The differential equation dy dx equals the quotient of the quantity x plus 1 and y minus 3 produces a slope field with vertical tangents at y = 3
produces a slope field with vertical tangents at x = −1
produces a slope field with rows of parallel segments
I only
II only
III only
I and III

I only

Step-by-step explanation:

dy/dx = x + 1 / y -3

(y - 3)dy = (x + 1) dx

integrate

1/2y^2 - 3x = 1/2x^2 + x

1/2y^2 = 1/2x^2 + 4x

y^2 = x^2 + 8x

y = (x^2 + 8x)^1/2

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.