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MissTica
3 years ago
5

Find direction numbers for the line of intersection of the planes x + y + z = 7 and x + z = 0. (enter your answers as a comma-se

parated list.)
Mathematics
1 answer:
yanalaym [24]3 years ago
6 0

The line of intersection has a direction vector that is the cross product of the normal vectors of the given planes.

... [1, 1, 1] × [1, 0, 1] = [1, 0, -1] . . . . . . using a suitable calculator


The direction numbers of the line of intersection are (1, 0, -1).

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A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the
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Answer:

Volume of cylinder = \pi r^2h

Step-by-step explanation:

Given : A cylinder fits inside a square prism.

To find : The volume of cylinder

Solution : Refer the attached graph.

Area of circle = \pi r^2

Area of square = s^2

Side of square = diameter of circle= D^2

Diameter = 2r

∴ Area of square=  2r^2=4r^2

\frac{Area of circle}{Area of Square}=\frac{\pi r^2}{4r^2}=\frac{\pi}{4}

Area of circle is \frac{\pi }{4}  of area of square.

Volume is always = area × height

Volume of prism = Area of square × h = 4r^2h

Volume of cylinder = Area of circle × h = \pi r^2h

Now, rate

\frac{Volume of cylinder}{Volume of prism}=\frac{\pi r^2h}{4r^2h}=\frac{\pi}{4}

⇒Volume of cylinder is  \frac{\pi }{4}  of Volume of prism.

Volume of Cylinder =\frac{\pi }{4}\times Volume of prism

Volume of cylinder = \frac{\pi }{4}\times 4r^2h

Volume of cylinder = \pi r^2h

6 0
3 years ago
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Hello!

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Hope this helps!
8 0
3 years ago
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