Two particles travel along the space curves r(t) and u(t). A collision will occur at the point of intersection if both particles are at P at the same time. (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list.) r(t) = t^2i + (9t - 20)j + t^2k u(t) = (3t + 4)i + t^2j + (5t - 4)k point of intersection (x, y, z) =
1. Do the particles collide?
a. Yes
b. No
2. Do their paths intersect?
a. Yes
b. No

Point of intersection (x, y, z) = (16, 16, 16)

1. a. Yes

2. a. Yes

Step-by-step explanation:

In order for the particles to colide (and therefore have their paths intersect), the values for the i, j, and k coordinates must be equal for a given 't':

For the i coordinate:

For the j coordinate:

For the k coordinate:

As we can see, for t =4, both paths have the same coordinates and therefore they intersect and the particles will colide.

Point of intersection (x, y, z) = (16, 16, 16)

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

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