Aparallelogram is formed by the vectors = (2, 3) and = (1,
1).
a) determine the lengths of the diagonals.
b) determine the perimeter of the parallelogram.

a)  5    and  √5

b) P =  2* √13  +  2* √2

Step-by-step explanation:

We add the two vector and for definition the result will be one of the diagonal of the parallelogram. Then

vector  OA   ( 2 , 3 )       vector  OB  ( 1 . 1 )

If vector OD  =  OA  + OB   then

coordinates of OD will be   ( 2 + 1 ,  3 + 1 )    ( 3 , 4 )

And the length of OD is according to Pythagoras Theorem

|OD| = √ (3)² + (4)²   =√ 9 + 16   = √25  =  5

For the other diagonal we need to apply the subtraction of vectors wich will give us the other diagonal

vector  OA  = ( 2 , 3 )   and vector   OB  =  ( 1 , 1 )

If vector BA is the difference between vectors  OA  - OB  then vector BA is

vector BA  =  (  2- 1 , 3- 1 )  =  ( 1 , 2 )  

And the length of BA is according to Pythagoras Theorem

BA = √(1)² + (2)²    =  √1 + 4  = √5

Then  the length of the other diagonal is √ 5

b) To find the perimeter of the parallelogram we need to apply

Perimeter  =  2 OA  + 2 OB

P  = 2 OA  + 2 OB        (1)

So length of  OA    is:

|OA|  =  √(2)² + (3)²  =  √ 13

and

|OB|  = √(1)² + (1)²   =  √2

Then by subtitution in  (1)

P =  2* √13  +  2* √2

the least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.