25 degrees decreased by 60%

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.

It is assumed that weight of pyramid is proportional to its volume.

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, $w = k*(\frac{1}{3}* a* h)=400$

Since, base and height of small pyramid and original pyramid are in proportion.

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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6 0

2 years ago

Read 2 more answers

After a 15% increase, a town has 115 people. What was the population before the increase?

Arte-miy333 [17]

Answer:

100 people

Step-by-step explanation:

Population Of People=115Percentagencrease=15%

The New Population corresponds to 115%

(That is 100+15)

We want to find the population that corresponds to 100% that is the original population.

Therefore Original Population;

 $\frac{100}{115}\times {115}{}$ 

 $100 \: people$ 

7 0

3 years ago

Bart uses 3/12 cup milk to make muffin. Write a fraction that is equivalent to 3/12

vichka [17]

Your fraction that is equal to 3/12 is 1/4

8 0

3 years ago

A carpenter charges a one-time fee of $50 plus $35 for each hour on the job. If n is the number of hours on the job and c is the

Mamont248 [21]

I think it's A because 35n is independent from the 50.

3 0

3 years ago

the graph shows the total number of inches of snow that fell in a town in february over ten year period. what is the approximate

VladimirAG [237]

Answer:

0.6 because its 58% chance which is 0.58 which rounds to 0.6

Step-by-step explanation:

6 0

3 years ago