Saturday 29 August 2015

POPULATION DECAY 1


A settlement has a population of 2000 people. Each year 12%of the people leave the settlement. How many people will remain after 3 years?

solution

f(t) = A ( 1 -12/100)t
= 2000(1 – 0.12)t
= 2000 x (0.88)3
= 2000 x 0.88x 0.88x 0.88
= 2000 x 0.681472
= 1362.944 (1363 approximate)

Therefore there will be 1363 people remaining after three years of decay

TRY THIS………….


A settlement has a population of 5000 people. Each year 5%of the people leave the settlement. How many people will remain after 4 years?

SETS 1


If n(A)= 36 , n(B)= 50 and n(AuB)=65, find n(AnB).

Solution

n(AuB) = n(A) + n(B) - n(AnB)
       65 = 36 + 50 - n(AnB)
       65 = 86  - n(AnB)
       65 - 86 = - n(AnB)
              -21 = - n(AnB)
21 = n(AnB) (after dividing by -1 on both sides)

Hence n(AnB) = 21 answer

TRY THIS……………………


If n(A)= 35 , n(B)= 45 and n(AuB)=70, find n(AnB).


MAKING THE SUBJECT 1


If M = u(b + s)    make s the subject of the formula.
             (b – s)
Solution


M = u(b + s)   
          (b – s)

(b – s) x M = u(b + s) x (b – s) multiply by(b-S) on both sides.
                         (b – s) 1

(b – s) x M = u(b + s) open the brackets on both sides.

Mb – Ms = ub + us

Mb – ub = Ms + us   (collect the terms containing s together)

Mb – ub = s(M + u)

Mb – ub = s(M + u) 1               Divide by (M + u) on both sides.
(M + u)         (M + u) 1

Mb – ub = s
(M + u)        

Hence  s =   Mb – ub
                      (M + u)   

   TRY THIS………………….

 If M = u(a + e)    make e the subject of the formula.

               (a – e)

%'GE PROFIT 1


A man got a profit of 200/= after selling an item for 7000/=. Find the percentage profit.

Solution

%’ge profit = Profit   X  100    where B. P. represents Buying Price.
                         B.P

%’ge profit = 200   X  100   
                        7000

%’ge profit = 26/7%   
                       
Hence Percentage Profit is 26/7%   

TRY THIS………………….


A man got a profit of 400/= after selling an item for 8000/=. Find the percentage profit.


RADIAN TO DEGREES 1


Change 5/4 radians into degrees.

Solution

Ө = 1800 x s                but s = 5/4
      

Ө = 180x  5              
       ∏     4

Ө =  45180  x  5 1             
          1    41

= 45 x 5

= 135

Hence 5∏/4 radian is equal to 1350.

TRY THIS………………….


Change 7/6 radians into degrees.


MAKING THE SUBJECT 1


If A = BCQ make Q the subject of the formula.

Solution

A = BCQ

  A   =   BCQ
BC      BC

 A   =   Q
BC     

Hence   Q =      A 
                         BC   

TRY THIS………………..


If A = WXN.  Make X the subject of the formula.

ARITHMETICS 1


Evaluate 44 x 237 + 463 x 44

Solution

= 44 x 237 + 463 x 44

= 44 x (237 + 463)

= 44 x 700

= 30800

Hence 44 x 237 + 463 x 44 = 30800

TRY THIS………….


Evaluate 376 x 516 + 484 x 376.

SUM OF A GP 1


The sum of the 1st five terms of a geometrical progression is 484. If the common ratio is 3, find the 1st term.

solution

S5 = 484, G1 = ?, r=3, n=5

Sn = G1(rn-1)/r-1
               

S5 = G1(r5-1)/r-1
               

484= G1(35-1)/3-1
               

484= G1(243-1)
                  2

2 x 484= G1(242)
                  
968= 242 G1

4 968   =  G1
  242

G1 = 4

Hence the 1st term is 4.

TRY THIS……………..


The sum of the 1st seven terms of a geometrical progression is 381. If the common ratio is 2, find the 1st term.