The acceleration, initial velocity, and initial position of a particle traveling through space are given below. a(t) = (2, −4, −8), v(0) = (−8, 1, 5), r(0) = (15, −2, 4) The particle's trajectory intersects the yz-plane exactly twice. Find these two intersection points. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y, z) = (x, y, z) =

The intesection points are:

Step-by-step explanation:

The acceleration vector is:

The velocity vector is found by integrating the previous vector as a function of time:

Afterwards, the position vector is constructed by means of integrating velocity  vector:

The particle trajectory intersects the yz-plane when x = 0, then:

The polynomial roots are:

The intesection points are:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

idk

step-by-step explanation: