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=?

A_n = 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

Ө = 180⁰ x s                but s = ^13∏/2

       ∏

Ө = 180⁰  x  13∏              

       ∏        2

Ө =  ⁹⁰180  x  13∏             

          ₁∏      2₁

Ө = 90⁰ x 13

Ө = 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.