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Mr. Cub is somewhere in the Chicago area and he wants to get to a warmer place. He knows that if he goes north for one mile, the temperature drops by 4 degrees (he just came from there), and if he goes west for one mile, the temperature drops by 3 degrees (his friend just came from there). Mr. Cub decides to go southeast. Estimate how the temperature changes after he goes for one mile.

Mr. Cub is somewhere in the Chicago area and he wants to get to a warmer place. He knows that if he goes north for one mile, the temperature drops by 4 degrees (he just came from there), and if he goes west for one mile, the temperature drops by 3 degrees (his friend just came from there). Mr. Cub decides to go southeast. Estimate how the temperature changes after he goes for one mile.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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EL- B-1 and EL B-2

Problem EL – B1. Find all points on the surface S = {(x,y, z)|x² – y² + 7 = -1}} that are closest to the point (0,0, 1). Problem EL – B2. Mr. Cub is somewhere in the Chicago area and he wants to get to a warmer place. He knows that if he goes north for one mile, the temperature drops by 4 degrees (he just came from there), and if he goes west for one mile, the temperature drops by 3 degrees (his friend just came from there). Mr. Cub decides the temperature changes after he goes for one mile. go southeast. Estimate how Problem EL – B3. Show that the vector field F(x,y): (3+ 2xy, x² – 3y²) is conservative, and then evaluate the line integral F. dr, where r is the vector curve r(t) = (e' sin t, e' cos t) for 0 < t < n. Problem EL – B4. A projectile is fired from the ground into the air with angle of elevation 0, at an initial speed of 20 m/s. There is a tailwind blowing in the same direction as the projectile's movement. giving a steady horizontal acceleration of 2 m/s². assume that the projectile lands on the ground exactly 2 seconds after it was fired. determine the angle 0, and the distance between the original position of the projectile and the point at which it lands.
Transcribed Image Text:Problem EL – B1. Find all points on the surface S = {(x,y, z)|x² – y² + 7 = -1}} that are closest to the point (0,0, 1). Problem EL – B2. Mr. Cub is somewhere in the Chicago area and he wants to get to a warmer place. He knows that if he goes north for one mile, the temperature drops by 4 degrees (he just came from there), and if he goes west for one mile, the temperature drops by 3 degrees (his friend just came from there). Mr. Cub decides the temperature changes after he goes for one mile. go southeast. Estimate how Problem EL – B3. Show that the vector field F(x,y): (3+ 2xy, x² – 3y²) is conservative, and then evaluate the line integral F. dr, where r is the vector curve r(t) = (e' sin t, e' cos t) for 0 < t < n. Problem EL – B4. A projectile is fired from the ground into the air with angle of elevation 0, at an initial speed of 20 m/s. There is a tailwind blowing in the same direction as the projectile's movement. giving a steady horizontal acceleration of 2 m/s². assume that the projectile lands on the ground exactly 2 seconds after it was fired. determine the angle 0, and the distance between the original position of the projectile and the point at which it lands.
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