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11 months ago

Ngth of the third side. If necessary, write in simplest radical form. 5 V11

Mathematics

1 answer:

statuscvo [17]11 months ago

3 0

Pythagoras theorem - The length of the third side is 6.71unit

What is Pythagoras theorem ?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The Pythagoras theorem's equation is as follows:

H² = P² + B²

The triangle's third side will be the following length:

Let x represent the triangle's third side's length.

9² = 6² + x²

81 = 36 + x²

x² = 45

x = 6.708

x = 6.71 units

Hence, the third side of the triangle is 6.71unit

To learn more about Pythagoras theorem's click on the link

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Match the statement to the property it shows.

xxMikexx [17]

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A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square

kondaur [170]

This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

V = length x width x height

That is:

$V = xxy = x^{2}y$

We also know that the bin is constructed from 48 square feet of sheet metal, so:

Surface area of the square base = $x^{2}$

Surface area of the rectangular sides = $4xy$

Therefore, the total area of the cube is:

$A = 48 ft^{2} = x^{2} + 4xy$

Isolating the variable y in terms of x:

$y = \frac{48- x^{2} }{4x}$

Substituting this value in V:

$V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3}$

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

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Solving for x:

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