The figure below shows the slope field for the equation y' = sin(x) cos(y).2,0On a print out of this slope field, sketch the solution that passes through the point (0, π/2).345TWhat is the equation of the solution passing through (0,y =

Given That : A differential equation is y'=sinxcosy, We have to find: a) Sketch the solution that…

Answered: On a print out of this slope field,…

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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The robotic arm you are working with extends to pick up components at various speeds. Its extension velocity changes over time due to the dynamics of the manufacturing process. The equation governing its extension velocity is given by where y represents the extension length in meters and t represents time in seconds. Calculate the extension length of the robotic arm at t=5 seconds.
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
The equation of a curve is y=4x²+ 4lx+12-k, where kis a constant. In the case where k =1, find the equation of the tangent to the curve which is parallel to the x-axis.
Suppose you are climbing a hill whose shape is given by the equation z = 1600 – 0.005x² – 0.01y², where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1566). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? ascend descend At what rate? (Round your answer to two decimal places.) vertical meters per horizontal meter (c) In which direction is the slope largest? What is the rate of ascent in that direction? vertical meters per horizontal meter At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.)
Give the slope and the y intercept of the line – 10x + ly – 5 = 0. Slope = y intercept = (0, Enter your answers as integers or as reduced fractions in the form A/B.

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On a print out of this slope field, sketch the solution that passes through the point (0, π/2). What is the equation of the solution passing through (0, 345)? y =