If S = \(\sqrt{t^2 - 4t + 4}\), find t in terms of S
S2 - 2
S + 2
S - 2
S2 + 2
Correct answer is B
S = \(\sqrt{t^2 - 4t + 4}\)
S2 = t2 - 4t + 4
t2 - 4t + 4 - S2 = 0
Using \(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Substituting, we have;
Using \(t = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(4 - S^2)}}{2(1)}\)
\(t = \frac{4 \pm \sqrt{16 - 4(4 - S^2)}}{2}\)
\(t = \frac{4 \pm \sqrt{16 - 16 + 4S^2}}{2}\)
\(t = \frac{4 \pm \sqrt{4S^2}}{2}\)
\(t = \frac{2(2 \pm S)}{2}\)
Hence t = 2 + S or t = 2 - S
{3,5,7,11,17,19}
{3,5,11,13,17,19}
{3,5,7,11,13,17,19}
{2,3,5,7,11,13,17,19}
Correct answer is C
P = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
Q = {-1, 3, 5, 7, 11, 13, 17, 19, 23}
P \(\cap\) Q = {3, 5, 7, 11, 13, 17, 19}
Simplify \(\frac{\sqrt{5}(\sqrt{147} - \sqrt{12}}{\sqrt{15}}\)
5
\(\frac{1}{5}\)
\(\frac{1}{9}\)
9
Correct answer is A
\(\frac{\sqrt{5}(\sqrt{147} - \sqrt{12}}{\sqrt{15}}\)
\(\frac{\sqrt{5}(\sqrt{49 \times 3} - \sqrt{4 \times 3}}{\sqrt{5 \times 3}}\)
\(\frac{\sqrt{5}(7\sqrt{3} - 2\sqrt{3}}{\sqrt{5} \times \sqrt{3}}\)
\(\frac{\sqrt{3} (7 - 2}{\sqrt{3}}\)
= 5
If log104 = 0.6021, evaluate log1041/3
0.3011
0.9021
1.8063
0.2007
Correct answer is D
log1041/3 = 1/3 log104
= 1/3 x 0.6021
= 0.2007
Simplify \(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
32
33
35
3
Correct answer is D
\(\frac{3^{-5n}}{9^{1-n}} \times 27^{n + 1}\)
\(\frac{3^{-5n}}{3^{2(1-n)}} \times 3^{3(n + 1)}\)
\(3^{-5n} \div 3^{2(1-n)} \times 3^{3(n + 1)}\)
\(3^{-5n - 2(1-n) + 3(n + 1)}\)
\(3^{-5n - 2 + 2n + 3n + 3}\)
\(3^{-5n + 5n + 3 - 2}\)
\(3^{1}\)
= 3