Mathematics: Determine the height of the triangular pyramid

Step-by-step explanation: Volume = area of base × height 270 = 1/2 ( 15×4) ×height 270 = 30 × height...

Determine the height of the triangular pyramid, №15257807, 21.02.2022 11:48

Mathematics

Two different cross sections are taken parallel to the base of a three-dimensional figure. the two cross sections are the same shape, but are not congruent. which could be the three-dimensional figure? check all that apply. -cone -cylinder -rectangular prism -triangular prism -triangular pyramid -square pyramid

Step-by-step answer

P Answered by PhD

1

The Answers are: A).Cone, E).Triangular Pyramid, & F)Square Pyramid. Hope this helps!

Mathematics

Two different cross sections are taken parallel to the base of a three-dimensional figure. the two cross sections are the same shape, but are not congruent. which could be the three-dimensional figure? check all that apply. -cone -cylinder -rectangular prism -triangular prism -triangular pyramid -square pyramid

Step-by-step answer

P Answered by PhD

1

The Answers are: A).Cone, E).Triangular Pyramid, & F)Square Pyramid. Hope this helps!

Mathematics

Show that the sets of upper-triangular and lower-triangular matrices are subspaces of f n,n . call them u and l respectively. what are their dimensions?

Step-by-step answer

P Answered by Specialist

dim L = dim U = $\frac{n(n+1)}{2}$

Step-by-step explanation:

We can do it only for the lower-triangular matrices, the case of the upper-triangular matrices is similar. We might caracterice nxn the lower-triangular matrices, as the nxn matrices $A=(a_{ij})$ such that the entry $a_{ij}=0$ if i<j.

Now let $A=(a_{ij})$ and $B=(b_{ij})$ be two lower triangular matrices, now if

$C=A+\lambda B$ for some $\lambda \in \mathbb{F}$

then the entry $c_{ij}$ of C is equal to

$c_{ij}=a_{ij}+\lambda b_{ij}$

Now, if i<j, it must hold that $a_{ij}=0 \quad \text{and} \quad b_{ij}=0$ . Therefore, if this is the case we must have that $c_{ij}=0$ and so we get that C is also a lower triangular matrix. This showa that L is closed under sum and scalar multiplcation, hence it is a linear subspace.

To find the dimension, note that all the entries of a lower-triangular matrix over the diagonal must be equal to zero. However, each entry of the matrix under the diagonal and in the diagonal might be any element of $\mathbb{F}$ , any entry that can be choosen add up to the dimension of L, we n such elemnts for the first column, (n-1) for the second column, (n-2) for the third column etc.... Therefore,

$\dimL=n+(n-1)+(n-2)+...+2+1=\dfrac{n(n+1)}{2}$

Mathematics

Which pair of figures has the same number of faces as vertices? triangular prism and triangular pyramidtriangular prism and rectangular prismrectangular pyramid and triangular pyramidrectangular pyramid and rectangular prism?

Step-by-step answer

P Answered by PhD

43

We know that
1) A triangular prism
has 6 vertices
has 4 faces

2) A triangular pyramid
has 4 vertices
has 4 faces

3) A rectangular prism
has 8 vertices
has 6 faces

4) A rectangular pyramid
has 5 vertices
has 5 faces

therefore
the answer is
rectangular pyramid and triangular pyramid

Mathematics

Show that the sets of upper-triangular and lower-triangular matrices are subspaces of f n,n . call them u and l respectively. what are their dimensions?

Step-by-step answer

P Answered by Master

dim L = dim U = $\frac{n(n+1)}{2}$

Step-by-step explanation:

We can do it only for the lower-triangular matrices, the case of the upper-triangular matrices is similar. We might caracterice nxn the lower-triangular matrices, as the nxn matrices $A=(a_{ij})$ such that the entry $a_{ij}=0$ if i<j.

Now let $A=(a_{ij})$ and $B=(b_{ij})$ be two lower triangular matrices, now if

$C=A+\lambda B$ for some $\lambda \in \mathbb{F}$

then the entry $c_{ij}$ of C is equal to

$c_{ij}=a_{ij}+\lambda b_{ij}$

Now, if i<j, it must hold that $a_{ij}=0 \quad \text{and} \quad b_{ij}=0$ . Therefore, if this is the case we must have that $c_{ij}=0$ and so we get that C is also a lower triangular matrix. This showa that L is closed under sum and scalar multiplcation, hence it is a linear subspace.

To find the dimension, note that all the entries of a lower-triangular matrix over the diagonal must be equal to zero. However, each entry of the matrix under the diagonal and in the diagonal might be any element of $\mathbb{F}$ , any entry that can be choosen add up to the dimension of L, we n such elemnts for the first column, (n-1) for the second column, (n-2) for the third column etc.... Therefore,

$\dimL=n+(n-1)+(n-2)+...+2+1=\dfrac{n(n+1)}{2}$

Mathematics

Which pair of figures has the same number of faces as vertices? triangular prism and triangular pyramidtriangular prism and rectangular prismrectangular pyramid and triangular pyramidrectangular pyramid and rectangular prism?

Step-by-step answer

P Answered by PhD

43

We know that
1) A triangular prism
has 6 vertices
has 4 faces

2) A triangular pyramid
has 4 vertices
has 4 faces

3) A rectangular prism
has 8 vertices
has 6 faces

4) A rectangular pyramid
has 5 vertices
has 5 faces

therefore
the answer is
rectangular pyramid and triangular pyramid

Mathematics

Iam calling all aces, experts, smarty pants, ! : )) (math 50 points) 10. the base of a triangular prism is a triangle with a base of 4 inches and a height of 3.5 inches. the height of the triangular prism is 3.3 inches. what is the volume of the triangular prism? the volume of the triangular prism is 23.1. 11. the base of a triangular pyramid is a triangle with a base of 4 inches and a height of 3.5 inches. the height of the triangular pyramid is 3.3 inches. what is the volume of the triangular pyramid? 12. what do the triangular pyramid and prism

Step-by-step answer

P Answered by PhD

8

10. The volume of the triangular prism is $V=A_{base}\cdot H=\dfrac{1}{2} height \cdot base\cdot H$ , then

$V=\dfrac{1}{2} \cdot 4\cdot 3.5\cdot 3.3=23.1$ .

11. The volume of the triangular pyramid is $V=\dfrac{1}{3}A_{base}\cdot H=\dfrac{1}{3}\cdot \dfrac{1}{2} height \cdot base\cdot H$ , then

$V=\dfrac{1}{3}\cdot \dfrac{1}{2} \cdot 4\cdot 3.5\cdot 3.3=7.7$ .

12. They have common base (common triangle). y=7.7, r=23.1, then r:y=23.1:7.7=3.

13. See 10 and 11 for notations in symbols.

Mathematics

Iam calling all aces, experts, smarty pants, ! : )) (math 50 points) 10. the base of a triangular prism is a triangle with a base of 4 inches and a height of 3.5 inches. the height of the triangular prism is 3.3 inches. what is the volume of the triangular prism? the volume of the triangular prism is 23.1. 11. the base of a triangular pyramid is a triangle with a base of 4 inches and a height of 3.5 inches. the height of the triangular pyramid is 3.3 inches. what is the volume of the triangular pyramid? 12. what do the triangular pyramid and prism

Step-by-step answer

P Answered by PhD

8

10. The volume of the triangular prism is $V=A_{base}\cdot H=\dfrac{1}{2} height \cdot base\cdot H$ , then

$V=\dfrac{1}{2} \cdot 4\cdot 3.5\cdot 3.3=23.1$ .

11. The volume of the triangular pyramid is $V=\dfrac{1}{3}A_{base}\cdot H=\dfrac{1}{3}\cdot \dfrac{1}{2} height \cdot base\cdot H$ , then

$V=\dfrac{1}{3}\cdot \dfrac{1}{2} \cdot 4\cdot 3.5\cdot 3.3=7.7$ .

12. They have common base (common triangle). y=7.7, r=23.1, then r:y=23.1:7.7=3.

13. See 10 and 11 for notations in symbols.

Mathematics

Which right triangular prism has the greatest volume? A triangular prism. The triangular base has a base of 7 meters and height of 9 meters. The height of the prism is 6 meters. A triangular prism. The triangular base has a base of 6 meters and height of 13 meters. The height of the prism is 5 meters. A triangular prism. The triangular base has a base of 11 meters and height of 8 meters. The height of the prism is 8 meters. A triangular prism. The triangular base has a base of 10 meters and height of 9 meters. The height of the prism is 8 meters.

Step-by-step answer

P Answered by PhD

6

The correct answer is option 4;

A triangular prism. The triangular base has a base of 10 metres and a height of 9 metres. The height of the prism is 8 metres.

Step-by-step explanation: A simple check for the result of each set of dimensions would give the correct answer.

The volume of a right triangular prism is derived as follows;

Volume = 1/2 * b * h * l

Where, b is the base of the triangle, h is the vertical height of the triangle and l is the length of the prism.

Note that the area of the right triangle is denoted by 1/2 * b * h, and multiplying this result by the length of the prism gives the entire depth or volume of the triangular prism. Let us examine the dimensions one after the other;

(1) A triangular prism. The triangular base has a base of 7 metres and height of 9 metres. The height of the prism is 6 metres.

Volume = 1/2 * 7 * 9 * 6

Volume = 189 cubic metres

(2) A triangular prism. The triangular base has a base of 6 metres and height of 13 metres. The height of the prism is 5 metres.

Volume = 1/2 * 6 * 13 * 5

Volume = 165 cubic metres

(3) A triangular prism. The triangular base has a base of 11 metres and a height of 8 metres. The height of the prism is 8 metres.

Volume = 1/2 * 11 * 8 * 8

Volume = 352 cubic metres

(4) A triangular prism. The triangular base has a base of 10 metres and a height of 9 metres. The height of the prism is 8 metres.

Volume = 1/2 * 10 * 9 * 8

Volume = 360 cubic metres

Mathematics

Amanda is building a soft triangular kennel for her dog. she has four wooden planks of lengths 2 feet, 3 feet, 5 feet, and 6 feet. determine which planks amanda should use to build the triangular-shaped kennel. enter the lengths from least to greatest.

Step-by-step answer

P Answered by Specialist

8

3 ft, 5ft, 6ft

Step-by-step explanation:

To build a kennel of my dog, I would try to make it the largest possible with what I have.

So, I would go with the 3 longest planks: 3ft, 5ft and 6ft.

By looking at the length, I see I could make something very close to a right triangle since I could use the 6ft as an hypotenuse, and have the two other sides as 3ft and 5 ft (6² is almost 3²+5², which equal 34).

That means my corner angle would be slightly over 90 degrees.

Determine the height of the
triangular pyramid

Step-by-step answer

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