[All solutions must start and draw from a fundamental equation on your equation sheet and your coordinate system; draw and reference each of these as appropriate and follow a logical progression to your final answer.]   A toy rocket is flying straight along the x-axis with an x-velocity component of 20 m/s; over 2.5 seconds, its velocity in that direction changes to 30 m/s in the exact opposite direction.   a) What is the average acceleration of the particle over that time interval?    b) Then, the rocket begins to accelerate in its new direction at a constant rate of 5 m/s^2 for 10 seconds. How far does it go in that second time interval?

[All solutions must start by writing an equation (or equations) and a coordinate system from the equation sheet on your paper, as appropriate.  The solution must then follow a logical progression from the equation(s) on the equation sheet to the answer(s).] You like running, and are beginning to train for a marathon. You start running from your house, first by running 3.3 kilometers North, followed by 2.6 kilometers East, then 5.9 kilometers South, and then finally 2.6 kilometers West. Your neighbor is a good friend and drone enthusiast and, at the conclusion of your run, flies a drone from your house [neglect vertical motion of the drone] to your final location for a celebratory photo.   a) Draw a coordinate system and annotate your position at the end of each segment of your run. b) How far did you run, in total? c) What is your final displacement relative to your house and your coordinate system? d) What is the minimum distance the neighbor’s drone would have to fly if it wanted to reach you from your house? e) If the drone made the flight in five minutes, what would its average velocity need to be?

On a velocity versus time graph, you can tell when an object is decelerating, because __________________.

Solve the equation by expressing each side as a power of the same base and then equating the exponents.  2(3x+7)=14{“version”:”1.1″,”math”:”2(3x+7)=14″}

Perform the matrix row operation (or operations) and write the new matrix.  11-1  1 30-43-3  040-3-13-320  3 -2 -4R1+R33R1+R4{“version”:”1.1″,”math”:”11-1  1 30-43-3  040-3-13-320  3 -2 -4R1+R33R1+R4″}

Write the partial fraction decomposition of the rational expression.  11×2-x-20x(x+1)(x-1){“version”:”1.1″,”math”:”11×2-x-20x(x+1)(x-1)”}

Solve the system of equations using matrices for y. Use Gauss-Jordan elimination.  8x – y – 4z = 205x + 7y + 3z = 1019x – 6y + z = 11{“version”:”1.1″,”math”:”8x - y - 4z = 205x + 7y + 3z = 1019x - 6y + z = 11″}

Use the Binomial Theorem to expand the binomial and express the result simplified form.  (x+2y)6{“version”:”1.1″,”math”:”(x+2y)6″}

Divide using synthetic division.  x5+x3-5x-2{“version”:”1.1″,”math”:”x5+x3-5x-2″}

Approximate the number using a calculator. Round your answer to three decimal places.  2.4π{“version”:”1.1″,”math”:”2.4π”}