Find the remainder when X3 - 2X2 + 3X - 3 is divided by X2 + 1
2X - 1
X + 3
2X + 1
X - 3
Correct answer is A
X2 + 1 \(\frac{X - 2}{\sqrt{X^3 - 2X^2 + 3n - 3}}\)
= \(\frac {- 6X^3 + n}{-2X^2 + 2X - 3}\)
= \(\frac{(-2X^2 - 2)}{2X - 1}\)
Remainder is 2X - 1
Make R the subject of the formula if T = \(\frac {KR^2 + M}{3}\)
\(\sqrt\frac{3T - K}{M}\)
\(\sqrt\frac{3T - M}{K}\)
\(\sqrt\frac{3T + K}{M}\)
\(\sqrt\frac{3T - K}{M}\)
Correct answer is B
T = \(\frac{KR^2 + M}{3}\)
3T = KR2 + M
KR2 = 3T - M
R2 = \(\frac{3T - M}{K}\)
R = \(\sqrt\frac{3T - M}{K}\)
49
170
21
210
Correct answer is D
The first poster has 7 ways to be arranges, the second poster can be arranged in 6 ways and the third poster in 5 ways.
= 7 x 6 x 5
= 210 ways
or \(\frac{7}{P_3}\) = \(\frac{7!}{(7 - 3)!}\) = \(\frac{7!}{4!}\)
= \(\frac{7 \times 6 \times 5 \times 4!}{4!}\)
= 210 ways
Simplify (\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
\(\frac{7}{3}\)
\(\frac{5}{3}\)
\(\frac{5}{2}\)
\(\frac{3}{2}\)
Correct answer is B
(\(\sqrt2 + \frac{1}{\sqrt3})(\sqrt2 - \frac{1}{\sqrt3}\))
\(\sqrt4 - \frac {\sqrt2}{\sqrt3} + \frac {\sqrt2}{\sqrt3} - \frac {1}{\sqrt9}\)
= 2 - \(\frac {1}{3}\)
= \(\frac {16 - 1}{3}\)
= \(\frac{5}{3}\)
Rationalize \(\frac{2 - \sqrt5}{3 - \sqrt5}\)
\(\frac{1 - \sqrt5}{2}\)
\(\frac{1 - \sqrt5}{4}\)
\(\frac{ \sqrt5 - 1}{2}\)
\(\frac{1 + \sqrt5}{4}\)
Correct answer is B
\(\frac{2 - \sqrt5}{3 - \sqrt5}\) x \(\frac{3 + \sqrt5}{3 + \sqrt5}\)
\(\frac{(2 - \sqrt5)(3 + \sqrt5)}{(3 - \sqrt5)(3 + \sqrt5)}\) = \(\frac{6 +2\sqrt5 - 3\sqrt5 - \sqrt25}{9 + 3\sqrt5 - 3\sqrt5 - \sqrt25}\)
= \(\frac{6 - \sqrt5 - 5}{9 - 5}\)
= \(\frac{1 - \sqrt5}{4}\)