Make 'n' the subject of the formula if w = \(\frac{v(2 + cn)}{1 - cn}\)
\(\frac{1}{c}(\frac{w - 2v}{v + w})\)
\(\frac{1}{c}(\frac{w - 2v}{v - w})\)
\(\frac{1}{c}(\frac{w + 2v}{v - w})\)
\(\frac{1}{c}(\frac{w + 2v}{v + w})\)
Correct answer is A
w = \(\frac{v(2 + cn)}{1 - cn}\)
2v + cnv = w(1 - cn)
2v + cnv = w - cnw
2v - w = -cnv - cnw
Multiply through by negative sign
-2v + w = cnv + cnw
-2v + w = n(cv + cw)
n = \(\frac{-2v + w}{cv + cw}\)
n = \(\frac{1}{c}\frac{-2v + w}{v + w}\)
Re-arrange...
n = \(\frac{1}{c}\frac{w - 2v}{v + w}\)
1
2
3
4
Correct answer is A
n(f \(\cap\) v) + n(f) + n(v) + n(f \(\cap\) v) = 46
3 + 19 + 23 + x = 46
22 + 23 + x = 46
45 + x = 46
x = 46 - 45
x = 1
{3}
{2,3}
{2,3,5}
{1,2}
Correct answer is B
P = {2,3,5}
Q = {2,3,6,9}
P \(\cap\) Q = {2,3}
Simplify \((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)
\(2\sqrt{6}\)
\(4\sqrt{6}\)
\(8\sqrt{6}\)
\(16\sqrt{6}\)
Correct answer is C
\((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)
= \([(\sqrt{6} + 2) + (\sqrt{6} - 2)][(\sqrt{6} + 2) - (\sqrt{6} - 2)]\)
= \((\sqrt{6} + 2 + \sqrt{6} - 2)(\sqrt{6} + 2 - \sqrt{6} + 2)]\)
= \((2\sqrt{6})(4)\)
= \(8\sqrt{6}\)
\(\frac{1}{3}\)
\(\frac{1}{9}\)
\(\frac{1}{27}\)
\(\frac{1}{81}\)
Correct answer is D
log3x2 = -8
x2 = 3-8
x = \(3^{-8 \times \frac{1}{2}}\)
x = 3-4
x = \(\frac{1}{3^4}\)
x = \(\frac{1}{81}\)