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9514 1404 393

  14.14

Step-by-step explanation:

The diagonal of a square is √2 times the side length.

  AC = AB×√2

  AC = 10√2 ≈ 14.14

The diagonal of a square is the hypotenuse of an isosceles right triangle. If the sides of that are s and the diagonal is d, the Pythagorean theorem tells us ...

  d² = s² + s²

  d² = 2s²

  d = (√2)(√s²) = s√2

This relation holds for any isosceles right triangle, not just for the diagonal of this square. It is useful to remember.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

for this case we have that by definition, the surface area of a cylinder is given by:

where:

r: it is the radius of the cylinder

h: it is the height of the cylinder

we can also rewrite it as:

where:

la: it's the lateral area

ba: area of the base

option a