Let R be the region bounded by the y-axis and the graphs and as shown in the figure to the right. The region R is the base of a solid. Find the volume of this solid, assuming that each cross section perpendicular to the x-axis is: a) a square. b) an equilateral triangle. Let R be the region bounded by the y-axis 4. and the graphs y = 1+x2 and y 4-2x 2x y = 4 as shown in the...
5. Let R be the region bounded by the graph of, y Inr + 1) the line y 3, and the line x - 1. (a)Sketch and then find the area of R (b) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is an equilateral triangle. (c) Another solid whose base is also the region R. For this solid, each cross section perpendicular to the x-axis is a Semi-circle...
1 Let R be a region bounded between two curves on the r, y-plane. Suppose that you are asked to find the volume of the solid obtained by revolving the region R about the r-axis If you slice the region R into thin horizontal slices, i.e., parallel to the r-axis, in setting up the Riemann sum, then which method will come into play? A. Disc method B. Washer method C. Either disc or a washer method depending on the shape...
4. (Calculator) Let R be the region bounded by the graphs of f(x)= 20+x-x2 and g(x)=x-5x. (a) Find the area of R. (b) A vertical line x k divides R into two regions of equal area. Write, but do not solve, an equation that could be solved to find the value of k (c) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse...
11. Find the volume of the given right tetrahedron. (Hint: Consider slices perpendicular to one of the labeled edges.) 3. The solid lies between planes perpendicular to the x-axis at x= -1 and x = 1. The cross-sections perpendicular to the I-axis between these planes are squares whose bases run from the semicircle y = -VI-to the semicircle y = VI- 4. The solid lies between planes perpendicular to the x-axis at x= -1 and .x = 1. The cross-sections...
Find the volume of the solid generated by revolving the region R bounded by the graphs of the given equations about the y-axis. 17)x= x=0, between y=- 4 and y = 4 17) 18) bounded by the circle x2 + y2 = 16, by the line x = 4, and by the line y = 4 18) Find the volume of the solid generated by revolving the region about the given line. 19) The region in the first quadrant bounded...
3. Let R be the region bounded by the graphs of y4, and the -axis Find the volume of the solid that has R as its base if every cross section by a plane perpendicular to the x-axis is a square. Please include a picture of the base and the slice and write the area and volume of the slice. 5.333 2 3 3. Let R be the region bounded by the graphs of y4, and the -axis Find the...
I'm getting it wrong for some reason and it's literally right?! Can someone explain to me what is going on Let S be the solid with flat base, whose base is the region in the z y plane defined by the curves y - e,y--1,0and a-1, and whose cross sections perpendicular to the x axis are equilateral triangles with bases that sit in the r y plane a) Find the area A() of the cross-section of S given by the...
Find the perimeter of the parametric curve given by cos3 t sin3t for 0sts2T (10) Find the volume of the solid whose base is the region bounded by the parabolas y2 and y 8- and whose cross-sections perpendicular to the y-axis are semicircles. Find the perimeter of the parametric curve given by cos3 t sin3t for 0sts2T (10) Find the volume of the solid whose base is the region bounded by the parabolas y2 and y 8- and whose cross-sections...
PLZ HELP ME...I am trying to understand calculus problems but they are not making sense 4. Consider the region R bounded between y = 1 and y=1 on the interval (0,2). (1 - 1) dr equal to the volume of the solid whose base is R and whose cross-sections perpen- dicular to the s-axis are squares? ") dr equal to the volume of revolution obatained by revolving R about the z-axis? Explain in 1 2 sentences why one of these...