Find the intersection point and the angle between the lines l1 and l2. l1: x = - l + 2t, y = 3 - t, z = 2 + 2t, l2: x = - 2 - t, y = 5 + 2t, z = - 2t.

(-1,3,2)

Step-by-step explanation:

For L1:

x= -1+2t

y= 3-t

z= 2+2t

and for L2:

x= -2-s

y= 5+2s

z=-2s

To find the intersection point we equalize the x, y and z:

-1+2t = -2-s

3-t = 5+2s

2+2t = -2s⇒ s= -1-t

We replace the s value -1-t in second equation:

3-t = 5+2(-1-t)

3-t = 5-2-2t

t = 0.

So, s = -1-t = -1-0 = -1.

We replace the s and t value in the parametric equations to find the interception point:

x= -1 +2(0) = -1

y = 3-0 = 3

z = 2 +2(0) = 2.

So, the interception point is (-1,3,2). The formula to calculate the angle is in the picture below, where α is the angle, u and v are the parallel vector of each line.

For L1: u=(2,-1,2) (the coefficients of t)

For L2: v=(-1,2,-2) (the coefficients of s)

So, the angle is:

cos(α) =

cos(α)=  

cos(α)=

cos(α)=

α =

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.

the answer to this would be 5x^3-6x^2-24 over 3x^2

hope this if needed hmu