If \(\frac{2}{x - 3} - \frac{3}{x - 2}\) is equal to \(\frac{p}{(x - 3)(x - 2)}\), find p
-x - 5
-(x + 3)
5x - 13
5 - x
Correct answer is D
\(\frac{2}{x - 3} - \frac{3}{x - 2}\) = \(\frac{p}{(x - 3)(x - 2)}\)
\(\frac{2(x - 2) - 3(x - 3)}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\)
= \(\frac{2x - 4 - 3x + 9}{(x - 3)(x - 2)}\) = \(\frac{p}{(x - 3)(x - 2)}\)
\(\frac{-x + 5}{(x - 3)(x - 2)} = \frac{p}{(x - 3)(x - 2)}\)
p(x - 3)(x - 2) = -x + 5(x - 3)(x - 2)
p = -x + 5 or p = 5 - x
Simplify \(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}\)
16
8
4
1
Correct answer is C
\(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}\)
= \(\frac{\sqrt{2^{3(2)} \times 2^{2(n + 1)}}}{2^{2n} \times 2^4}\)
= \(\frac{\sqrt{2^6 \times 2^{2n + 2)}}}{2^{2n} + 4}\)
= \(\frac{\sqrt{2^6 + 2^{2n + 2)}}}{2^{2n} + 4}\)
= \(\frac{\sqrt{2^{2n + 8}}}{2^{2n} + 4}\)
= \(\sqrt{2^{2n + 8} \div 2^{2n} + 4}\)
= \(\sqrt{2^{2n - 2n} + 8 - 4}\)
= \(\sqrt{2^4}\)
= \(\sqrt{16}\)
= 4
Approximate 0.0033780 to 3 significant figures
338
0.338
0.00338
0.003
Correct answer is C
No explanation has been provided for this answer.
Given that cos x = \(\frac{12}{13}\), evaluate \(\frac{1 - \tan x}{\tan x}\)
\(\frac{5}{13}\)
\(\frac{5}{7}\)
\(\frac{7}{5}\)
\(\frac{13}{5}\)
Correct answer is C
cos x\(\frac{12}{13}\)
132 = 122 + a2
169 = 144 + a2
a2 = 169 - 144
a2 = 25
a \(\sqrt{25}\)
a = 5
tan x = \(\frac{5}{12}\)
\(\frac{1 - \tan x}{\tan x} = \frac{1 - \frac{5}{12}}{\frac{5}{12}}\)
\(\frac{\frac{1 - \frac{5}{12}}{12 - 5}}{12} = \frac{\frac{7}{12}}{\frac{5}{12}}\)
= \(\frac{7}{2} \div \frac{5}{12}\)
= \(\frac{7}{12} \times \frac{12}{5} = \frac{7}{5}\)
If x : y = 3 : 2 and y : z = 5 : 4, find the value of x in the ratio x : y : z
8
10
15
20
Correct answer is C
No explanation has been provided for this answer.