Assuming the result that the centroid of a solid hemisphere lies on the axis of symmetry...
(For 5b, please use the y-axis as the axis of symmetry for the
cylinder)
5) a-b Set-up the flux integrals for the given surfaces in the variables indicated. Your final answer should be a scalar- valued double integral. That is, the double integral should does not contain any vector quantities. The differential is given. Do not solve the integrals you setup in a. and b. No work is needed for a-b. a. F(x, y, z) = 5î + 10ủ +...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1,
above the xy-plane, and below the plane z = 1 + x. Let S be the
surface that encloses E. Note that S consists of three sides: S1 is
given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2
+ y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
(1 point) Consider a right circular solid cone S standing on its tip at the origin. The height of the cone is 3 and the radius of the top is 8. Find the centroid of the cone by following the steps below. Assume the density of the cone is constant 1. a. The mass of the cone is m Jls 1 d(x, y, 2) b. Let Q(2) be the disk that is the intersection of the cone with the horizontal...
Compute the volume of the solid whose base is the area bounded by the z-axis and the curve y = 1- 24 between x = -1 and a 1 and whose vertical cross sections are rectangles with height 2. Enter your answer as a decimal to three places.
uestion 5 The base of a solid is the circle x 9. Find the volume of the solid given that the cross sections perpendicular to the x-axis are squares. а) @ 146 b) 147 e) 148 d) 144 e) 143 uestion 7 ketch the region bounded by the following curves and etermine the centroid of the region. y=x2-2x and y=5x-x2 (12) 21 7 15 21 b) 16 7 21 13 7 7 13 8' 8 Review Later Question 8 Find...
7. Assume (x, y,x)(2xy, y',5z - y). Let E be the solid upright cylinder between the planes z 0 and z-3 with base the disc x2 + y2 < 9, and let S be the outwardly oriented boundary surface of E. Note that S consists of three smooth surfaces; the surface Si of the cylinder, plus the top disc Di and the bottom disc D2. Follow the steps to verify the Divergence Theorem. (a) [12 pts.] Evaluate dS directly
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plz? help sir
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A transparent glass hemisphere with radius R and mass m has an index of refraction n. In the medium outside the hemisphere, the index of refraction is equal to one. A parallel beam of monochromatic laser light is incident uniformly and normally onto the central portion of its planar surface, as shown in Figure 3. The acceleration of gravity g is vertically downwards. The radius 8 of the circular cross-section of the laser beam is much...
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,...
Heres example 10.2
(3) (30 points) In Example 10.2, the moment of inertia tensor for a uniform solid cube of mass Mand side a is calculated for rotation about a corner of the cube. It also worked out the angular momentum of the cube when rotated about the x-axis - see Equation 10.51. (a) Find the total kinetic energy of the cube when rotated about the x-axis. (b) Example 10.4 finds the principal axes of this cube. It shows that...
We've been using L'Hopitals as well as family of functions and
modeling. stuff from chapter 4 in the 7th Edition of single
variable calculus book.
1. (7 points) A rectangle is located with its base along the x axis, one corner at (8,0) and the opposite corner on the graph y = ln(x) for some 1 x 10. Draw a picture of the given scenario. a. If the other corner along the x axis an x value of e, what...