Math Answers

An investment of Ksh1,000,000 in an account accumulated to Ksh 2,500,000 after 5 years.

(i) State the accumulation factor A(0,5) . (2 marks)

(ii) (a) Find the simple annual interest rate which would give the accumulation

factor in part (i). (3 marks)

(b) Find the annual compound interest rate which would give the

accumulation factor in part (i). (3 marks)

show that

1²+3²⁺5²+.....(2n+1)²=(n+1)(2n+1)(2n+3)/3

where n is a nonnegative integer.

For the function f(x)= x^2-2 defined over[1,5],

Verify L(P,f)≤U(P,f) where is the partition which divide [1,5] into four equal intervals

orthogonal trajectories of y' = - (x/y)

Let R1 and R2 be symmetric relations. Is R1 ∩ R2 also symmetric? Is R1 ∪ R2 also

symmetric?

F or the follow ing differential equation locate and classify its singular points on the x-axis

𝑥

2

𝑦

′′ + (2 − 𝑥 )𝑦

′ = 0.

real of the form a + b 2 , a; b ∈ Z form s a ring.

the following are the ages of husbands and wives for six couples. husbands age: (43, 57, 28, 19, 35, 39) wifes age: (37, 51, 32, 20, 33, 38)

S how that y = c 1

e

x + c 2

e

2 x

is the general solution of y

′′ − 3 y

′ + 2y = 0 on any

interval, and find the particular solution for w hich y 0 = − 1 a n d y

′

( 0) = 1.

There are two bags A and B. Bag A contains 5 red balls and 3 blue balls. Bag B contains

3 red and 5 blue balls. A fair die is rolled, if 3 or 5 turns up a ball is drawn from the bag

A else the ball is drawn from the bag B. Find the probability that a blue ball is drawn.