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Mutilplying and Evaluating Polynomials: a....

Mutilplying and Evaluating Polynomials:

a. Program speed, or runtime, is an important concept in computer programming, and it is measured in terms of the number of mathematical operations made during one run of the program..For example, the expression x3-2x+3 has five operations If we write it as x*x*x-2x+3, we see that there are three multiplications, one addition, and one subtraction.

If you had to compute the polynomial (x+3(x-3) for a certain value of x (the actual value of x does not matter),how many mathematical operations (addition, subtraction, multiplication, or division)would be made? (Count the number of each type of operation you see in the expression). Now mutiply the original (x+3)(x-3) polynomial (FOIL. In the new version of the expression (polynomial),how many operations are there?

b. The time is takes to multiply two matrices of size n is determined by the polynomial expression 2n3-n2. For example, it takes 45 operations to multiply two 3x3 matrices. Compute the number of operations required to run a program that multiplies two matrices of size 20.

Functions and Graphing: Your company needs to temporarily hire a programmer to work on a project. Two proposed payment schemes for this work are as follows:

A flat rate of $1,000, p;us $20 per hour or (2) $25 per hour. For each of the two plans, write a function for the amount of each payment (y) as a function of the hours worked (x). Graph each function scenario and which represents the second. Notice in the graph where one function is higher than the other, and interpret this in terms of which pay plan costs the company more (compared to the other plan)for certain number of hours worked.

Solving Inequalities: Set up and solve an inequality that would enable your company to deteremine possible job lengths (in hours) for which the person is paid less according to plan 1 than for plan 2.

a. Program speed, or runtime, is an important concept in computer programming, and it is measured in terms of the number of mathematical operations made during one run of the program..For example, the expression x3-2x+3 has five operations If we write it as x*x*x-2x+3, we see that there are three multiplications, one addition, and one subtraction.

If you had to compute the polynomial (x+3(x-3) for a certain value of x (the actual value of x does not matter),how many mathematical operations (addition, subtraction, multiplication, or division)would be made? (Count the number of each type of operation you see in the expression). Now mutiply the original (x+3)(x-3) polynomial (FOIL. In the new version of the expression (polynomial),how many operations are there?

b. The time is takes to multiply two matrices of size n is determined by the polynomial expression 2n3-n2. For example, it takes 45 operations to multiply two 3x3 matrices. Compute the number of operations required to run a program that multiplies two matrices of size 20.

Functions and Graphing: Your company needs to temporarily hire a programmer to work on a project. Two proposed payment schemes for this work are as follows:

A flat rate of $1,000, p;us $20 per hour or (2) $25 per hour. For each of the two plans, write a function for the amount of each payment (y) as a function of the hours worked (x). Graph each function scenario and which represents the second. Notice in the graph where one function is higher than the other, and interpret this in terms of which pay plan costs the company more (compared to the other plan)for certain number of hours worked.

Solving Inequalities: Set up and solve an inequality that would enable your company to deteremine possible job lengths (in hours) for which the person is paid less according to plan 1 than for plan 2.

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