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Imagine that the filter of a dishwasher machine, that looks like the boundary of V =...
Imagine that the filter of a dishwasher machine, that looks like the boundary of V =...
Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x, y, z) e R3 : Vx2 + y2 <z<1}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(yº) + x3,2xz cos(x²)+y3,0) Compute the flux through the filter (SJ, F. nds). Is there more water entering the filter or leaving it? O Entering O Same Leaving
Imagine that the filter of a dishwasher machine, that looks like the boundary of V =...
Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x, y, z) € R3 : Vx2 + y2 <2<1}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(yº) + x3,2xz cos(x?) + y3,0) Q1.1 3 Points Draw a sketch of the filter, and mark any points you think will be relevant. Please select file(s) Select file(s) Q1.2 8 Points Compute the flux through the filter (SS, F....
Q1 13 Points Imagine that the filter of a dishwasher machine, that looks like the boundary...
Q1 13 Points Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x,y,z) € R3 : x2 + y2 <z<1}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(yº) +23, 2cz cos(x2) + y,0) Q1.1 3 Points Draw a sketch of the filter, and mark any points you think will be relevant. Please select file(s) Select file(s) Q1.2 8 Points Compute the flux through the filter (SS,...
13 Points .. Imagine that the filter of a dishwasher machine, that looks like the boundary...
13 Points .. Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x, y, z) € R3 : Vx2 + y2 <z 51}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(y2) + x3,2x2 cos cos(x2) + 43,0) Q1.1 3 Points Draw a sketch of the filter, and mark any points you think will be relevant. Q1.2 8 Points Compute the flux through the filter (Sſs F....
answer all parts, please! (5) Consider the closed volume V contained by the cylinder r2+2-4 and the planes y =-2 and r +y-3. Let the surface S be the boundary of this region. Note that this boundary...
answer all parts, please!
(5) Consider the closed volume V contained by the cylinder r2+2-4 and the planes y =-2 and r +y-3. Let the surface S be the boundary of this region. Note that this boundary consists of three smooth pieces. (a) Clearly sketch and label S. (You may use GeoGebra for this.) (b) In complete sentences, verbally describe what this surface looks like. (c) Find a parametric representation for each of the three parts of the boundary S...
1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and ...
please help with Q1 and 3
1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are s...
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are skew lines. 3 marks 2. Let S be the region given by S-((z, y) E R: z2 + y2 4,z? + y2-4y2 0,#2 0, y 20} 1 mark (a) Sketch the region S; (b) Consider the change of variables given by u2 , a2 +y-4y. Describe the region S as set in terms of the variables u and v. Call this...
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t)...
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t) = (cost, sint, sin 2t), 0<t<27 and let v be the vector field in space defined by v(x, y, z) = (et - yº, ey + r), e) (a) Show that C lies on the cylinder x2 + y2 = 1 and the surface z = 2cy. (b) This implies that C can be seen as the boundary of the surface S which is...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
NO.25 in 16.7 and NO.12 in 16.9 please. For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs...
NO.25 in 16.7 and NO.12 in
16.9 please.
For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...
Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x, y, z) e R3 : Vx2 + y2 <z<1}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(yº) + x3,2xz cos(x²)+y3,0) Compute the flux through the filter (SJ, F. nds). Is there more water entering the filter or leaving it? O Entering O Same Leaving
Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x, y, z) € R3 : Vx2 + y2 <2<1}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(yº) + x3,2xz cos(x?) + y3,0) Q1.1 3 Points Draw a sketch of the filter, and mark any points you think will be relevant. Please select file(s) Select file(s) Q1.2 8 Points Compute the flux through the filter (SS, F....
Q1 13 Points Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x,y,z) € R3 : x2 + y2 <z<1}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(yº) +23, 2cz cos(x2) + y,0) Q1.1 3 Points Draw a sketch of the filter, and mark any points you think will be relevant. Please select file(s) Select file(s) Q1.2 8 Points Compute the flux through the filter (SS,...
13 Points .. Imagine that the filter of a dishwasher machine, that looks like the boundary of V = {(x, y, z) € R3 : Vx2 + y2 <z 51}, is immersed by water with a flow given by: F(x, y, z) = (2yz cos(y2) + x3,2x2 cos cos(x2) + 43,0) Q1.1 3 Points Draw a sketch of the filter, and mark any points you think will be relevant. Q1.2 8 Points Compute the flux through the filter (Sſs F....
answer all parts, please!
(5) Consider the closed volume V contained by the cylinder r2+2-4 and the planes y =-2 and r +y-3. Let the surface S be the boundary of this region. Note that this boundary consists of three smooth pieces. (a) Clearly sketch and label S. (You may use GeoGebra for this.) (b) In complete sentences, verbally describe what this surface looks like. (c) Find a parametric representation for each of the three parts of the boundary S...
please help with Q1 and 3
1. Let V be the solid region in R3 that lies within the sphere 2+y+z2-4, above the zy-plane, and below the cone z -Vx2 + y2 (a) Sketch the region V (b) Calculate the volume of V by using spherical coordinates. (c) Find the surface area of the part of V that lies on the sphere z2 y 24, by calculatinga surface integral. (d) Verify your solution to (c) by calculating the surface integral...
1. Are £i and C2 skew lines? Explain your answer and find the distance between them if they are skew lines. 3 marks 2. Let S be the region given by S-((z, y) E R: z2 + y2 4,z? + y2-4y2 0,#2 0, y 20} 1 mark (a) Sketch the region S; (b) Consider the change of variables given by u2 , a2 +y-4y. Describe the region S as set in terms of the variables u and v. Call this...
(7.5 points) Let C be the oriented closed space curve traced out by the parametrization r(t) = (cost, sint, sin 2t), 0<t<27 and let v be the vector field in space defined by v(x, y, z) = (et - yº, ey + r), e) (a) Show that C lies on the cylinder x2 + y2 = 1 and the surface z = 2cy. (b) This implies that C can be seen as the boundary of the surface S which is...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
NO.25 in 16.7 and NO.12 in
16.9 please.
For the vector fied than the vecto and outgoing arrows. Her can use the formula for F to confirm t n rigtppors that the veciors that end near P, are shorter rs that start near p, İhus the net aow is outward near Pi, so div F(P) > 0 Pi is a source. Near Pa, on the other hand, the incoming arrows are longer than the e the net flow is inward,...
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