Correct Answer: A. 10 units

Explanation

Intersecting Chords Theorem states that If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal.

⇒ AE * EB = CE * ED

⇒ 6 * \(x\) = 4 * (\(x\) + 5)

⇒ 6\(x\) = 4\(x\) + 20

⇒ 6\(x\) - 4\(x\) = 20

⇒ 2\(x\) = 20

∴ \(x = \frac{20}{2}\) = 10 units

Correct Answer: D. 17 units

Explanation

|MN| = \(\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

= \(\sqrt{(-3 -5)^2 + (8 - 7)^2}\)

= \(\sqrt{(-8)^2 + (8 + 7)^2}\)

= \(\sqrt{64 + (15)^2}\)

= \(\sqrt{64 + 225}\)

= \(\sqrt{289}\)

= 17 units

Correct Answer: D. √17

Correct Answer: D. \(x^{2} + y^{2} - 8x - 10y + 21 = 0\)

Explanation

On the y-intercept, x=0. At this point, y = 5(0) - 2y = -6; y = 3, so the y- intercept has coordinates (0,3).

The equation of the circle is given as \((x-a)^{2} + (y-b)^{2} = r^{2}\), where (a,b) is the centre and r is the radius.

The radius of the circle through the y- intercept = \(\sqrt{(4-0)^{2} + (5-3)^{2}} = \sqrt{20}\)

The equation of the circle is \((x-4)^{2} + (y-5)^{2} = 20\); expanding, we have

\(x^{2} + y^{2} + 8x - 10y + 21 = 0\)

Correct Answer: A. 35.75m

Explanation

\(\tan 40° = \frac{30}{|PQ|}\)

\(|PQ| = \frac{30}{\tan 40°} = \frac{30}{0.839}\)

= 35.75m

Correct Answer: B. 13

Correct Answer: D. 6

Explanation

\(y = x^{2} - 6x + 11\)

\( y = a(x - h)^{2} + k\)

\(a(x - h)^{2} + k = a(x^{2} - 2hx + h^{2}) + k\)

\(ax^{2} - 2ahx + ah^{2} + k = x^{2} - 6x + 11\)

Comparing, we have

\(a = 1\)

\(2ah = 6 \implies 2h = 6; h = 3\)

\(ah^{2} + k = 11 \implies (1 \times 3^{2}) + k = 11\)

\(9 + k = 11 \implies k = 2\)

\(\therefore a + h + k = 1 + 3 + 2 = 6\)

Explanation

(a) Area of curved surface of cylinder = \(2\pi r h\)

= \(2 \times \frac{22}{7} \times 7 \times 10cm^{2} = 440 cm^{2}\)

Area of the base of cylinder = \(\pi r^{2}\)

= \(\frac{22}{7} \times 7 \times 7 = 154 cm^{2}\)

Surface area of hemisphere = \(\frac{4\pi r^{2}}{2} = 2 \pi r^{2}\)

= \(2 \times \frac{22}{7} \times 7 \times 7 = 308 cm^{2}\)

\(\therefore\) Total surface area = 440 + 154 + 308 = 902cm\(^{2}\)

(b) Volume of cylinder = \(\pi r^{2} h\)

= \(\frac{22}{7} \times 7 \times 7 \times 10 = 1540 cm^{3}\)

Volume of hemisphere = \(\frac{1}{2}(\frac{4\pi r^{3}}{3})\)

= \(\frac{4 \times 22 \times 7 \times 7 \times 7}{2 \times 7 \times 3}\)

= \(718.67 cm^{3}\)

Total volume = 1540 + 718.67 = 2258.67 cm\(^{3}\).

Correct Answer: A. 8/19

Explanation

Probability that a student in favor is group A

= \(\frac{128}{128 + 32 + 96 + 48}\)

= \(\frac{128}{304}\)

= \(\frac{8}{19}\)

Correct Answer: B. 121