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Solve the inequalities for which \(\frac{x+4}{3}-\frac{x-3}{2} < 4\)
A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)
If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?
A binary operation \(\oplus\) defined on the set of real number is such that x\(\oplus\)y = xy/6 for all x, y ∈ R. Find the inverse of 20 under this operation when the identity element is 6
The solution set of the shaded area above is
If the locus of the points which are equidistant from point P and Q meets line PQ at point N, then PN equals
What is the locus of points equidistant from the lines ax + by + c = 0?
In the diagram above, POQ is a diameter of the circle PQRS. If ∠PSR = 145°, find x°
In triangle XYZ, ∠XYZ = 15o, ∠XZY = 45o and lXYl = 7 cm. Find lYZl.
PQ and RS are two parallel lines. If the coordinates of P, Q, R, S are (1,q), (3,2), (3,4), (5,2q) respectively, find the value of q
In the diagram above, QR is the diameter of the semicircle QR. Find the area of the figure to the nearest whole number. [\(\pi = \frac{22}{7}\)]
Convert 2232\(_4\) to base six
Simplify \((25)^{\frac{-1}{2}} \times (27)^{\frac{1}{3}} + (121)^{\frac{-1}{2}} \times (625)^{\frac{-1}{4}}\)
Evaluate \(\frac{2}{6-5\sqrt{3}}\)