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Where S is the hemisphere x 2 + y 2 + z 2 = 16, z ≥ 0. ... Unlock. Previous question Next question. Transcribed image text: Let S be the hemisphere x2 + y2 + z2 = 16, with z 2 0, and evaluate the surface integral in the counterclockwise direction. S[ (x2 + y2)z ds 161 . Not the question you’re looking for? Post any question and get expert ...
We find the surface integral ∫ ∫ ( x 2 + y 2) d S where S be the hemisphere x 2 + y 2 + z 2 = 4 with z ≥ 0. The parameterization of S is. r ( ϕ, θ) = 2 sin ϕ cos θ, 2 sin ϕ sin θ, 2 cos ϕ , 0 ≤ θ ≤ 2 π, 0 ≤ ϕ ≤ π 2 ∴ r ϕ = 2 cos ϕ cos θ, 2 cos ϕ sin θ, − 2 sin ϕ . View the full answer Answer. Unlock.
EJERCICIO 7 : Halla el mínimo de la función z = 3 x + 2 y con las siguientes restricciones: ≥ ≥ + ≥ + ≤ 0 0 3 2 2 3 4 12 y x x y x y Solución: − + = → = − + = → = • 2 2 3 3 2 2 4 12 3 3 4 12 Representa mos las rectas x x y y x x y y y hallamos la región que cumple las condiciones del problema, teniendo en cuenta que x ≥ ...
Use the surface integral in Stokes’ theorem to calculate the circulation of field F, F (x, y, z) = x 2 y 3 i + j + z k F (x, y, z) = x 2 y 3 i + j + z k around C, which is the intersection of cylinder x 2 + y 2 = 4 x 2 + y 2 = 4 and hemisphere x 2 + y 2 + z 2 = 16, z ≥ 0, x 2 + y 2 + z 2 = 16, z ≥ 0, oriented counterclockwise when viewed ...
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Q 5. Minimize Z = x + 2y, subject to constraints are 2x + y ≥ 3, x + 2y ≥ 6 and x, y ≥ 0. Show that the minimum of Z occurs at more than two points. View Solution. Click here:point_up_2:to get an answer to your question :writing_hand:minimize z x 2ysubject to the constraints2x y geq 3x 2y.
