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Sphinxa [80]
3 years ago
6

A pyramid is placed inside a prism as shown. The pyramid has the same base area, B, as the prism but half the height, h, of the

prism. Which expression gives the volume of the pyramid?
V = 2/3bh
V = 1/4bh
V = 2bh
V = 1/6bh
Mathematics
1 answer:
Alona [7]3 years ago
4 0
The general formula of a pyramid with any base is 1/3 bh where b is the area of the base and h is the height. In this case, the height of the pyramid is said to be twice the height of the prism, h. Hence the area becomes 1/3 b*2h or equal to option A. 2/3 bh
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The area of rectangle ABCD is 72. If point A and the midpoints of BC and CD are joined to form triangle, the area of that triang
vredina [299]

Answer:

  27

Step-by-step explanation:

Name the midpoint of BC point M and the midpoint of CD point N.

Triangle ABM has the 1/4 the area of the rectangle, 18. Triangle ADN also has 1/4 the area of the rectangle, 18. Triangle CMN has 1/8 the area of the rectangle, 9. That is, of the rectangle area, ...

  18 + 18 + 9 = 45

are not included in triangle AMN. So, the area of that triangle is ...

  72 -45 = 27 . . . . units²

_____

<em>Comment on the triangle area</em>

The triangle created by joining the midpoint of the side of a rectangle with an opposite vertex will have the same dimension as the rectangle in one direction (L), and half the dimension of the rectangle in the other direction (W). Thus, where the rectangle area is LW, the triangle area is (1/2)(L)(1/2W) = (1/4)LW, 1/4 the area of the rectangle.

Similarly, if the midpoints of adjacent sides are joined to form a triangle, the area of that is (1/2)(1/2L)(1/2W) = (1/8)LW, or 1/8 the area of the rectangle.

3 0
3 years ago
Use Euler's Theorem to calculate how many vertices a polyhedron has if it has 6 faces and 12 edges.
Sav [38]
v+f-e=2\\&#10;v=2-f+e\\&#10;v=2-6+12\\&#10;v=8
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Your school wants to have 5 computers for every 12 students.There are now 125 computers and 924 students.How many more computers
Oksana_A [137]
First, determine the number of computers that are needed for 924 students.

    n =  (924 students)(5 computers / 12 students)
                 n = 385 computers

Since, there are only 125 computers, the difference can be calculated.
     
       d = 385 computers - 125 computers
   
                d = 260 computers

Hence, 260 more computers are still needed. 
3 0
3 years ago
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 9/ms . The ball's height h (in meters) af
Alecsey [184]

A ball is thrown from an initial height of 2 meters with an initial upward velocity of 9/ms

Balls height h= 2 +9t -5t^2

To find all values of t for which the ball's height is 3 meters

We plug in 3 for h and solve for t

h= 2 +9t -5t^2

3 = 2 +9t -5t^2

Solve for t

0= -1+ 9t -5t^2

5t^2 - 9t + 1 = 0

Solve using quadratic formula

t= \frac{-b+- \sqrt{b^2-4ac} }{2a}

t= \frac{9+- \sqrt{(-9)^2-4*5*1} }{2*5}

After simplifying this,

t= \frac{9+\sqrt{61}}{10} = 0.11898

t= \frac{9-\sqrt{61}}{10} = 1.68102

the values of t for which the ball's height is 3 meters= 0.12 sec , 1.68 sec

5 0
3 years ago
When simplifying 4x^3-10x^2+6x/2x^3+x^2-3x, what are the term(s) that can be cancelled
brilliants [131]

Answer:

x can be cancelled

Step-by-step explanation:

we are given

\frac{4x^3-10x^2+6x}{2x^3+x^2-3x}

Firstly, we will factor numerator and denominator

and then we can factor it

4x^3-10x^2+6x=2x(2x^2-5x+3)

4x^3-10x^2+6x=2x(2x+1)(x-3)

now, we can factor denominator

2x^3+x^2-3x=x(2x^2+x-3)

2x^3+x^2-3x=x(x-1)(2x+3)

now, we can replace it

\frac{4x^3-10x^2+6x}{2x^3+x^2-3x}=\frac{2x(2x+1)(x-3)}{x(x-1)(2x+3)}

we can see that

both terms are having x common

so, x can be cancelled

So,

x can be cancelled

3 0
3 years ago
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