EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Textbook Question
Chapter 71, Problem 18A
For each angle, sketch a right triangle. Label the sides of the triangles
179.90°
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2. Consider the ODE
u' = ƒ (u) = u² + r
where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r:
(a) Sketch ƒ(u) = u² + r and determine the equilibrium points.
(b) Draw the phase line.
(d) Determine the stability of the equilibrium points.
(d) Plot the direction field and some sample solutions,i.e., u(t)
(e) Describe how location of the equilibrium points and their stability change as you increase the
parameter r.
(f) Using the matlab program phaseline.m generate a solution for each value of r and the initial
condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption.
(g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode
over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to
turn in a plot for (g), just describe what happens.
True or False and why
10
5
Obtain by multiplying matrices the composite coordinate transformation of two transformations, first
x' = (x + y√√2+2)/2
y' =
z'
(x√√2-2√2)/2
z = (-x+y√√2-2)/2
followed by
x"
=
(x'√√2+z'√√2)/2
y" = (-x'y'√√2+2')/2
z" = (x'y'√√2-2')/2.
Chapter 71 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 71 - Prob. 1ACh. 71 - Find the distance y to the nearest hundredth of an...Ch. 71 - Prob. 3ACh. 71 - If A = 3650', determine sin A, cos A, tan A, cot...Ch. 71 - Prob. 5ACh. 71 - Find x.Ch. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 9ACh. 71 - For each angle, sketch a right triangle. Label the...
Ch. 71 - Prob. 11ACh. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 13ACh. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 15ACh. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 17ACh. 71 - For each angle, sketch a right triangle. Label the...
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- Not use ai pleasearrow_forward4 The plane 2x+3y+ 6z = 6 intersects the coordinate axes at P, Q, and R, forming a triangle. Draw a figure and identify the three points on it. Also find vectors PQ and PR. Write a vector formula for the area of the triangle PQR and find its value.arrow_forwardAND B A Ꭰarrow_forward
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