Are three points coplanar

Mathematics

1 answer:

Ratling [72]3 years ago

5 0

Coplanar points are 3 or more points which lie in the same plane, so any set of 3 points is coplanar

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Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by the plane z = x and below by

fiasKO [112]

$\displaystyle\iiint_R\mathrm dV=\int_{y=-7}^{y=7}\int_{x=-\sqrt{49-y^2}}^{x=0}\int_{z=x}^{z=0}\mathrm dz\,\mathrm dx\,\mathrm dy$

Converting to cylindrical coordinates, the integral is equivalent to

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}\int_{z=r\cos\theta}^{z=0}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}-r^2\cos\theta\,\mathrm dr\,\mathrm d\theta$
$=-\displaystyle\left(\int_{\theta=\pi/2}^{3\pi/2}\cos\theta\,\mathrm d\theta\right)\left(\int_{r=0}^{r=7}r^2\,\mathrm dr\right)$
$=\dfrac{2\times7^3}3=\dfrac{686}3$

4 0

2 years ago

a rectanglar solid has a base with lint 2 cm and width 8 cm. If the volume of the solid is 106 cm 3 to the highest, find the hei

Vanyuwa [196]

The hint says that volume of a rectangular solid = l*w*h, where l = length, w = width, and h = height. Use this to solve for the height of the solid by plugging in the numbers you know.

You know that length, l = 2cm, width, w = 8cm, and, *EDITED* volume = 160 cm^3. Plug these values into the equation for volume (the hint) and solve for h, the height:
Volume = lwh
160 = (2)(8)(h)
160 = 16h
h = 10cm

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Answer: The height is 10 cm

4 0

2 years ago

Read 2 more answers

For part A and B, the options are positive and negative.

ipn [44]

Answer:

Coordinates: (2, -1)

Part A

X coordinate is positive

Y coordinate is negative

Part B

Coordinates after Y-axis reflection: (-2, -1)