Evaluate 1 − (\(\frac{1}{5}\) x 1\(\frac{2}{3}\)) + (5 + 1\(\frac{2}{3}\))
4
3
\(\frac{22}{3}\)
3\(\frac{2}{3}\)
Correct answer is C
1 − (\(\frac{1}{5}\) x 1\(\frac{2}{3}\)) + (5 + 1\(\frac{2}{3}\))
1 − (\(\frac{1}{5}\) x \(\frac{5}{3}\)) + (5 + \(\frac{5}{3}\))
1 − \(\frac{1}{3}\) + \(\frac{20}{3}\)
= \(\frac{22}{3}\)
Find the range of the following set of numbers 0.4, −0.4, 0.3, 0.47, −0.53, 0.2 and −0.2
1.03
0.07
0.03
1.0
Correct answer is D
0.4, −0.4, 0.3, 0.47, −0.53, 0.2, −0.2 Range is the difference between the highest and lowest value i.e Highest − Lowest − 0.53, −0.4, −0.2, 0.2, 0.3, 0.4, 0.47 0.47 is the highest − 0.53 is the lowest ∴ = 0.47 − (− 0.53) ∴0.47 + 0.53 = 1.0
If α and β are the roots of the equation 3x2 + 5x - 2 = 0, find the value of 1/α + 1/β
\(\frac{-5}{3}\)
\(\frac{-2}{3}\)
\(\frac{1}{2}\)
\(\frac{5}{2}\)
Correct answer is D
1/α + 1/β = β+α/αβ
3x2 + 5x - 2 = 0
x2 + 5x/3 - 2/3 = 0
αβ = -2/3
β+α = -5/3
Thus; β+α/αβ = -2/3 -2/3 = -5/2
1, − 2
− 2, n = 1
\(\frac{-2}{5}\), 1
\(\frac{2}{3}\)
Correct answer is B
\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\)= m + n√6
\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\) x \(\frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - \sqrt{2}}\)
\(\frac{2 \sqrt{3} (\sqrt{3} - 2 \sqrt{2}) - \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}{\sqrt{3}(\sqrt{3} - 2 \sqrt{2}) + 2 \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}\)
\(\frac{2 \times 3 - 4\sqrt{6} - 6 + 2 \times 2}{3 - 2 \sqrt{6} + 2 \sqrt{6} - 4 \times 2}\)
= \(\frac{6 - 4 \sqrt{6} - \sqrt{6} + 4}{3 - 8}\)
= \(\frac{0 - 4 \sqrt{6} - 6}{5}\)
= \(\frac{10 - 5 \sqrt{6}}{5}\)
= − 2 + √6
∴ m + n\(\sqrt{6}\) = − 2 + √6
m = − 2, n = 1
4a
\(\frac{1}{8a}\)
8a
\(\frac{1}{4a}\)
Correct answer is D
(3√64a3)\(^{-1}\)
\(\frac{1}{(3√64a^3)
= \(\frac{1}{4a}\)