Tutorial ExerciseFind the area of the part of the plane 3x + 2y + z = 6 that lies in the first octant.Part 1 of 52The surface S is the graph of a function z = f(x, y) over a region D in the xy-plane. The surface area of S can be calculated by A(S) =az1 +dzdA.дуf(x, y) = 6 – 3xaz2y. We, therefore, haveaxəz-3 and-2The plane 3x + 2y + z = 6 is the graph of the function z =3.xдуPart 2 of 5Therefore,=7 V1+(-3)² + (-2)² dA =V14dA.Since we want the area of the section of the plane that lies above the first octant, then the region D will be the triangular region bounded by the x-axis, the y-axis, and the line formed by the intersection of the plane with the plane z = 0. Substituting z = 0 into 3x + 2y + z = 6 and solving for y, we find that this line of intersection has the equationy =x +SubmitSkip (you cannot come back)

Find the area of the part of the plane 3x 2y 6 that les in the first octant. Part1ofs The surface Sis the graph of a function zx. y) over a region Din the xy-plane. The surface area of S can be calculated by A(S) -L V-()-() dA. The plane 3r+ 2y+6 is the graph of the function z fx, y)-6- -2y. We, therefore, have - and - 2 Part 2 ofS Therefore. Since we want the area of the section of the plane that les abeve the first octant. then the region D will be the triangular region bounded by the axis, the y-axis, and the line formed by the intersection of the plane with the plane z-0. Substituting z0 into 3x + 2y 6 and solving for y, we find that this line of intersection has the equation Semt Shyocnot.come bac

Find the area of the part of the plane 3x 2y 6 that les in the first octant. Part1ofs The surface Sis the graph of a function zx. y) over a region Din the xy-plane. The surface area of S can be calculated by A(S) -L V-()-() dA. The plane 3r+ 2y+6 is the graph of the function z fx, y)-6- -2y. We, therefore, have - and - 2 Part 2 ofS Therefore. Since we want the area of the section of the plane that les abeve the first octant. then the region D will be the triangular region bounded by the axis, the y-axis, and the line formed by the intersection of the plane with the plane z-0. Substituting z0 into 3x + 2y 6 and solving for y, we find that this line of intersection has the equation Semt Shyocnot.come bac

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 53E

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