Help me somebody please

Mathematics

1 answer:

STatiana [176]3 years ago

5 0

It’s A because 25x4 is 100 then plus 40 is 140 and the 25x shows that the 25 is going to be multiplied or changed and the 40 just stays the same so it would be A, y=40+25x

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The base of a solid is the region in the first quadrant bounded by the line x=-2y+6 and the coordinate axes. What is the volume

nika2105 [10]

Answer:

$V = \frac{4y^3}{3} -12y^2 +36 y \Big|_0^3$

$V= \frac{4(3)^3}{3} -12(3)^2 +36 (3) -0 = 36-108+108= 36$

Step-by-step explanation:

For this case we have the following plot on the figure attached.

We know on this case that $x = -2y+6$ represent our radius for the square, since we need cross sections perpendicular to the y axis.

We find the intersection points like this:

$x= 0 , y=3$

$y=0, x=6$

Since we are assuming squares for the cross sections the area is given by $A = r^2$ where r = x= -2y+6.

Since our radius is on terms of x we can create a integral with limits on x in order to find the volume, And we can use the following integral in order to find the volume.

$V = \int_{0}^3 (-2y+6)^2 = \int_{0}^3 4y^2 -24y +36 dy$