(e) Given that loga 4 = p and loga 3 = q, express loga 2.25 in terms of p and q. Question 4 (a) (i) Suppose a and B are the roots of 2x2 - 4x + 7 = 0. Find the value of: (a) (c) a3 + B3 (ii) The roots of the quadratic equation x2 - 5x - 10 = 0 are a and B. Find a quadratic %3D equation whose roots are 2a and 2B.
(e) Given that loga 4 = p and loga 3 = q, express loga 2.25 in terms of p and q. Question 4 (a) (i) Suppose a and B are the roots of 2x2 - 4x + 7 = 0. Find the value of: (a) (c) a3 + B3 (ii) The roots of the quadratic equation x2 - 5x - 10 = 0 are a and B. Find a quadratic %3D equation whose roots are 2a and 2B.
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:(e) Given that loga 4 = p and loga 3 = q, express loga 2.25 in terms of p and q,
Question 4
(a) (i) Suppose a and ß are the roots of 2x2 -4x + 7 = 0. Find the value of:
(c) a3 + B3
(a) +
(b)
(ii) The roots of the quadratic equation x2 - 5x - 10 = 0 are a and ß. Find a quadratic
equation whose roots are 2a and 2B.
(b) Decompose the following expressions into partial fractions:
6x+7
(iii)
(x+2)2
5x-3
3x
x2-2x-3
(ii)
(x-1)(x-2)(x-3)
(c) Express each of the following in the form a + bi:
3+41
(i) (5 – 2i) + (-8- i)
(ii) (3+ 4i)(5 – 5i)
(ii)
4-21
(d) Sketch the graph of f (x) = -2x² + 12x – 16 showing clearly the intercepts, axis of
symmetry and the turning point.
Question 5
(a) A pharmacist observes that she is dispensing 5% less of a particular drug every week. In
the first week she dispensed 1000 tablets. In which week will it be the first dispensing
less than 250 tablets?
(b) The first three terms of a geometric progression are 3x +5,8, 2. Find the:
(i)
common ratio and the value of x,
(ii)
sum of the first 20 terms,
(ii)
sum to infinity.
(c) Prove the following identities:
(i)
cosece -
sine
= cote
(d) Solve the following equations:
1+cose
(ii) (1+ secx)(1 – cosx) = sinxtanx
(i)
5sine - 13cose = 0
(ii) 2tan?y = secy +1
%3D
DUE DATE: 29th March, 2021
Lecturer: Mr Mubanga, S. (0967223034/0979273034)
Transcribed Image Text:Assignment 1
INSTRUCTIONS
1. Answer all the questions in this assignment.
2. Show all the essential working.
3. Be neat and orderly in your working.
Question 1
Discuss five (5) reasons why Mathematics is essential in the training curriculum of an EHS.
Question 2
(a) Express the following repeating decimals in the form, where a and b are integers.
0.131313....
(i)
(b) If one syrup mixture contains substance A, B, C and D in the ratio 5 :9:4:2 and there
are 15 millilitres of substance A in the mixture, how many millilitres of substance D are
(ii) 0.325
(iii) 7.555....
there in the mixture?
(c) Show that 2x-1 x 8*+1 = 42x+1.
(d) Solve the simultaneous equations 3* x 99 = 1 and 22x x 4 =
Question 3
(a) (i) If the equation (p + 3)x² + 2px + p = 1 has two real and distinct roots, find the
range of values of p.
(ii) If the equation x2 - (q – 2)x +1 = q(x – 2) is satisfied by only one value of x,
what are the possible values of q?
(b) Solve the simultaneous equations
3x = y +7
x2 + xy = y2 +1
(c) Evaluate the following:
(i) logs 7
(ii) logs 9 x log3 7 x log, 2 x log2 25
(d) Solve the following equations:
(i) 4-7(2) = 8
(iii) logs (x+ 4)-1= logs x
(ii) 3*-1 = 2*+2
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