LENGTH OF AN ARC - 1

Find the length of an arc if the radius of the circle is 20cm.

Solution

r = 20cm

L = ∏r

      180⁰

L = ∏ x  20

             180⁰

L = ∏ cm

      9

Hence length of an arc is ^∏/9 cm

TRY THIS………………….

Find the length of an arc if the radius of the circle is 30cm.

SIMPLE INTEREST 2

Dikshi deposited the amount of 6000/= in a bank which gives an interest rate of 3% for 2 years. Find the simple interest she got?

Solution

I = ?,  P = 7,000/=, T = 2 years, R = 5%

I  = PRT

      100

I  = 7000 x 5 x 2

            100

I  = 7000 x 5 x 2

            100

I  = 70 x 5 x 2

          

I  = 700/=

Hence the simple interest was Tsh 700/=

TRY THIS……………………

Hiren deposited the amount of 9000/= in a bank which gives an interest rate of 4% for 2 years. Find the simple interest she got?

CONGRUENCE - 1

Prove that the following triangle is isosceles. (diagram not to scale).

Solution

Given: triangle UTW with T produced to V.

Required to prove: ∆UTW is isosceles

Proof: UV = VW (given)

        <UVT = <WVT = 90⁰ (given)

         TV = VT (common line)

         ∆UVT ≡ ∆WVT by SAS rule

        TU = TW (Equal corresponding sides)

Hence ∆ UTW is isosceles (proved)

Learn Math By Video

 

COMPOUND INTEREST 2

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 4000 sh at the end of 2 years?

Solution

n=2, t=1, R=10%, A₂=4000, 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=4000,

4000 = P(1.1)²  

4000 = 1.21P

4000  =  1.21P

1.21       1.21

4000  =  P

1.21      

P = 3305.79

Hence at the start she invested Tsh 3305.79

TRY THIS………………………

Nishita invested a certain amount of money in a bank which gives an interest rate of 6% compounded annually. How much did she invest at the start if she got 6000 sh at the end of 4 years?