Make x the subject of the relation \(\frac{1 + ax}{1 - ax}\) = \(\frac{p}{q}\)
\(\frac{p + q}{a(p - q)}\)
\(\frac{p - q}{a(p + q)}\)
\(\frac{p - q}{apq}\)
\(\frac{pq}{a(p - q)}\)
Correct answer is B
\(\frac{1 + ax}{1 - ax}\) = \(\frac{p}{q}\) by cross multiplication,
q(1 + ax) = p(1 - ax)
q + qax = p - pax
qax + pax = p - q
∴ x = \(\frac{p - q}{a(p + q)}\)
If \(\sqrt{x^2 + 9}\) = x + 1, solve for x
5
4
3
2
1
Correct answer is B
\(\sqrt{x^2 + 9}\) = x + 1
x2 + 9 = (x + 1)2 + 1
0 = x2 + 2x + 1 - x2 - 9
= 2x - 8 = 0
2(x - 4) = 0
x = 4
If N225.00 yields N27.00 in x years simple interest at the rate of 4% per annum, find x
3
4
12
17
Correct answer is A
Principal = N255.00, Interest = 27.00
year = x Rate: 4%
∴ 1 = \(\frac{PRT}{100}\)
27 = \(\frac{225 \times 4 \times T}{100}\)
2700 = 900T
T = 3 years
Solve without using tables log5(62.5) - log5(\(\frac{1}{2}\))
3
4
5
8
Correct answer is A
log5(62.5) - log5(\(\frac{1}{2}\))
= log5\(\frac{(62.5)}{\frac{1}{2}}\) - log5(2 x 62.5)
= log5(125)
= log553 - 3log55
= 3
If 2log3 y + log3 x2 = 4, then y is
4 - log3
\(\frac{4}{log_3 x}\)
\(\frac{4}{x}\)
\(\pm\) \(\frac{9}{x}\)
Correct answer is D
2log3y + log3x2 = 4
log3y2 + log3x2 = 4
∴ log3 (x2y2) = log381(correct all to base 4)
x2y2 = 81
∴ xy = \(\pm\)9
∴ y = \(\pm\)\(\frac{9}{x}\)