
Mark a line segment OB = 9.3 on number line. Further, take BC of 1 unit.
Find the midpoint D of OC and draw a semi - circle on OC while taking D as its centre.
Draw a perpendicular to line OC passing through point B. Let it intersect the semi - circle at E.
Taking B as centre and BE as radius, draw an arc intersecting number line at F.
Hence BF is \(\sqrt9.3\).
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 _____.
Classify the following numbers as rational or irrational:
(i) \(2 - \sqrt5\)
(ii) \((3 + \sqrt23) - \sqrt23\)
(iii) \(\frac{2 \sqrt{7}} { 7 \sqrt7}\)
(iv) \(\frac{1}{\sqrt{2}}\)
(v) 2π
Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
(i) 2x + 3y = 9.35
(ii) x – \(\frac{y}{5}\)– 10 = 0
(iii) –2x + 3y = 6
(iv) x = 3y
(v) 2x = –5y
(vi) 3x + 2 = 0
(vii) y – 2 = 0
Which one of the following options is true, and why? y = 3x + 5 has
(i) a unique solution,
(ii) only two solutions,
(iii) infinitely many solutions