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Question 1. Find the roots of the equation x4 - 2x3 + 4x2 + 6x - 21 = 0, given that sum of two of its roots is zero.
Question 2. The Ellipse E1: x2/4 + y2/9 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point (0 , 4) circumscribes the rectangle R. Find the eccentricity of the ellipse E2.
Hiking on a level trail going due east, you decide to leave the trail and climb toward the mountain on your left.
Make a change of variable that decouples the equation x' = Ax. Write the equation x (t) = Py (t) and show the calculation that leads to the uncoupled system.
A cord can bear a maximum force of 100 N without breaking. A body of mass 1 kg tied to one end of a cord of length 1 m is revolved in a horizontal plane. What is the maximum linear speed of the body so that the cord does not break?
Let xn be a sequence of real numbers.
find the 95% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to be accurate within 25 milligrams?
How fast is the radius changing at the instant when the radius is 4 inches? How fast is the surface area changing at the same instant?
Why does the argument that "anything that is legal is ethical" is insufficient? Please write a 3 page paper using APA citations. Please cite absolutely everything used from outside sources.
A MIXTURE PROBLEM A tank initially contains 10 gal of brine with 2 lb of salt. Brine with 1.5 lb of salt per gallon enters the tank at the rate of 3 gal/min.
Determine whether the following disputes are verbal, factual, or some combination of the two. If verbal, discuss whether the dispute arises from vagueness or ambiguity.
Find each of the following probabilities when n independent Bernoulli trials are carried out with probability of success p.
The cost of renting a truck is $230 per week plus a charge of $0.50 per mile driven. Write a linear equation that relates the cost C for a weekly rental in which the truck is driven x miles.
Can the sample standard deviations s1 and s2 be used in place of the population standard deviations σ1 and σ2?
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