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Math and Computers, Math 165 Programming Project homework 1-
1. Prove that every univariate polynomial with complex coefficients and degree m has at most m distinct roots.
2. Use MAPLE to find all the real roots of the polynomial 3x5-25x3 + 60x - 20.
3. Is the polynomial x2 - 4 in the ideal generated by the polynomials x3 + x2 - 4x - 4, x3 - x2 - 4x + 4, -2x2 - x - 2.
4. Given univariate polynomials f1, . . . , fs. Prove that the set of common roots of these polynomials (the variety) is empty if and only if their GCD is 1.
5. Use MAPLE to find the square-free part of the polynomial x11 - x10 + 2x8 - 4x7 + 3x5 - 3x4 + x3 + 3x2 - x - 1.
6. FIRST PROJECT ASSIGNMENT:
Write a formula for the population of flies after t weeks. How many fruit flies will there be after 6 months? How many fruit flies will there be after 3 weeks?
Exercise 10. A chemical manufacturer produces three chemicals: A, B and C. These chemical are produced by two processes: 1 and 2. Running process 1 for 1 hour costs $4 and yields 3 units of chemical A, 1 unit of chemical B and 1 unit of chemical C..
a piece of cardboard is twice as it is wide. It is to be made into a box with an open top by cutting 2-in squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard.
The world population at the beginning of 1980 was 4.5 billion. What does Q(t) = and what will the world population be at the beginning of 2019?
Find the constant of integration, C if: y = ò (9x2 + 2x - 9)dx and the curve passes through the point (2, 4)
Julia Robertson is a senior at Tech, and she's investigating differ- ent ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia k..
Inventory Management , 1. Cooper Automotive Products manufactures components used in the automotive industry. The company purchases parts for use in its manufacturing operation from a variety of different suppliers
Find the age of the father
measure of angle of elevation of the top of a cliff is 25. on walking 100m towards the cliff measure of angle of elevation of the top is 45. find the height of the cilff.
Use the fact that the derivative of the function g(x)= √ x is g'(x)=1/2√x to find the equation of the tangent line to the graph of g'(x) at the point x=25.
The letter grade will be based upon demonstrated mastery of the content and ability to articulate and apply the concepts in the assignment. Keep this in mind while writing your paper.
A conducting loop in the shape of a square of edge length 12cm carries a current of 15A. A) calculate the magnitude and direction of the magnetic field at the center of the loop. B) Calculate the magnetic field at the center if the same wire is fo..
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