On her way home from school, Palama walked 5 blocks west to the grocery store, 2 blocks south to visit her aunt, then 5 blocks north to go home. What direction is her home from school?

the home is

5.83 blocks 31° North of west of the school

Step-by-step explanation:

Resolving the displacement to vertical and horizontal axis

Let north and south represent positive and negative vertical axis, also east and west represent positive and negative horizontal axis;

Vertical axis; , 2 blocks south to visit her aunt, then 5 blocks north to go home

Ry = -2 + 5

Ry = +3

Horizontal axis; 5 blocks west to the grocery store

Rx = -5

Resultant distance = R = √(Rx^2 + Ry^2)

R =√(-5^2 + 3^2)

R = √34

R = 5.83 blocks

For the direction;

∅ = arctan(Ry/Rx) = arctan(3/5)

∅ = 31°

Therefore, the home is

5.83 blocks 31° North of west of the school.

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.