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An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. The figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T₁,..., T4 denote the temperatures at the four interior nodes of the figure. The temperature at a node is approximately equal to the average of the four nearest nodes-to the left, above, to the right, and below. Solve the system of equations below to find the temperatures T₁,..., T4- 4T₁ - T₂ - T4 = 35 -T₁ +4T₂ - T3 - T₂+4T3 -T₁ = 65 T4 = 70 - T3 +4T4 = 40 10° B. The system has infinitely many solutions. OC. The system has no solution. 10° Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The unique solution of the system is (11-1). (Type integers or decimals rounded to the nearest thousandth as needed.) 25° 25° 1 2 4 3 30° 30° 40° 40°

An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. The figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T₁,..., T4 denote the temperatures at the four interior nodes of the figure. The temperature at a node is approximately equal to the average of the four nearest nodes-to the left, above, to the right, and below. Solve the system of equations below to find the temperatures T₁,..., T4- 4T₁ - T₂ - T4 = 35 -T₁ +4T₂ - T3 - T₂+4T3 -T₁ = 65 T4 = 70 - T3 +4T4 = 40 10° B. The system has infinitely many solutions. OC. The system has no solution. 10° Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The unique solution of the system is (11-1). (Type integers or decimals rounded to the nearest thousandth as needed.) 25° 25° 1 2 4 3 30° 30° 40° 40°

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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An important concern in the study of heat transfer is to determine the​ steady-state temperature distribution of a thin plate when the temperature around the boundary is known. The figure represents a cross section of a metal​ beam, with negligible heat flow in the direction perpendicular to the plate. 

An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. The figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T₁,..., T4 denote the temperatures at the four interior nodes of the figure. The temperature at a node is approximately equal to the average of the four nearest nodes-to the left, above, to the right, and below. Solve the system of equations below to find the temperatures T₁,..., T4- 4T₁ - T₂ - T4 = 35 -T₁ +4T₂ - T3 -T₁ = 65 - T₂+4T3 T4 = 70 - T3 +4T4 = 40 10° B. The system has infinitely many solutions. OC. The system has no solution. 10° Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The unique solution of the system is (11-1). (Type integers or decimals rounded to the nearest thousandth as needed.) 25° 25° 1 2 4 3 30° 30° 40° 40°
Transcribed Image Text:An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. The figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T₁,..., T4 denote the temperatures at the four interior nodes of the figure. The temperature at a node is approximately equal to the average of the four nearest nodes-to the left, above, to the right, and below. Solve the system of equations below to find the temperatures T₁,..., T4- 4T₁ - T₂ - T4 = 35 -T₁ +4T₂ - T3 -T₁ = 65 - T₂+4T3 T4 = 70 - T3 +4T4 = 40 10° B. The system has infinitely many solutions. OC. The system has no solution. 10° Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The unique solution of the system is (11-1). (Type integers or decimals rounded to the nearest thousandth as needed.) 25° 25° 1 2 4 3 30° 30° 40° 40°
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