All categories

3 years ago

Find the volume of this figure.

Mathematics

1 answer:

Bogdan [553]3 years ago

4 0

Answer:

The volume of the figure is $320\ units^{3}$

Step-by-step explanation:

we know that

The figure is a pyramid

The volume of a pyramid is equal to

$V=(1/3)BH$

where

B is the area of the rectangular base of pyramid

H is the height of pyramid

The area of the base B is equal to

$B=AB*AC$

we have that

$AB=8\ units$ ---> see the graph

$AC=10\ units$ ---> see the graph

substitute

$B=8*10=80\ units^{2}$

we have

$H=EF=12\ units$ ---> see the graph

<em>Find the volume</em>

$V=(1/3)(80*12)=320\ units^{3}$

You might be interested in

Lindsey bought supplies for a class project and brought the receipt to school. The 6 items cost:

DochEvi [55]

Answer:

Step-by-step explanation:

$5 appeared more in the prices

5 0

2 years ago

Read 2 more answers

Multiply (−4) × (−2) × (−5).

babunello [35]

Answer: -40 or negative forty

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

2x – 4y = 16<br> -2x - 3y = 7

noname [10]

Bro use the app Socratic

5 0

3 years ago

2. Find the general relation of the equation cos3A+cos5A=0

mars1129 [50]

<h2>Answer:</h2>

$A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi$

<h2>Step-by-step explanation:</h2>

<h3>Find angles</h3>

$cos3A+cos5A=0$

________________________________________________________

<h3>Transform the expression using the sum-to-product formula</h3>

$2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0$

________________________________________________________

<h3>Combine like terms</h3>

$2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\ 2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Divide both sides of the equation by the coefficient of variable</h3>

$cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Apply zero product property that at least one factor is zero</h3>

$cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0$

________________________________________________________

<h3>Cross out the common factor</h3>

$cos\ 4A=0$

________________________________________________________

<h3>Solve the trigonometric equation to find a particular solution</h3>

$4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}$

________________________________________________________

<h3>Solve the trigonometric equation to find a general solution</h3>

$4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}$

________________________________________________________

<h3>Reduce the fraction</h3>

$cos(-A)=0$

________________________________________________________

<h3>Simplify the expression using the symmetry of trigonometric function</h3>

$cosA=0$

________________________________________________________

<h3>Solve the trigonometric equation to find a particular solution</h3>

$A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}$

________________________________________________________

<h3>Solve the trigonometric equation to find a general solution</h3>

$A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z$

________________________________________________________

<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{2}+n\pi$

________________________________________________________

<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z$

<em>I hope this helps you</em>

5 0

2 years ago

Help please! Calculate the exact value of cos (a-b) given that sin a= 12/13 with pi/2

zloy xaker [14]

Answer:

56/65

Step-by-step explanation:

First, we know that cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

We know what sin(a) and sin(b) are, and to get cos(a), we can take the equation sin²a + cos²a = 1

Thus,

(12/13)² + cos²a = 1

1 - (12/13)² = cos²a

1- 144/169 = cos²a

cos²a = 25/169

cos(a) = 5/13

Similarly,

(3/5)² + cos²b = 1

1 - (3/5)² = cos²b

1 - 9/25 = cos²b

cos²b = 16/25

cos(b) = 4/5

Our answer is

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

cos(a-b) = (5/13)(4/5) + (12/13)(3/5)

cos(a-b) = 20/65 + 36/65

cos(a-b) = 56/65

4 0

2 years ago