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horsena [70]
3 years ago
13

14. A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the c

ube to the surface of the sphere?
Mathematics
1 answer:
DedPeter [7]3 years ago
8 0

Answer:

5(√3 - 1)

Step-by-step explanation:

Edge of cube = 10

If the sphere is inscribed in a cube, the edges of the cube is equal to the diameter of the sphere.

Diameter = 10

We will then find the diagonal of the cube.

Diagonal = √10^2 + 10^2 + 10^2

= √300

= 10√3

Let X be the distance between the vertex of the cube and the surface of the sphere

X = (diagonal - diameter) /2

X = (10√3 - 10)/2

X = (10(√3 - 1))/2

X = 5(√3 - 1)

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If the first number is increased by 7 and the second number is reduced by 6 times, the sum of these numbers is 29.
Marta_Voda [28]

Answer:

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Explanation:

Let the 1st number be x

Let the 2nd number be y

=====================

Condition 1

\sf \rightarrow  x + 7 + \dfrac{y}{6}  = 29

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=====================

Condition 2

\rightarrow \sf 2y - (x - 5) = 9

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=====================

Substitute equations

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=====================

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7 0
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Step-by-step explanation:

You're welcome :)

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