Ask question

Ask question

All categories

3 years ago

9

A pyramid has a base that is a right triangle with legs measuring 15 cm and 24 cm. The height of the pyramid is 13 cm. What is t

he volume of the pyramid? Enter your answer in the box. cm³

1 answer:

DENIUS [597]3 years ago

3 0

Answer:

$\boxed{780}\ cm^3$

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

V = 1/3·B·h

where B represents the area of the base and h represents the height.

The area of a triangle is given by the formula ...

A = 1/2·b·h

where b represents the length of the base of the triangle, and h represents the height of the triangle.

For a right triangle, the base and height can be taken to be the lengths of the two legs. Then we have

A = 1/2·(15 cm)·(24 cm) = 180 cm²

The volume of the pyramid is then ...

V = 1/3·(180 cm²)(13 cm) = 780 cm³

The volume of the pyramid is 780 cm³.

You might be interested in

The function d(s) = 0.0056s squared + 0.14s models the stopping distance

victus00 [196]

Answer:

The car must have a speed of 25 kilometres per hour to stop after moving 7 metres.

Step-by-step explanation:

Let be $d(s) = 0.0056\cdot s^{2} + 0.14\cdot s$ , where $d$ is the stopping distance measured in metres and $s$ is the speed measured in kilometres per hour. The second-order polynomial is drawn with the help of a graphing tool and whose outcome is presented below as attachment.

The procedure to find the speed related to the given stopping distance is described below:

1) Construct the graph of $d(s)$ .

2) Add the function $d = 7\,m$ .

3) The point of intersection between both curves contains the speed related to given stopping distance.

In consequence, the car must have a speed of 25 kilometres per hour to stop after moving 7 metres.

4 0

3 years ago

(x +y)^5<br> Complete the polynomial operation

Vesna [10]

Answer:

Please check the explanation!

Step-by-step explanation:

Given the polynomial

$\left(x+y\right)^5$

$\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

$a=x,\:\:b=y$

$=\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}y^i$

so expanding summation

$=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5$

solving

$\frac{5!}{0!\left(5-0\right)!}x^5y^0$

$=1\cdot \frac{5!}{0!\left(5-0\right)!}x^5$

$=1\cdot \:1\cdot \:x^5$

$=x^5$

also solving

$=\frac{5!}{1!\left(5-1\right)!}x^4y$

$=\frac{5}{1!}x^4y$

$=\frac{5}{1!}x^4y$

$=\frac{5x^4y}{1}$

$=\frac{5x^4y}{1}$

$=5x^4y$

similarly, the result of the remaining terms can be solved such as

$\frac{5!}{2!\left(5-2\right)!}x^3y^2=10x^3y^2$

$\frac{5!}{3!\left(5-3\right)!}x^2y^3=10x^2y^3$

$\frac{5!}{4!\left(5-4\right)!}x^1y^4=5xy^4$

$\frac{5!}{5!\left(5-5\right)!}x^0y^5=y^5$

so substituting all the solved results in the expression

$=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5$

$=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$

Therefore,

$\left(x\:+y\right)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$

6 0

3 years ago

A triangle has sides of length 2, 2, and 3. Which of the following is the measure of the obtuse angle of the triangle?

kramer

Answer:

$97.18^{\circ}$

Step-by-step explanation:

An obtuse angle in the triangle is opposite to the greatest side. The greatest side in the triangle with sides lengths 2, 2 and 3 is side with length 3. By the cosine rule,

$3^2=2^2+2^2-2\cdot 2\cdot 2\cdot \cos \alpha,\\ \\9=4+4-8\cos \alpha,\\ \\-8\cos \alpha=9-4-4=1,\\ \\\cos \alpha=-\dfrac{1}{8},\\ \\\alpha\approx 97.18^{\circ}.$

7 0

4 years ago

PLS HELP!!!!!!!!!!!!

seropon [69]

Answer:

72 55/76

Step-by-step explanation:

it's right trust me <3

8 0

2 years ago

Read 2 more answers

WILL GIVE BRAINLEST

bearhunter [10]

Answer:

b

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers