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laila [671]
2 years ago
9

For what value of a is the volume of the tetrahedron formed by the coordinate planes and the plane (x/a) (y/10) (z/6)

Mathematics
1 answer:
kotykmax [81]2 years ago
3 0

This question is incomplete, the complete question is;

For what value of a is the volume of the tetrahedron formed by the coordinate planes and the plane (x/a) + (y/10) + (z/6) = 1 equal to 10?

Answer: the value of a is 1

Step-by-step explanation:

Given that;

Volume of tetrahedron bounded by plane (x/a) + (y/10) + (z/6) = 1

and coordinate plane is; V = 1/6|abc|

(x/a) + (y/10) + (z/6) = 1

volume = 10

so

10 = 1/6 | a × 10 × 6 |

60 = a × 10 × 6

60 = 60a

a = 60 / 60

a = 1

Therefore the value of a is 1

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Find the perimeter of a rectangle whose length is 3 cm greater than its height, and whose area is 40 cm².
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Step-by-step explanation:

The perimeter of a rectangle can be calcualated with this formula:

P=2l+2h

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A=lh

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In this case we know that:

A=40\ cm^2

Therfore, we can susbsitute them into A=lh and solve for "h" in  order to find its value:

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Find two number whose sum is 3 and whose product is -40. These are -5 and 8. Then, factorizing, we get:

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The positive value is the height. Then:

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Since the length is 3 centimeters greater than its height, we get that this is: Then:

l=5\ cm+3\ cm\\\\l=8\ cm

Substituting values into P=2l+2h, we get that the perimeter is:

P=2(8\ cm)+2(5\ cm)\\\\P=26\ cm

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