Thursday, 13 March 2025

GEOMETRY J3

 Find the midpoint of a line from (3, 12) to (5, 20)


Solution

x1=3, x2=5, y1=12,y2=20.


Mid point = (x1 + x2y1 + y2)
                         2           2

Mid point = (3 + 5,  12 + 20)
                         2          2

Mid point = (832)
                     2    2

Hence midpoint = (4, 16)

TRY THIS……………………..



Find the midpoint of a line from (-9, 18) to (17, -4)

BINARIES J1


p*q =(p-q)(6p+q) Find (2*-3)

solution

=(p-q)(6p+q)

=[2-(-3)][(6x2)+(-3)]

=[2+3][12+(-3)]

=(5)(9)

=45

Hence (2*-3) = 15


TRY THIS……………….

 

 If p*q =(5p-q)(6p+q) Find (3*-4)



 




Friday, 18 October 2024

GP J1

 

The 1st term of a geometric progression is 2 and the 5th term is 512. Find the common ratio.

 

Solution

 

G1=2, G5=512, n=5

 

Gn = G1rn-1;

 

G5 = G1r5-1;

 

G5 = G1r4;

 

512 = 2 x r4;

 

512 = 2r4;

 2       2

 

256 = r4;  Finding the fourth root of 256,

We do prime factorization of 256.

 

2

256

2

128

2

64

2

32

2

16

2

8

2

4

2

2

 

1

 



 

 

 

 

 

 

 

 

 

 


44 = r4;  [equal powers will cancel out]

 

4 = r

 

r = 4

 

 

Hence the common ratio is 4.

 

TRY THIS …………..

The 1st term of a geometric progression is 3 and the 5th term is 9375. Find the common ratio.


GEOMETRY J3

 

The total interior angles of a regular polygon is 5,5800. Find the interior angle.

 

Solution

 

(n-2)1800= Total interior angles.

(n-2)1800 = 5,5800

(n-2)1800 = 5,5800      Dividing by 1800 both sides

    1800              1800

 

(n-2)     =   558279     After canceling by 2

    1                 18 9

 

(n-2)         = 279 93     After canceling by 3

   1                        9  3

 

(n-2)          = 93 31     After canceling by 3 again

    1                      3  1

 

 

(n-2)  = 31

 

n  = 31+2

n = 33

 

i = (n-2)1800

       n            .

 

i = (33-2)1800

        33          

 

i = 31 x1800

        33           

 

i = 31 x 600

        11           

 

 

i = 1860/110

 

Interior angle=1860/110

 

 

TRY THIS……………….

 

 

The total interior angles of a regular polygon is 68400. Find the interior angle.