JAMB Mathematics Past Questions & Answers - Page 15

No explanation has been provided for this answer.

Let T be the time taken and D is the distance

For the case given in the problem, the distance covered is directly proportional to the time taken i.e D α T

⇒ D = ST where S is the constant speed

D = 225 km and T = 4.5 hrs

∴ 225 = S x 4.5

S = \(\frac {225}{4.5}\) = 50km/hr

When D = 150km

D = ST

150 = 50 \(\times\) T

T = \(\frac {150}{50}\) = 3 hrs

So it will take 3 hrs

From ∆PSR

|PS| = |SR| (If two tangents are drawn from an external point of the circle, then they are of equal lengths)

∴ ∆PSR is isosceles

∠PSR + ∠SRP + ∠SPR = 180\(^o\) (sum of angles in a triangle)

Since |PS| = |SR|; ∠SRP = ∠SPR

⇒ ∠PSR + ∠SRP + ∠SRP = 180\(^o\)

∠PSR + 2∠SRP = 180\(^o\)

36\(^o\) + 2∠SRP = 180\(^o\)

2∠SRP = 180\(^o\) - 36\(^o\)

2∠SRP = 144\(^o\)

∠SRP = \(\frac {144^o}{2} = 72^0\)

∠SRP = ∠PQR (angle formed by a tangent and chord is equal to the angle in the alternate segment)

∴ ∠PQR = 72\(^0\)

3(x – 1) ≤ 2 (x – 3)

= 3x – 3 ≤ 2x – 6

Add 3 to both sides

= 3x – 3+ 3 ≤ 2x – 6+ 3

= 3x ≤ 2x – 3

Subtract 2x from both the sides

= 3x – 2x ≤ 2x – 3 – 2x

∴ x ≤ -3

y = \(\frac {3x - 9c}{4x + 5d}\)

\(\frac {y}{1} = \frac {3x - 9c}{4x + 5d}\)

= y(4x + 5d) = 3x - 9c

= 4xy + 5dy = 3x - 9c

= 4xy - 3x = -9c - 5dy

= (4y - 3)x = -9c - 5dy

= x = \(\frac {-9c - 5dy}{4y - 3}\)

x = \(\frac {-(9c + 5dy)}{4y - 3}\)