Solve ut + uux = 0 with the initial condition u(x, 0) = 1 for x ≤ 0, 1 − x for 0 ≤ x ≤ 1, and 0 for x ≥ 1. solve it for all t ≥ 0, allowing for a shock wave. find exactly where the shock is and show that it satisfies the entropy condition. sketch the characteristics.

Students are given 3 minutes for each multiple-choice question and 5 minutes for each free-response question on a test. there are 15 questions on the test, and students are given 51 minutes to take it.how many multiple-choice questions are on the test?

The function a represents the cost of manufacturing product a, in hundreds of dollars, and the function b represents the cost of manufacturing product b, in hundreds of dollars. a(t) = 5t + 2 b(t) = 7t - 2t +4 find the expression that describes the total cost of manufacturing both products, a(t) + b(t). a. 7t^2 - 7t + 2 b. 7t^2 + 3 +6 c. 7t^2 + 7t - 6 d. 7t^2 - 3t + 6

If a is a nonzero real number then the reciprocal of a is