64. The area bounded by the curve y = 3 + 2x – x² and the line y = 3 is rotated completely about the line y = 3. Find the volume of the solid of revolution obtained.
64. The area bounded by the curve y = 3 + 2x – x² and the line y = 3 is rotated completely about the line y = 3. Find the volume of the solid of revolution obtained.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.6: Permutations
Problem 47E
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Question
Solve Q64 explaining detailly each step
Transcribed Image Text:62. The table below shows corresponding values of x and y which approximately satisfy a
relation of the form. y = ax"
X
2
3
4
6.
7
50
250
775
1875
390
7200
Where a and n are constants. By drawing a suitable linear graph, determine the values of a
and n, correct to one decimal place.
1+x
63. Sketch the graph of
showing clearly the asymptotes and the points where the curve meets
1-x
the coordinates axes.
64. The area bounded by the curve y = 3 + 2x – x and the line y= 3 is rotated completely about
the line y = 3. Find the volume of the solid of revolution obtained.
%3D
65. Express
in partial fractions. Hence, or otherwise, solve the differential equation
(1+x)(1+3x)
dy
2(y+2)
given that y = -1 when x = 0.
dx
(1+x)(1+3x)'
66. The table below shows values of a continuous variable y corresponding to given values of x.
3
4
6.
X
13.6
27.2
54.4
108.8
217.6
Use the trapezium rule to find an estimate for , ydx(
67. The expression y= ax²+ bx, is an approximation to a relation connecting two variables x and
y, where a and b are constants. By using the values given in the table below, draw a suitable
straight line graph and use it to estimate the values of a and b.
2
3
4
6.
1
126
162
172
175
144
74
dy
= xy, given that y = 1, when x= 0
68. Solve the differential equation: (1 + x2)
dx
69. (In this question, you are advised to work throughout with 2 decimal places.)
The table below shows corresponding values ofx and y obtained in a certain experiment.
2.39
4.16
6.31
8.70
12.01
1.59
6.91
16.59
31.70
52.48
87.10
3.63
The relation connecting x and y is: y = x" where'2 and n are constants.
By drawing a suitable linear graph relating log10 xand log10 y, calculate the values of 1 and
n.
dy
X =
-
70. Obtain in the form: y = f(x), a particular solution of the differential equation:
dx
2xy, given that y = 0 when x = 0.
71. Solve the differential equation x(1 – y) = -2y given that y = 2when x = e. Hence, show that
dx
dy
y = In (2)(-
dy
72. Solve the differential equation x
dx
y(2x² + 1)(.
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