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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:
Consider the transformation w = (z + 2)2 where w = u+ jv and z = x + jy. Determine the image in the W-plane of the line y = x + 1 in the Z-plane.
question biologists stocked a lake with 400 fish and estimated the carrying capacity the maximal population for the
the everton college store paid $1824 for an order of 52 calculators. The store paid $ 8 for each scientific calculator. The others, all graphing calculators, cost the store $ 52 each. How many of each type of calculator was ordered?
Factor z5 + z + 1 into two polynomials with integer coefficients. Find all roots of z6 + z4 + z3 + z2 + 1 = 0
an object is propelled straight up from ground level. this translates to y=-16t^2+80t where y is the height of the object meaasured in feet and t is the time in seconds after it is propelled. when does the object hit the ground?
Let (a, b) ⊆ R be a non-degenerate open bounded interval, and let f: (a, b) → R be a function. Prove that F is continuous
what are the domain and the image of the absolute value function?
ased upon statistical studies it has been found that 3.32% of all births in the United States will result in twins being born. If 17,300 births are selected at random what is the probability that: Find the Probability of Twin Births
The assembly line that produces an electronic component of a missile system has historically resulted in a 2% defective rate. A random sample of 50 components is drawn. What is the standard error of the proportion?
Explain Working with half life of a radioactive material, If a sample has a mass of 200 mg find a function describing the mass that remains after t days
What does Marriott pay Macy?
Parts being manufactured at a plant are supposed to weigh 40 grams. Suppose the distribution of weights has a Normal distribution with mean 40 grams and a standard deviation 2 grams. Quality control inspectors randomly select 16 parts, weigh each,..
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