Question

There is a line through the origin that divides the region
bounded by the parabola y=8x−7x2 and the *x*-axis into two
regions with equal area. What is the slope of that line?

Answer #1

Consider the region bounded by the line y = 2x and the parabola
y = 2x2-2x.
a. Evaluate the volume obtained by rotating this region about
the line x = -5
b. Evaluate the volume obtained by rotating this region about
the line y = -10

1) Find the area of the region bounded by the curves y = 2x^2 −
8x + 12 and y = −2x + 12
a) Find the volume when the area in question 1 is revolved
around the x-axis.
b)Find the volume when the area in question 1 revolved around
the y-axis.

Find the volume generated by revolving the area bounded by the
parabola y^2 = 8x and its latus rectum about the latus rectum. Use
the shell method.

Find the area of the region bounded by the parabola y = 1 + 2x -
x^2 and the parabola y = 1 + x^2. Please show the steps involved to
obtain the boundaries.
Please be legible and do not use cursive. Please show all work,
including ALL algebra. Thank you for your help!

Find an equation of the normal line to the parabola y = x2 − 8x
+ 4 that is parallel to the line x − 4y = 5.
y =

Find the centroid of the region that is bounded by the line Y =
3X, the line X = 2 and the X
axis.

A. For the region bounded by y = 4 − x2 and the x-axis, find
the volume of solid of revolution when the area is revolved
about:
(I) the x-axis,
(ii) the y-axis,
(iii) the line y = 4,
(iv) the line 3x + 2y − 10 = 0.
Use Second Theorem of Pappus.
B. Locate the centroid of the area of the region bounded by y
= 4 − x2 and the x-axis.

Find the area of the region bounded by the curves y=3x2 and
y=−8x+3. please show work. thanks

Consider the region R bounded in the first quadrant by y = 1 −
x. Find the horizontal line y = k such that this line divides the
area of R equally in half.

Find the area of the region in the ?? x y -plane bounded above
by the graph of the function ?(?)=9 , below by the ? -axis, on the
left by the line ?=8 , and on the right by the line ?=19 . The area
is

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