Problem 2. Find all pairs (s, t) of Gaussian integers s,t e Z[i] that satisfy (7+4i)s+ (11+2i)t =3+i. You must provide a brief justification of why the solutions satisfy the equation and why thereare no other solutions.

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Answered: 3+i. You must provide a brief…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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#14
A classic physics problem states that if a projectile is shot vertically up into the air with an initial velocity of 155 feet per second from an initial height of 59 feet off the ground, then the height of the projectile, h, in feet, t seconds after it's shot is given by the equation: h=-16t2 + 155t +59 Find the two points in time when the object is 95 feet above the ground. Round your answers to the nearest hundredth of a second (two decimal places). Answer: The object is 95 feet off the ground at the following times: Enter your two answers separated by a comma.
Solve and check for extraneous solutions. V20-2x = x - 6 Give both solutions, smaller one first, and state whether they are extraneous (Y or N). Smaller solution: x = Extraneous? Larger solution: x = Extraneous7 Blank 1: Blank 2: Blank 3: Blank 4: Submit
2. Consider the function y(x) = 5x over the interval [0, 10]. (a) If the points A(0, y(0)), B(5, y(5)), and C(10, y(10)) are on the curve represented by the above function, find the slope of the lines (secants) AB, and AC, respectively. (b) If x represents time and y represents the displacement of a particle moving along a line, what is the physical meaning of your results to part (a)? (c) Now consider a point D(10 – h, y(10 – h)) on the curve represented by the given function, find the slope of the line DC. (d) As h → 0, what is the limiting value of your result to part (c)? (e) What is its physical meaning of your result to part (d) if again x represents time and y represents the displacement?
-5V12x +17 b. 621x - 14 + 8 = 5 a. 2. Show how to solve the equation. Remember to check for extraneous solutions x - 5 = V10 - 2x
Isolate the variable and solve. To isolate x, we must eliminate the negative sign in front of the x. Because -x means –1x, we can do this by multiplying (or dividing) both sides of the inequality by -1. We are multiplying by a negative number. Thus, we must reverse the direction of the inequality symbol. (-1)(-x) = (-1)(-14) Multiply both sides by -1 and change the sense of the inequality. x < 14 Simplify.

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3+i. You must provide a brief justification of why the solutions satisfy the equation and why there are no other solutions.