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dimaraw [331]
3 years ago
5

What is an equation of the line that passes through the point (5,-2)(5,−2) and is parallel to the line 2x-5y=352x−5y=35?

Mathematics
1 answer:
xxMikexx [17]3 years ago
5 0

Answer:

2x-5y=20.

Step-by-step explanation:

1) according to the condition the required line is parallel to the given line, it means, that the equation of the required line is:

2x-5y=C, where C - unknown number;

2) in order to calculate unknown 'C' it needed to substitute the given coordinates into the equation of the required line, then:

2*5-5*(-2)=C; ⇒ C=20.

3) the required equation of the line is:

2x-5y=20.

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Find the volume of the solid that lies inside both the cylinder x 2 y 2 = 1 and the sphere x 2 y 2 z 2 = 16
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The volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16 is 24.74 cubic units.

<h3>What is the volume of the solid?</h3>

Find the volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16

From the sphere and cylinder, the cylindrical coordinate will be

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And the radius of the cylinder is |r| < 1 and the 0 ≤ θ ≤ 2π.

Then the volume will be given as

\rm V = \int _0^{2\pi} \int _0^1 \int _{- \sqrt{16 - r^2}}^{\sqrt{16-r^2}} \left ( r \ dz \ dr \ d\theta  \right ) \\\\\\V = 2\pi \int_0^1 \left ( 2r\sqrt{16-r^2} \right ) \ dr\\\\\\V = 4\pi \left [ -\dfrac{1}{3} (16 - r^2)^{3/2} \right ]\\\\\\V = \dfrac{4\pi}{3} \left ( 16^{3/2} - 15^{3/2} \right )\\\\\\V = 24.74

More about the volume of the solid link is given below.

brainly.com/question/23705404

#SPJ4

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