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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.

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

Please help, I I beg you please

Tatiana [17]

Answer:

The volume of the cube is $\mathit{\frac{27}{z^3x^{9}}}$ cu in.

Step-by-step explanation:

The Volume of a Cube

Let's have a cube of side length a. The volume of the cube is:

$V=a^3$

The cube of the image has a side length of

$\displaystyle a=\frac{3x^{-3}}{z}\ inches$

Simplifying the expression of the base by converting the negative exponent in the numerator to the denominator:

$\displaystyle a=\frac{3}{zx^{3}}\ inches$

Now find the volume:

$\displaystyle V=\left(\frac{3}{zx^{3}}\ inches\right)^3$

Applying the exponents:

$\displaystyle V=\frac{3^3}{z^3x^{9}}\ inches^3$

$\displaystyle V=\frac{27}{z^3x^{9}}\ inches^3$

The volume of the cube is $\mathbf{\frac{27}{z^3x^{9}}}$ cu in.

8 0

3 years ago

Match each description to the appropriate provider or service.

lys-0071 [83]

Explanation:

Urgent care centers: care for basic needs after regular doctor hours

Hospitals: treat time-sensitive emergencies

Medical specialists: offer treatment in a specific field of medicine, such as cardiology

General practice doctors and nurse practitioners: care for routine medical needs

Crisis pregnancy centers: provide counseling for unplanned pregnancies

__

Discussion

Urgent care centers are often open all hours, but may not be as fully equipped (or staffed) to provide the sort of emergency medicine that a fully-equipped hospital can provide. While a general- or nurse-practitioner can provide routine care, they will consult with specialists when expertise is needed in a specific area.

Various kinds of pregnancy centers can provide counseling and perhaps some medical services for planned or unplanned pregnancies.

6 0

3 years ago

Find the length of the third side to the nearest tenth. Hurry need help asap!!

gavmur [86]

Answer:

2.8

Step-by-step explanation:

6 0

2 years ago

What is 150/100 in decimal form and percent form

Andrews [41]

Decimal : 1.5
Percent : 150%

3 0

2 years ago