Question

Calculus

A graphing calculator is recommended.

A particle moves according to a law of motion s = f(t), t > 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.)

f(t)=t^{3}-9 t^{2}+24 t

(a) Find the velocity (in ft/s) at time t.

(b) What is the velocity (in ft/s) after 1 second?

(c) When is the particle at rest? (Enter your answers as a comma-separated list.)

(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)

(e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds.

(f) Find the acceleration (in ft/s^2) at time t.

Find the acceleration (in ft/s^2) after 1 second.

(g) Graph the position, velocity, and acceleration functions for 0 <= t <= 6.

(h) When is the particle speeding up? (Enter your answer using interval notation.)

When is it slowing down?

Verified

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Calculus

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Calculus

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### Question 45627

Calculus

I. Find the total area of the infinitely many triangles shown in the figure below.

### Question 45477

Calculus

The bandwidth of a video being delivered on the internet has a continuous distributionon the interval (0,4), with a probability density function (PDF)
f_{X}(x)=\left\{\begin{array}{ll} \frac{c}{(1+x)^{2}} & \text { for } 0<x<4 \\ 0 & \text { otherwise. } \end{array}\right.
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### Question 45476

Calculus

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### Question 45456

Calculus

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### Question 45455

Calculus

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### Question 45454

Calculus

\text { a) Consider the sphere } S:(x-2)^{2}+(y+3)^{2}+(z-1)^{2}=16
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### Question 45453

Calculus

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### Question 45452

Calculus

\text { Consider the function } f(x, y)=x-y^{2}+3 \text {. Sketch the cross-section of } f(x, y) \text { with }
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\text { (b) } y=-1