Describe the motion of a particle with position (x, y) as t varies in the given interval. (for each answer, enter an ordered pair of the form x, y.) x = 1 + sin(t), y = 6 + 2 cos(t), π/2 ≤ t ≤ 2π

Path followed by the particle is an incomplete ellipse whose points do not lie on first quadrant.

Step-by-step explanation:

x = 1+sint

y = 6+2cost

sint = x-1

cost = (y-6)/2

We know

Substituting for sint and cost in the above equation,we get:

The above equation represents an ellipse with center at (1,6) with major axis length as 4 and minor axis length as 2.

But since π/2 ≤ t ≤ 2π

It represents an incomplete ellipse which does not have any points on the first quadrant.

the two may have that, even a breakdown is probably offered

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.