PURE MATHEMATICS (a) The radius of a spherical balloon is increasing at the rate of 3 cms'. Find the rate of increase in the surface area of the balloon when the radius is 10 cm.
PURE MATHEMATICS (a) The radius of a spherical balloon is increasing at the rate of 3 cms'. Find the rate of increase in the surface area of the balloon when the radius is 10 cm.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:PURE MATHEMATICS
(a) The radius of a spherical balloon is increasing at the rate of 3 cms'. Find the rate of increase
in the surface area of the balloon when the radius is 10 cm.
(b) A function fis defined on the set R of real numbers byf:x pxr +qx +2, wherep and q
are constants. If /(-2) = 10 and f (1) 13, find:
(i) the values of p and q;
(ii) f(-3).
(a) If (x +3), (2r-3) and (x+5) are the first three consecutive terms of an Arithmetic Progression
(A.P.), find the :
(i) value of x;
(ii) common difference;
(iii) first term;
(iv) sum of the first ten terms.
5
de
(3x- 2)*
(b) Evaluate |
21x-7
Express
in partial fractions.
(x-2)(x+3)(x+x+1)
PART II
STATISTICS AND PROBABILITY
- The lengths of some pieces of sticks were measured and recorded as shown in the table.
Length of
wood(x cm)
14
15
26
29
40
47
50
56
60
Number of
pieces (y)
10
14
8
15
21
14
13 19
(a) (i) Represent this information in a scatter diagram.
(ii) Find i andy , the means of x and y respectively.
(iii) Plot the point ( .), on your diagram.
(iv) Draw an approximate line of best fit to pass through(, y) and (18, 9).
(b) Using the graph, find the equation of the line of best fit.
4012/20/fad/wpS2ng
7
4,
Transcribed Image Text:Calculate the area of the shaded region below, given that AC is an are of a circle centre
B. AB=BC=14cm CD=8cm and angle ABD = 75°
14 cm
750
14 cm
8 cm
The scale of a map is 1:50000. A lake on the map is 6.16cm. find the actual area of the
lake in hactares.
The figure below is a rhombus ABCD of sides 4cm. BD is an arc of circle centre C.
Given that ZABC = 138°, Find the area of shaded region.
3.
4cm
4.
The figure below sows the shape of Kamau's farm with dimensions shown in meters
140m
100m
20 m
80m
Find the area of Kamau's farm in hectares
In the figure below AB and AC are tangents to the circle centre 0 at B and C respectively.
the angle AOC = 6o
5.
1.
2.
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