5. Let R be the region bounded by the graph of, y Inr + 1) the line y 3, and the line x - 1. (a)S...
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...
Let R be the region in the first quadrant bounded by the x-axis and the graphs of y = in(x) and y=5-x, as shown in the figure above. a) Find the area of R. b) Region R is the base of a solid. For the solid, each cross-section perpendicular to the x-axis is a right isosceles triangle whose leg falls in the region. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid. c)...
1) Problem 12 The area of the region bounded by the parabola x y-3) and the line y x is Problem 13 The base of a solid S is the parabolic region [(x.y):x s y S 1). Cross-sections perpendicular the y-axis are squares. Find the volume of the solid S 1) Problem 12 The area of the region bounded by the parabola x y-3) and the line y x is Problem 13 The base of a solid S is the...
B and C Please! Rate for sure Letf be the function given by f(x)--16x2 +64x and let line l be the line tangent to the graph off atx-2, as shown in the figure to the right. Let R be the region bounded by the graph of f and the x-axis and let S be the region bounded by the graph of f line I, and the x-axis. a. Find the equation of line 1 C2- 64+61-12 - 72 C2,72 b....
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...
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...
4. Let R be the region bounded by x = y2 and x = 4. see picture. Find the volume of the solid of base R, whose cross-sections are equilateral triangles perpen- dicular to the x-axis. 2 y R х 1 2 3 -1 -2
8. Consider the region bounded by the y = x2 - 2x + 1 and y = 1 + 2x - x? Find the area of the region. a. b. Find the volume of the solid when the region is rotated about the x-axis. c. Find the volume of the solid when the region is rotated about the y-axis. d. Find the volume of the solid when the region is rotated about the line x = 5. e. If the...
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...
A volume is described as follows: 1. the base is the region bounded by x y2 + 6y + 109 and x-y2-26y + 187; 2. every cross section perpendicular to the y-axis is a semi-circle. Find the volume of this object. Preview volune A volume is described as follows: 1. the base is the region bounded by x y2 + 6y + 109 and x-y2-26y + 187; 2. every cross section perpendicular to the y-axis is a semi-circle. Find the...