Find the midpoint of the line segment with the given endpoints (-3,1 -2,8) (-4.92,-3.3)

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

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Simply the following expression: 8x + 5y - 4z + 9y - 3x + 13z

oksian1 [2.3K]

Answer:

5x+14y+9z

Step-by-step explanation:

combine 8x and -3x to get 5x

combine 5y and 9y to get 13y

combine -4z and 13z to get 9z

7 0

2 years ago

Triangle ABC is an isosceles with a base AC. The base angles are 60 degrees. Find the length of the base and the length of the a

lisabon 2012 [21]

Answer:

base =5 because all angles=60, so an equilateral triangle

height=4.33

Step-by-step explanation:

height^2+1/2(5)^2=5^2

height^2+6.25=25

height^2=18.75

height=4.33

8 0

2 years ago

What is the solution of the equation when solved over the complex numbers? x^2+27=0

Luba_88 [7]

Answer:

(0,27)

Step-by-step explanation:

x2 + 27 = 0

Solutions based on quadratic formula:

x1

= −0 − √ 02 − 4×1×27 2×1 = 0 − 6 × √ 3 i 2 ≈ −5.196152i

x2

= −0 + √ 02 − 4×1×27 2×1 = 0 + 6 × √ 3 i 2 ≈ 5.196152i

Extrema:

Min = (0, 27)

8 0

3 years ago

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HELP! Mr johnson needs a shelf to hold a set of textbooks, each <img src="https://tex.z-dn.net/?f=%201%5Cfrac%7B3%7D%7B4%7D%

inysia [295]

How many 1 3/4 inches are there in 35 inches?
Or in math talk:

35" ÷ 1 3/4
The answer is that 20 books will fit on the shelf.
I used a calculator and used 1.75 instead of 1 3/4

6 0

3 years ago