Delta College Wk 3 Multivariable Calculas Questions

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wbuaan1234

Mathematics

Delta College

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Wk 03 Wednesday Breakout Session Wednesday, June 23, 2021 Team Members with Roster #s ____________________________________________________ As with all Wednesday Breakout Session, only one person will submit the answers for the group. It is the time to brainstorm, discuss, share potential answers, and come up with a consensus for submission. Be sure that everyone has input because once it is submitted, there can be no modifications after the deadline. Also, if you are not the “submitter” for the Breakout Session, what will appear on your gradebook page is a comment that no submission was entered. A classmate, Krystal, submitted a place-holder. If you want to submit some personal words of wisdom, a math cartoon, or Internet quote, I may select your words of wisdom to share with the class with my solutions. Math People (Think of it as you are learning a new language) Computer People (Think Before You Code. The computer may calculate fast, but it just does what you tell it to do.) Physics (Projectile Motion. There is more to this class than projectile motion.) Problem #1 for the early or veteran visualists on the team. (2 points, ½ point each) The image below (in red) is the domain of a function z = f(x, y). Illustrate what the graph might look like. (Note: The single dots and line segment (in white) are two points or a line in the xy-plane but are not in the domain of z = f(x, y).) Illustrate both the domain and the points in the function, z = f(x, y). Domain #1 Domain #2 Possible image of z = f(x, y) Possible image of z = f(x, y) Domain #3 Possible image of z = f(x, y) Domain #4 Possible image of z = f(x, y) Problem #2 (1 point) The line AC and BC are tangent to the surface, z = f(x, y), at point C(1, 2, 4). What is the expression AND value of the total differential, dz, at the point (1,2,4), if x = 0.03 and y = -0.01. Problem #3: (potential of 1 point with a possibility of a BONUS point) A rectangular box 8’ by 4’ by 4’ is illustrated at the right. If I give the box an orientation, a spider is located at on the left wall 1 foot above the floor and 1 foot from the front wall, and a fly is caught in the spider’s web that is one the right wall 1 foot from the ceiling and 1 foot from the back wall. It may be a 3D-world, but the spider is not Spiderman. Draw the shortest path from the spider to the fly. (Bonus Point) A bonus point would be given if the group describes the method you have selected to determine the solution AND the shortest distance (in feet) approximated to 2 decimal places. The group need not show the work. The description and answer would be sufficient to get the bonus. Explain and Deliver: Describer your method: What is the shortest path based on your calculations? Bonus Point Answer: ________________
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