Simplify 52.4 – 5.7 – 3.45 – 1.75

Evaluate $\frac{0.21\times 0.72\times 0.00054}{0.006\times 1.68\times 0.063}$ correct to four significant figures. 

If $\frac{dy}{dx}=2x-3$and y = 3 when x = 0. Find y in terms of x

The slope of the tangent to the curve $y=3{{x}^{2}}-2x+5$at the point (1,6) is

A circle with radius 5cm has its radius increasing at the rate of 0.2cms^-1. What will be the corresponding increase in the area?

Use the graph above to find the value if $px+qy\le 4$

The time taken to a piece of work is inversely proportional to the number of men employed. If it takes 45 men to do a piece of work in 5 days, how long will it take 25 men?

Find the range of values of x for which $\frac{x+2}{4}-\frac{2x-3}{3}<4$

If the 9^th term of an AP is fives times the 5^th term, find the relationship between a and d

The inverse of the function $f(x)=3x+4$ is

The binary operation $*$ is defined on the set of integers p and q by $p*q=pq+p+q,$find $2*(3*4)$

The sum to infinity of the series $1+\tfrac{1}{3}+\tfrac{1}{9}+\tfrac{1}{27}+---$ is

In the diagram above, PST is a straight line $PQ=QS=RS$, if $\angle RST={{72}^{\circ }}$, find x 

Find the equation of the set of points which are equidistant from the parallel line x =1 and x = 7

If $\tan \theta =\tfrac{4}{3}$, calculate ${{\sin }^{2}}\theta -{{\cos }^{2}}\theta $

A bucket is 12cm in diameter at the top, 8cm in diameter at the bottom and 4cm deep. Calculate its volume.

The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?

A hunter 1.6m tall views a bird on top of a tree at an angle of 45^o. If the distance between the hunter and the tree is 10.4m. Find the height of the tree.

Find the value of $\alpha $if the line $2y-\alpha x+4=0$is perpendicular to the line $y+\tfrac{1}{4}x-7=0$