Use your result in (a) to solve the system:
Question#2 (5) (modified from #13 p. 102 in your book)
Solve the matrix equation for X
Question#3 (5) (modified from #9 p. 102 in your book) Let
[■(a&0&b&2@0&a&3&6@0&a&b&c+2)] be the augmented matrix of a linear system.
Find for what values of a,b,c the system has:
(i) a unique solution
(ii) a one-parameter solution
(iii) a two-parameter solution
iv) no solution
Question#4 (7) Write the matrix A=[■(-1&1&-1@1&1&-1@1&-1&2)] as a product of elementary matrices
Question#5 (3) Find the determinant by any method:
Question#6 (3-2)Given thissystem:
a) Use Cramer’s method to solve for x_1 only
b) Solve for the other variables by any method.
lve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.
Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
Let f be a twice-differentiable function such that f′(2)=0 . The second derivative of f is given by f′′(x)=x2e2−x−1 for 0≤x≤6 .
(a) On what open intervals contained in 0View More
mining ship has a mass of 10,000 kg. The first rocket stage provides a thrust of 80 kN and is used over a
distance of 100,000 km. The second rocket stage provides a thrust of 40 kN and is used over a distance
of 200,000 km. The third rocket stage provides a thrust of 30 kN and is used over a distance of 400,000
1) Calculate the final velocity of the rocket using two methods:
a. Using the work-energy theorem.
b. Using kinematics and Newton’s laws of motion. Hint: You might need to use the
quadratic formula to solve for t:
2) Calculate the total amount of time it takes for the mining ship to reach the other asteroid.
3) If the ship has a reverse thruster that provides 200 kN of thrust, how many km before reaching
the destination should the mining ship engage the reverse thrusters?