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1. Consider the following ODE: u'' + 5u' - 24u = 0.
a. Convert the second order ODE into a system of 2 first order ODEs in to the form of iT=Au.
b. Find the eigenvalues and eigenvectors of matrix A.
2. Find the characteristic equation and the corresponding roots for the following ODEs and identify its case
a. y'' + 8y' + 16y = 0b. 3y'' - 18y' + 75y = 0c. 6y'' + 17y' + 10y = 0.
3. Solve the initial value problems (i. e. find particular solutions)
a. Problem 2a. with y(0)=2 and y'(0)= -5.b. Problem 2b. with y(0)= 1. 5 and y'(0)= 14.5.c. Problem 2c. with y(0)= -7 and>''(0)=l.
4. a. Write the general solution for problem 1 in terms of eigenvalues and eigevectors obtained in the problem.
b. Find The particular solution for problem I if u(0)=3 and u'(0)=2.
Kim has a strong first serve; whenever it is good (that is, in) she wins the point 73% of the time. Whenever her second serve is good, she wins the point 60% of the time. Seventy percent of her first serves and 70% of her second serves are good.
Calculate the probability that a person for whom the test result is positive has the disease
They report that 80% of huge successes received favorable reviews, 70% of moderate successes received favorable reviews, 40% of the breakeven texts received favorable review and 20% of the loser texts received favorable reviews. Revise the initial..
How do you solve for real valued general solutions for differential equations of the first, second, or third order?
Rita has a collection of 114 coins consisting of nickels, dimes, and quarters. The number of dimes is 4 more than one-third the number of nickels, and the number of quarters is twice the number of dimes. How many coins of each kind does she have?
A company wishes to manufacture a box with a volume of 48 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material.
The cost per unit of producing each product will be determined by whether a new union labor contract passes or fails. The cost per unit of each product, giving each contract result is shown in the following pay off table.
How many employees should we sample if we want to change the ME to 2.5 with 90% confidence?
If I have a right prism with the prism height being 8 and the prism base being an isosceles triangle with a base of 3 (sides of 6) what is the lateral area and the volume of the prism
How many batches of the topping must she make to complete her torte? (Use ? = 3.14 as an approximate value)
Complement of Events, Guessing. How do I setup a Guessing problem?, Six popular brands of cola are to be used in a blind taste study for consumer recognition.
Two observation points A and B are 1500 feet apart. From those points the angles of elevation of a hot-air balloon are 43° and 47°. Find the height of the balloon to the nearest foot.
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