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s3w7 FC Non-linear systems of equations

Last updated 5 months ago

12 questions

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Question 1

1.

Review: Find the common denominator and add these two fractions

Question 2

2.

Undoing the problem above (starting with the answer, and ending with the question) is called partial fraction decomposition, and is a simple example of a use for linear systems of equations. Take the following fraction
what would you need to do to decompose this into two fractions without a common denominator? First things first - factor the denominator.

Question 3

3.

You should have split the quadratic into two factors a and . That means that
and therefore
where b and a are both binomial factors of the denominator of the original fraction. plug in the b and a you have, and distribute c and d across the binomials. what do you get?

Question 4

4.

using like terms, set up two linear equations to solve for c and d. separate with a comma.

Question 5

5.

You can easily see that if the numerator of equations like this are not constants, things might get hairy, and you can see that not all equations like this would end with a neat set of linear equations, so we need to know how to deal with non-linear systems of equations. watch the following video, do you have any questions.

Question 6

6.

I don't have a lot of conceptual questions to throw at you with this one. You are well-versed in using substitution method, and you can see where different parent functions will intersect other parent functions in a variety of different ways. give an example of a system of two non-linear equations that may have 0,1,or 2 solutions.

Question 7

7.

The rest of the questions in your homework are review from algebra 2. They include graphing linear inequalities, graphing nonlinear inequalities, and linear programming. Here is one helping out with graphing nonlinear inequalities, do you have any questions?

Question 8

8.

Last video - we spent some time on this last year, and it was a good way to apply non-linear equations to systems of linear inequalities, so it make for good practice for the stuff we have already done.

Question 9

9.

Find the area of constraints for the following linear programming problem. Note the vertices. An office manager is purchasing file cabinets and wants to maximize storage space. The office has 60 sq. ft. of floor space for the cabinets and $600 in the budget to purchase them. Cabinet A requires 3 sq. ft. of floor space, has a storage capacity of 12 cubic ft., and costs $75. Cabinet B requires 6 sq. ft. of floor space, has a storage capacity of 18 cubic ft. and costs $75. How many of each cabinet should the office manager buy? Find the constraint equation for the floor space. us a for cabinet A and b for cabinet B

Question 10

10.

Write the constraint equation for the cost of the cabinets.

Question 11

11.

What is the objective function (the function you are trying to maximize or minimize) using a for cabinet A and b for cabinet B.

Question 12

12.

tell me how you are feeling about...

what is partial fraction decomposition used for
how to do partial fraction decomposition
what makes a set of equations non-linear
how to solve a set of non-linear equations graphically
how to solve a set of non-linear equations algebraically
how to solve a linear programming problem

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