\Delta x \to 0} \frac{\Delta y}{\Delta x}\)

\(\frac{\mathrm d y}{\mathrm d x} = \lim \limits_{\Delta x \to 0} (3x^{2} + 3x \Delta x + (\Delta x)^{2} + 2 = 3x^{2} + 2\)

Correct Answer: A. 3