Aparticle moves on x-axis blah its initial position is x(0)=27 and velocity is v(t)=4t^3-30t^2+72t-54 on the time interval 0
a) write an expression for the position function (general)
t^4-10t^3+36t^2-54t+c
b) when does the particle change direction?

c) find t when particle is moving to the right

d) find velocity when acceleration is 0.
ez, don't need for this one.

b) The particle changes direction when its velocity changes sign. Use the first derivative test to find the critical points:

Then for , we have ; for , we have ; and for , we have again. These three facts indicate that the velocity only changes once at .

c) Pick "to the right" to be the positive direction. Then you need to find where . We already did that above and found for .

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

answer: 1 + 1 = 11

step-by-step explanation: