Show that S, and S, touch externally and obtain the equation of the common tangent T at the point of contact (it) A father and a mother have 5 children..This family is to occupy a particular front-line bench in church on a special thanksgiving service. Given that this bench has a capacity of 7 persons, in how many ways can this family be seated on the bench. (a) If the parents must seat adjacent to each other (h) If the parents must seat adjacent to each other at one end of the bench.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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9ii

8) () Given that,
-(++3i) =1-2i, express the complex number 2
2-i
are real constants.
(ii) The vector equations of two lines L1 and L2 are given by
L:r = 13i + 4j + 11k +2(3i - 8j - 6k)
L2:r = 5i + 22j + 9k + u(7i - 17j – 5k)
Find
(a) The position vector of the point of intersection of L, and L2
(b) The cosine of the acute angle between L, and L2
-9) (i) The equations of two circles S, and S2 are given by
S:x +y +2x+2y+1=0,
Sr +y-4x +2y+1=0.
Show that S and S, touch externally and obtain the equation of the cemmon tangent T at the point of contact
(it) A father and a mother have 5 children.This family is to occupy a particular front-line bench in church on a
special thanksgiving service.
Given that this bench has a capacity of 7 persons, in how many ways can this family be seated on the bench,
(a) If the parents must seat adjacent to each other
(b) If the parents must seat adjacent to each other at one end of the bench.
0) (i) Given that
f(x)=-
x(x+1)(x+2)
Express f(x) in partial fractions.
27
Hence show that f(x)= In
Transcribed Image Text:8) () Given that, -(++3i) =1-2i, express the complex number 2 2-i are real constants. (ii) The vector equations of two lines L1 and L2 are given by L:r = 13i + 4j + 11k +2(3i - 8j - 6k) L2:r = 5i + 22j + 9k + u(7i - 17j – 5k) Find (a) The position vector of the point of intersection of L, and L2 (b) The cosine of the acute angle between L, and L2 -9) (i) The equations of two circles S, and S2 are given by S:x +y +2x+2y+1=0, Sr +y-4x +2y+1=0. Show that S and S, touch externally and obtain the equation of the cemmon tangent T at the point of contact (it) A father and a mother have 5 children.This family is to occupy a particular front-line bench in church on a special thanksgiving service. Given that this bench has a capacity of 7 persons, in how many ways can this family be seated on the bench, (a) If the parents must seat adjacent to each other (b) If the parents must seat adjacent to each other at one end of the bench. 0) (i) Given that f(x)=- x(x+1)(x+2) Express f(x) in partial fractions. 27 Hence show that f(x)= In
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