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2 years ago

If the triangles below are similar, find the value of x. 42 х 11 22

Mathematics

1 answer:

stepan [7]2 years ago

3 0

9514 1404 393

Answer:

Step-by-step explanation:

Corresponding sides are proportional.

x/42 = 22/(22+11)

x = 42(2/3)

x = 28

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a pyramid whose altitude is 5ft weighs 800lbs. at what distance from its vertex must it be cut by a plane parallel to its base s

slavikrds [6]

A structure which has a square base and four triangular sides meeting at a point is called pyramid.

At distance of 3.97 feet from its vertex , pyramid is cut by plane so that the two solids of equal weight will be formed.

<u>It is assumed that weight of pyramid is proportional to its volume.</u>

So, $w = k V$ , where V is volume of original pyramid and v is volume of small pyramid and k is constant.

Let us consider that at h distance, pyramid is cut from its vertex. So a small pyramid is also formed.

Assume that base area of original pyramid is A and base of small pyramid is a.

Volume of original pyramid is, $V= \frac{1}{3} *A* 5$

So, weight of original pyramid, $W = k *(\frac{1}{3} *A* 5) = 800$

Volume of small pyramid is, $v = \frac{1}{3}* a* h$

So, weight of small pyramid, $w = k*(\frac{1}{3}* a* h)=400$

<u>Since, base and height of small pyramid and original pyramid are in proportion.</u>

So, $\frac{a}{A} = (\frac{h}{5}) ^{2}$

$a = (\frac{h}{5} )^{2}A$

Substituting value of a in equation $k*(\frac{1}{3}* a* h)=400$

So, $k*(\frac{1}{3}* \frac{h^{2} }{25}A * h)=400$

$(k*\frac{1}{3}* A*5)*\frac{1}{5} *\frac{h^{2} }{25} * h)=400$

Since, $(k *\frac{1}{3} *A* 5) = 800$ , substitute in above equation.

So, $800*\frac{h^{3} }{125}=400\\\\h^{3}=\frac{125}{2}\\\\h=\sqrt[\frac{1}{3} ]{62.5}\\\\h=3.97 feet$

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2 years ago

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What is the difference 6 - 3 2/5 =

Luba_88 [7]

It depends on what the question looks like. If it looks like this:
(6-3)(2/5)=
(3)(0.4)=
1.2

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3 years ago

What is the mean in math?

sertanlavr [38]

Adding all vakus in data set and divide by the number of values in the data set

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3 years ago

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How much would the sales tax be on a $66 meal?

vovangra [49]

Answer:

$71.61

Step-by-step explanation:

66/22 = 3

3 · $1.87 = $5.61

$66 + $5.61 = $71.61

$23.87 · 3 = $71.61

Sorry if this is wrong!

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3 years ago

Perry finished a 100-meter race in 7/8 of a minute. The winner of the race used 14/15 of Perry's time to finish the race. How mu

konstantin123 [22]

Answer:

49 seconds

Step-by-step explanation:

The time perry used is 7/8 of a minute

a minute equals to 60 seconds

so the time perry used is 7/8 x 60 = 52.5 seconds

The winner used 14/15 of 52.5 seconds (perrys time)

so 14/15 x 52.5 = 49 seconds

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