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1 year ago

What is the reciprocal of 5 5/11

2 answers:

7 0

Multiply 5x11, and add it to 5/11, to turn the number into a single fraction; 60/11. The reciprocal is this number flipped upside down, so the solution is 11/60.

Therefore the solution is 11/60.

Allushta [10]1 year ago

3 0

To find the reciprocal of a fraction you'd switch the numerator with the denominator but since this is a mixed number, multiply the whole number by the denominator then add the numerator and you get a improper fraction and if you get that to find the reciprocal of it, switch the numerator with the denominator(ex. 3 4/5= 3X5=15, 15+4=19, 19/5, reciprocal: 5/19)

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The larger cross section is 24 meters away from the apex.

Step-by-step explanation:

The cross section of a right hexagonal pyramid is a hexagon; therefore, let us first get some things clear about a hexagon.

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$A=\frac{3\sqrt{3} }{2} r^2$

Where $r$ is the radius of the inscribing circle (or the length of side of the hexagon).

Now we are given the areas of the two cross sections of the right hexagonal pyramid: $A_1=216\:ft^2\: \:\:\:A_2=486\:ft^2$

From these areas we find the radius of the hexagons:

$r_1=\sqrt{\frac{2A_1}{3\sqrt{3} } } =\sqrt{\frac{2*216}{3\sqrt{3} } }=\boxed{9.12ft}$

$r_2=\sqrt{\frac{2A_2}{3\sqrt{3} } } =\sqrt{\frac{2*486}{3\sqrt{3} } }=\boxed{13.68ft}$

Now when we look at the right hexagonal pyramid from the sides ( as shown in the figure attached ), we see that $r_1$ $r_2$ form similar triangles with length $H$

Therefore we have:

$\frac{H-8}{r_1} =\frac{H}{r_2}$

We put in the numerical values of $r_1$ , $r_2$ and solve for $H$ :

$\boxed{H=\frac{8r_2}{r_2-r_1} =\frac{8*13.677}{13.68-9.12} =24\:feet.}$

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