If \(T = 2\pi \sqrt{\frac{l}{g}}\), make g the subject of the formula
(4π l2) / T
(4π2l) / T2
(4π2l2) / T2
(2π√l) / T
Correct answer is B
\(T = 2\pi \sqrt{\frac{l}{g}}\)
\(\frac{T}{2\pi} = \sqrt{\frac{l}{g}}\)
\((\frac{T}{2\pi})^{2} = \frac{l}{g}\)
\(\therefore g = \frac{4 \pi^{2} l}{T^{2}}\)
The sum of the first n positive integers is
1/2 n(n-1)
n(n+1)
n(n-1)
1/2 n(n+1)
Correct answer is D
Let the positive integers be 1, 2, ,3, 4, .....n
∴ a = 1, d = 1 and n = n
Sn = n/2(2a + (n-1)d)
= n/2 (2 + n – 1)
= 1/2n(n + 1)
The cost of renovating a 6 m square room is N540. What is the cost of renovating a 9 m square room?
N1215
N720
N1620
N810
Correct answer is D
Cost of removing a 6m\(^2\) room = N540
Cost of renovating a 1m\(^2\) room = 540 / 6
Cost of removing a 9m\(^2\) room
= (540 / 6) * 9
= N810
Solve the inequalities for which \(\frac{x+4}{3}-\frac{x-3}{2} < 4\)
x < 7
x > -7
x < -7
x > 7
Correct answer is B
\(\frac{x+4}{3}-\frac{x-3}{2} < 4\\
\frac{(2(x+4))-(3(x-3))}{6}<4\)
2(x+4) – 3(x-3) < 4 x 6
2x + 8 – 3x+9 < 24
-x + 17 < 24
-x < 24 – 17
-x < 7
x > -7
10
8
-10
-8
Correct answer is C
F(x) = Q x D + R
Kx3 + x2 - 5x – 2 = Q(2x+1)+R
If 2x+1 = 0 implies x = -1/2
∴k(-1/2)3 + (-1/2)2 -5(-1/2) -2
= Q(2(-1/2) + 1) +2
K(-1/8) + 1/4 + 5/2 - 2 = Q(-1+1)+2
-k/8 + 1/4 + 5/2 - 2 = 0+2
(-k+2+20-16) / 8 = 2
(-k+6) / 8 = 2
-k+6 = 2*8
-k+6 = 16
-k = 16-6
-k = 10
∴k = -10