Answer:
x=4
Step-by-step explanation:
Answer:
Step-by-step explanation:
To answer question 12, you first need to know the definition of a <em>prism</em> and a<em> pyramid.
</em>A <em>pyramid </em> is a 3-D structure with one base, whose outer faces are made of triangles, and meet at a single point at the top.
A <em>prism</em> is any 3-D shape with a base of any number of sides, another base with the same amount of sides, and faces joining the two together on every side of the bases.
12.
Shape A is a <em>pyramid</em>, because it has one base, and all the faces join together in at one point.
Shape B is a <em>prism</em>, because it has two bases, and faces joining every side of the bases.
Shape C is a <em>prism.</em>
Shape D is a <em>pyramid.
</em>For #13, you have to know the definition of a cube to figure out the math of how many cubes there are.
A cube is a 3-D shape with six sides, all made up of squares of the same size.
The box has a volume of 120 cubic inches, and each cube is 1 inch. Since every side of a cube is equal, a 1-inch cube is one cubic inch.
This means that a box with a volume of 120 cubic inches will fit 120 of the 1 inch cubes.
1 layer of the cubes, in the diagram, is 8 cubes by 3 cubes, or 24 cubes total.
To find the number of layers needed to fill the box, you divide 120 by 24.
120 ÷ 24 = 5
The answer to #13 is 5 layers.
Answer:
The volume of the tetrahedron is:
Step-by-step explanation:
The volume of the tetrahedron is given by the intersection of the planes x = 0, y = 0, z = 0 and the plane formed by the three points given.
The equation of the plane formed by the three points is:
Points: (2,0,0);(0,5,0);(0,0,4)
It can also be expressed as:
We have to calculate the triple integral, therefore we must define the domain:
The values of x are given by:
0≤x≤2
We will integrate the values of y between the y = 0 axis and the line formed when z = 0:
z=0 ⇒ 10x + 4y=2 ⇒ 
We will integrate the values of z between the plane z = 0 and the plane 10x + 4y+5z=20
10x + 4y+5z=20 ⇒ 
The volume of the tetrahedron is:
I'm pretty sure its 1,000 pounds
