In this section you will find it useful to draw a set of coordinate axes and update your diagram as information becomes available. i) Find the equation of the line l which passes through <(−3,1) and =(0,5). ii) Find the distance from the point ?(2,1) to the line l .
iii) Hence, or otherwise, verify that the line l is a tangent to the circle x2+y2-4x-2y-11=0
iv) Show that the equation of the line through C which is parallel to l is given by 4x-3y-5=0
v) Hence, or otherwise, write down the equation of k, the other tangent to the circle which is parallel to L. vi) Write down the equations of the two horizontal lines, m and n, which are tangents to this circle. vii) Find the area of the parallelogram defined by the lines k, l, m and n.
A particle starts from rest at O and moves along the x axis so that its acceleration after t secs is (24t − 12t2) m/sec. i) Find when the particle again returns to O and its velocity at that time. ii) What is the farthest that the particle travels from O during this interval.
In the diagram, AC=6cm, BC-7cm and ∠ACB=30° Find the length of AB correct to the nearest centimeter.
In the diagram, BC=BC, ref lex∠ABC=220°, ∠BCD=40°. Prove that AB∥EC.
The diagram shows the points A(-4,0) , C(313 ,-8 ) and D(913 ,0) If ABCD is a parallelogram, what are the coordinates of B? Find the equation of CD in general form. Show that the exact perpendicular distance of A from CD is 1023 units. Prove ∆AOE and ∆AFD are similar. Hence, or otherwise, find AE.
The diagram shows the parts of the graphs y=x2+1 and y=9-x2 in the positive quadrant. Show that the co-ordinates of the point P are (2, 5) Copy the diagram into your examination booklet and shade the region represented by the inequalities: x≥0, y≥0, y≤x2+1, and y≤9-x2 Calculate the area of this shaded region
For the graph above: Is the following statement correct for the function shown? Explain why or why not. ∫0.2cf(x)dx =∫0.2bf(x)dx +∫bcf(x)dx Find the values of the pronumerals a, b and c.
The diagram shows a field which is bounded by a river, a highway and two fences. Use Simpson’s rule with 5 function values to approximate the area of the field.
A mould for a vase is formed by rotating that part of the curve y= logex between y=0 and y=2 about the y-axis. Find the volume of the mould. Leave your answer in simplest exact form.
Below is the graph of y=f(x) which has a horizontal point of inflection at A and a minimum turning point at B. Copy this diagram onto your answer sheet and sketch the graph of its derivative on the same axes.
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