Mathematics, 24.03.2020 17:46, Mariela2699

Let R be the triangular region in the first quadrant, with vertices at points (0,0), (0,2), and (1,2). The region R is the base of a solid. For the solid, each cross section perpendicular to the y-axis is an isosceles right triangle with the right angle on the y-axis and one leg in the xy-plane. What is the volume of the solid?13

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answered: YourFinalsAreHere

The volume of the solid is 1/3 cubic unit.

Given-

Triangular region is R.

Vertices of this region is at points (0,0) (0,2) and (1,2).

The equation for the line by which the point (0,0) and (1,2) passes can be given as ,

y=2x

$x=\dfrac{y}{2}$

We have given that each cross section perpendicular to the y-axis is an isosceles right triangle with the right angle on the y-axis and one leg in the xy-plane. Hence, the height and base of the triangle are equal which is,

$\dfrac{y}{2}$

Area of the cross section is the product of the half of the base and height of the triangle. Therefore,

$A=\dfrac{1}{2} \times \dfrac{y}{2} \times \dfrac{y}{2}$

$A=\dfrac{y^2}{8}$

Now this cross section exist between point (0,2). Thus the volume of the solid is,

$V=\int\limits^2_0 {\dfrac{y^2}{8}} \, dy$

$V=\dfrac{2^3}{24}$

$V=\dfrac{1}{3}$

the volume of the solid is 1/3 cubic unit.

For more about the volume, follow the link below

link

answered: rileyeddins1010

The line through (0, 0) and (1, 2) has equation y=2x .

Each cross section has a leg in the -plane whose length is the horizontal distance from the -axis to the line y=2x , which is $x=\frac y2$ .

The cross sections are isosceles right triangles, so the legs that lie perpendicular to the -plane have the same length as the legs *in* the -plane, hence these triangles haves bases and heights equal to $\frac y2$ . Then the area of each cross section is

$\dfrac12\left(\dfrac y2\right)^2=\dfrac{y^2}8$

where the cross sections are generated over the interval $0\le y\le2$ .

The volume of the solid is then

$\displaystyle\int_0^2\frac{y^2}8\,\mathrm dy=\frac1{24}y^3\bigg|_0^2=\frac{2^3}{24}=\frac13$

answered: Guest

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

A. name the streets that are parallel to golden gate. b. name the streets that intersect 6th street.

answered: Guest

Here, feel free to ask if there are any questions

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Let R be the triangular region in the first quadrant, with vertices at points (0,0), (0,2), and (1,2...