(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.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![(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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8a452bc-ebd6-46dc-8fc3-701a9bf6501c%2F7f21d7c7-0c51-4f7d-a33c-66336e78e35b%2Fq06p6qs_processed.jpeg&w=3840&q=75)
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8a452bc-ebd6-46dc-8fc3-701a9bf6501c%2F7f21d7c7-0c51-4f7d-a33c-66336e78e35b%2Foh4o2n_processed.jpeg&w=3840&q=75)
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