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Q1 (10 points) We want to compute the volume when we revolve a region about an...
Math232 2 Consider the region in first quadrant area bounded by y x,x=6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method, and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution Find the moment of inertia of the solid of revolution with respect to the x-axis. d)
Math232 2 Consider...
Math23 2 Consider the region in first quadrant area bounded by y x, x 6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution. c) Find the coordinates of the centroid of the plate; on the sketch above, show the vertical...
Q4a (10 points) a) Name and explain the two roles banks play in the economy discussed in class. + Drag and drop your files or click to browse.. Q4b (10 points) Use the following information to answer parts 4b, 4c, and 4d: Consider an economy with a large number of restaurants. The restauranteur lacks the funds to start the restaurant. There is an equal number of investors who have the funds but no desire run a restaurant, say 2 trillion...
Question 5 +(-12) and y= la. We assume that the density of We want to compute the centre- f mass (or centroid) of the region enclosed by the curves y this flat regian is constant. a) Find the -coordinate of the points of intersection of these two curves. List your values separated by semicolons. 1 point How Did I Do? Answer: of the region R. b) Find the area A=Number c) Find the moment My of the region R about...
both parts please
Consider the region in the first quadrant bounded by the curves y = 3x, y = 3 - (x - 1)2, and y = 2. (a) Sketch the region. Note all points of intersection. (You may use GeoGebra if necessary, but you can probably do it faster by hand.) (b) Using either the washer or shell method, set up (but do not solve) an integral that computes the volume obtained when the region is revolved about the...
7. Match the volume of the solid obtained by rotating the region bounded by the given curves about about the given axis to the corresponding integra 1, the region bounded by y-V , х--8 and the x-axis about the x-axis. 2. the region bounded by 8 and the r-axis about the y-axis. 3, the region bounded by y-V , y-2 and the y-axis about the x-axis. 4. the region bounded by V2 and the y-axis about the y-axis. 5, the...
2/6 2" (10%) (a) Sketch the graphs of the two functions y=z(4-z) and y=z and mark the finite region (R) enclosed between them. (Identify (R) carefully!) (b) Let W be the volume of the solid of revolution obtained by revolving the above region (R) around the y-axis. (i) Use the shell method to write down the integral for W. (No need to evaluate the integral.) (ii) Repeat part(i) by using the disk method.
2/6 2" (10%) (a) Sketch the graphs...
+ Drag and drop your files or click to browse. Q4 (10 points) You are at a circular lake with radius 30 km, centered at the point(0,0). You want to travel from (30,0) to (-30,0). You will row from (30, 0) in a straight line to a point on the shore that is angle 8 radians around the lake from where you started, and then you will walk the rest of the way along the circular shore to (-30,0). Your...
(10 points) 4. Find the volume of the solid obtained by rotating about the x-axis the region between the graph of y = e*, the x-axis, and the lines x 1 x 2 in the first quadrant about the x-axis. Draw a sketch of this solid. 5 3- 2- 1- -4 -1 5 3 0 1 2 5
(10 points) 4. Find the volume of the solid obtained by rotating about the x-axis the region between the graph of y...
3. (a) If the region sketched in (1) above is revolved about the line y -0 (x-axis), sketch and label the typical rectangle(s) needed to use the shell method to find the volume of the resulting solid. (b) Use the shell method to find the volume of the resulting solid 2 pts [9 pts] 4. (a) If the region sketched in (1) above is revolved about the line x-O。-axis), sketch and label the typical rectangle(s) needed to use the disk/washer...