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et the temperature T in degrees at the point (x,y,z), with distances measured in cm, be T(x,y,z)=4x -4y+3z. Let q be the real numb uch that the rate at which the change in temperature at (-2,0,2) per unit change in the distance travelled in the direction of the vector (1,q,1> is 4°/cm. Find q. (Note that the "direction" of a vector is always a unit vector "pointing the same way.") none of the other answers -7/40 17/56 1/12 1/2

et the temperature T in degrees at the point (x,y,z), with distances measured in cm, be T(x,y,z)=4x -4y+3z. Let q be the real numb uch that the rate at which the change in temperature at (-2,0,2) per unit change in the distance travelled in the direction of the vector (1,q,1> is 4°/cm. Find q. (Note that the "direction" of a vector is always a unit vector "pointing the same way.") none of the other answers -7/40 17/56 1/12 1/2

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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**Problem Statement:** Let the temperature \( T \) in degrees at the point \( (x, y, z) \), with distances measured in cm, be given by \( T(x, y, z) = 4x - 4y + 3z \). Let \( q \) be the real number such that the rate at which the change in temperature at \( (-2, 0, 2) \) per unit change in the distance traveled in the direction of the vector \(\langle 1, q, 1 \rangle\) is \( 4^\circ/\text{cm} \). Find \( q \). (Note that the "direction" of a vector is always a unit vector "pointing the same way.") **Answer Choices:** - ○ none of the other answers - ○ \(-7/40\) - ○ \(17/56\) - ○ \(1/12\) - ○ \(1/2\)
Transcribed Image Text:**Problem Statement:** Let the temperature \( T \) in degrees at the point \( (x, y, z) \), with distances measured in cm, be given by \( T(x, y, z) = 4x - 4y + 3z \). Let \( q \) be the real number such that the rate at which the change in temperature at \( (-2, 0, 2) \) per unit change in the distance traveled in the direction of the vector \(\langle 1, q, 1 \rangle\) is \( 4^\circ/\text{cm} \). Find \( q \). (Note that the "direction" of a vector is always a unit vector "pointing the same way.") **Answer Choices:** - ○ none of the other answers - ○ \(-7/40\) - ○ \(17/56\) - ○ \(1/12\) - ○ \(1/2\)
**Solve the problem.** Find the equation for the tangent plane to the surface \( z = e^{9x^2 + 7y^2} \) at the point \( (0, 0, 1) \). - \( z = -1 \) - \( z = 2 \) - \( z = 1 \) - \( z = 0 \)
Transcribed Image Text:**Solve the problem.** Find the equation for the tangent plane to the surface \( z = e^{9x^2 + 7y^2} \) at the point \( (0, 0, 1) \). - \( z = -1 \) - \( z = 2 \) - \( z = 1 \) - \( z = 0 \)
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