Simplify ( \(\frac{1}{2 - √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)
\(\frac{-1}{33}\)(6 + √3)
\(\frac{-1}{33}\)(6 - √3)
\(\frac{1}{33}\)(6 + √3)
\(\frac{1}{33}\)(6 - √3)
Correct answer is C
( \(\frac{1}{2 - √3}\) + \(\frac{2}{2 + √3}\) )\(^{-1}\)
= \(\frac{2 + √3 + 2(2 - √3)}{(2 - √3)(2 + √3)}\)
= 2 + √3 + 4 - 2√3
= (6 - √3)\(^{-1}\)
= \(\frac{1}{6 - √3}\)
= \(\frac{6 + √3}{6 - √3 * 6 + √3}\)
= \(\frac{6 + √3}{33}\)
x: Birds fly
y: The sky is blue
Which of the following statements can be represented as x \(\to\) y?
When birds fly, the sky is blue
Birds fly if and only if the sky is blue?
Either the bird is flying or the sky is blue.
When the sky is blue, the bird flies.
Correct answer is B
No explanation has been provided for this answer.
If log 5(\(\frac{125x^3}{\sqrt[ 3 ] {y}}\) is expressed in the values of p, q and k respectively
3, \(\frac{-1}{3}\), 5
\(\frac{-1}{3}\), 3, 5
3, \(\frac{-1}{3}\), 3
3, \(\frac{-1}{3}\), 3
Correct answer is D
log\(_5\) (\(\frac{125x^3}{\sqrt[3] {y}}\))
= \(\log_5 125 x^3 - \log _1 x^3 - log_5 y\frac{1}{3}\)
= \(3 log_5 5 + 3 log_5 x - \frac{1}{3} log _5 y\)
= 3, - \(\frac{1}{3}\), 3
If the sum of the roots of 2x\(^2\) + 5mx + n = 0 is 5, find the value of m
-2.5
-2.0
2.0
2.5
Correct answer is B
Sum of roots = \(\frac{-a}{b}\)
= \(\frac{-5m}{2}\) = 5
\(\frac{-5m}{m} = \frac{10}{-5}\)
m = -2
\(\frac{1}{5}\)(-3i - 4j)
\(\frac{1}{5}\)(-3i + 4j)
\(\frac{1}{5}\)(3i - 4j)
\(\frac{1}{5}\)(3i + 4j)
Correct answer is C
Resultant
(- 2i - 3j) + (5i - j)
= 3i - 4j
Unit vector
= \(\frac{3i - 4j}{|3i - 4j|} = \frac{3i - 4j}{\sqrt{3i } + (-4)}\)
= \(\frac{3i - 4j}{\sqrt{25}}\)
= \(\frac{3i - 4j}{5}\)
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