Rationalise the denominators of the following:
(i) \(\frac{1 }{ \sqrt{7 }}\)
(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)
(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)
(iv) \(\frac{1 }{ \sqrt{7}-2}\)
(i) \(\frac{1 }{ \sqrt{7 }}\) =\(\frac{1}{\sqrt7}=\frac{1}{\sqrt7} ×\frac{ √7 }{√7}\)
= \(\frac{ √7 }{√7}\)
(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)
\(= \frac{1}{ (√7 + √6)} ×\frac{(√7 - √6)}{(√7 + √6)}\)
= \(\frac{(√7 - √6)}{7 - 6}=\sqrt7+\sqrt6\)
(iii) \(\frac{1 }{ \sqrt{7}-2}\)
\(\frac{\sqrt5+\sqrt2}{3}\)
(iv) \(\frac{1 }{ \sqrt{7}-2}\)
\(=\frac{\sqrt7+2}{7-2}=\frac{\sqrt7+2}{3}\)
For real number a, b (a > b > 0), let
\(\text{{Area}} \left\{ (x, y) : x^2 + y^2 \leq a^2 \text{{ and }} \frac{x^2}{a^2} + \frac{y^2}{b^2} \geq 1 \right\} = 30\pi\)
and
\(\text{{Area}} \left\{ (x, y) : x^2 + y^2 \geq b^2 \text{{ and }} \frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1 \right\} = 18\pi\)
Then the value of (a – b)2 is equal to _____.
A driver of a car travelling at \(52\) \(km \;h^{–1}\) applies the brakes Shade the area on the graph that represents the distance travelled by the car during the period.
Which part of the graph represents uniform motion of the car?