Monday 19 January 2015

CIRCLES 1




Find y in the figure below;



Solution

According to rectangle properties of a circle

(PX)(XJ) = (HX)(XK)

(4)(y) = (8)(10)

4y = 80

4y = 80 
4        4

y = 20

Hence y = 20 cm

TRY THIS……….

Find a in the figure below;




COMPOUND INTEREST 1




Salma invested a certain amount of money in a bank which gives an interest rate of 10% compounded annually. How much did she invest at the start if she got 5000 sh at the end of 2 years?

solution

n=2, t=1, R=10%, A2=5000, P=?
An = P(1 + RT/100)n
A2 = P(1 + (10x1)/100)2
A2 = P(1 + 10/100)2
A2 = P(100/100 + 10/100)2
A2 = P(110/100)2  But A2=5000,
5000 = P(1.1)2  
5000 = 1.21P
5000  =  1.21P
1.21       1.21

5000  =  P
1.21      

P = 4132.23 (to 2 d.p.)

Hence at the start she invested Tsh 4132.23

TRY THIS……….

Salome invested a certain amount of money in a bank which gives an interest rate of 5% compounded annually. How much did she invest at the start if she got 12,000 sh at the end of 2 years?

SIMPLE INTEREST 3




Ashish deposited the amount of 20,000/= in a bank for 3 years and got a profit of 7200/=. Find the interest rate?

Solution

I = 7200/=, P = 20,000/=, T = 3 years, R = ?

I  = PRT
      100

7200  = 20,000 x R x 3
                      100

7200  = 20,000 x R x 3
                      100

7200  = 200 x R x 3
                     
7200  = 600R
          
127200  = 600R
   600       600

Hence the interest rate was 12%

TRY THIS…………………..

Sonali deposited the amount of 30,000/= in a bank for 6 years and got a profit of 2700/=. Find the interest rate?

RADIAN TO DEGREES 1




Change 13/2 radians into degrees.

Solution

Ó¨ = 1800 x s                but s = 13/2
      

Ó¨ = 1800  x  13              
               2

Ó¨ =  90180  x  13             
          1     21

Ó¨ = 900 x 13

Ó¨ = 11700

Hence 13/2 radian is equal to 11700.

TRY THIS…………….
  
Change 7/10 radians into degrees.

LENGTH OF AN ARC 1




Find the length of an arc if the radius of the circle is 60cm.

Solution

L = r
      1800

L = x  60
             1800

L = cm
      3

Hence length of an arc is /3 cm

TRY THIS………………..

Find the length of an arc if the radius of the circle is 3.6cm.