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Dmitry [639]
2 years ago
13

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:

  28

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

Learn more:

brainly.com/question/17950304

6 0
2 years ago
Read 2 more answers
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
3 0
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
3 0
3 years ago
Read 2 more answers
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

OR

$23.87 · 3 = $71.61

Sorry if this is wrong!

5 0
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

3 0
3 years ago
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