MAE101_FE_SUMMER24

The function s(t) = t²cost + 4t² represents the position of a particle moving along a horizontal line. Find the velocity of the particle at time t = π.

• 4π

• 8π

• 6π

• 2π

Find the volume of the parallelepiped determined by 2u, -3v, 5w, provided that u=[1, 2, -1]T, v=[0, 2, 4], w=[1, 4, 1]T.

• 100

• 80

• 120

• 60

• 30

Find the second row of Ax.

• [2 2 9 7]

• [-8 2 1 8]

• -8x₁+2x₂+x₃+8x₄

• 2x₁+2x₂+9x₃+7x₄

Choose 1 answer

• A. -5

• B. -3

• C. 3

• D. 7

• E. None of the other choices is correct

Let U = {(a,b,c,d)| a+2d = 3b+c} be a subspace in R⁴. Find the dimension of U.

• 0

• 1

• 2

• 3

• 4

Two cars start moving from the same point. One travels south at 28 mi/h and the other travels west at 70 mi/h. At what rate is the distance between the cars increasing 5 hours later? Round the result to the nearest hundredth.

• 75.38 mi/h

• None of the other choices is correct

• 75.39 mi/h

• 75.49 mi/h

• 76.4 mi/h

Choose 1 answer

• A. None of the other choices is correct

• B. 2

• C. 12

• D. 10

• E. 4

Evaluate the Riemann sum for f(x) = 2 - x², 0 ≤ x ≤ 2 with 4 equal subintervals, taking right endpoints.

• 4/3

• 1/4

• None of the other choices is correct

• 9/2

• 1/3

Choose 1 answer

• A. None of the other choices is correct

• B. (i)

• C. (ii)

• D. (iv)

• E. (iii)

Let A be an 3×3 matrix. Find det A if AA^T = 3I.

• 1

• 3√3 or 1

• 3√3 or -3√3

• √3 or -√3