Answer:
w = 18
Step-by-step explanation:
6(33 - w) = 90
33 - w = 15
-w = -18
w = 18
The volume prism refers to the number of cubic units that will exactly fill the figure. The volume of a rectangular prism can be found or calculate by using the formula
V=Bh, where
B represents to the area of the base or in other words the length and width of the rectangle.
In this exercise is given that the measurements of a prism are 5/2ft, 3/2ft, and 7/2ft; and it is asked to find its volume. In order to find the volume of the prism, you should substitute the given values into the previous mention formula.
V=Bh
V=(5/2 ft)(7/2 ft)(3/2 ft)
V=(35/4 ft²)(3/2 ft)
V=105/8ft³ or
ft³The volume of the rectangular prism is
ft³.
5p squared - 2p - 8 - 8 over p+3
Step-by-step explanation:
First factor out the negative sign from the expression and reorder the terms
That's
![\frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \cot(6A) - \cot(2A) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20-%20%28%28%20%5Ctan%282A%29%20-%20%20%5Ctan%286A%29%20%20%29%7D%20%20-%20%20%5Cfrac%7B1%7D%7B%20%5Ccot%286A%29%20%20-%20%20%5Ccot%282A%29%20%7D%20)
<u>Using trigonometric </u><u>identities</u>
That's
<h3>
![\cot(x) = \frac{1}{ \tan(x) }](https://tex.z-dn.net/?f=%20%5Ccot%28x%29%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%5Ctan%28x%29%20%7D%20)
</h3>
<u>Rewrite the expression</u>
That's
![\frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \frac{1}{ \tan(6A) } } - \frac{1}{ \frac{1}{ \tan(2A) } }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%20-%20%28%28%20%5Ctan%282A%29%20-%20%20%5Ctan%286A%29%20%20%29%7D%20-%20%20%20%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7B1%7D%7B%20%5Ctan%286A%29%20%7D%20%7D%20%20-%20%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7B1%7D%7B%20%5Ctan%282A%29%20%7D%20%7D%20)
We have
<h3>
![- \frac{1}{ \tan(2A) - \tan(6A) } - \frac{1}{ \frac{ \tan(2A) - \tan(6A) }{ \tan(6A) \tan(2A) } }](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B1%7D%7B%20%20%5Ctan%282A%29%20-%20%20%5Ctan%286A%29%20%20%7D%20-%20%20%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7B%20%5Ctan%282A%29%20-%20%20%5Ctan%286A%29%20%20%7D%7B%20%5Ctan%286A%29%20%5Ctan%282A%29%20%20%7D%20%7D%20)
</h3>
<u>Rewrite the second fraction</u>
That's
<h3>
![- \frac{1}{ \tan(2A) - \tan(6A) } - \frac{ \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) }](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B1%7D%7B%20%20%5Ctan%282A%29%20-%20%20%5Ctan%286A%29%20%20%7D%20-%20%20%20%5Cfrac%7B%20%5Ctan%286A%29%20%20%5Ctan%282A%29%20%7D%7B%20%5Ctan%282A%29%20-%20%20%5Ctan%286A%29%20%20%7D%20)
</h3>
Since they have the same denominator we can write the fraction as
![- \frac{1 + \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) }](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B1%20%2B%20%20%5Ctan%286A%29%20%5Ctan%282A%29%20%20%7D%7B%20%5Ctan%282A%29%20-%20%20%5Ctan%286A%29%20%20%7D%20)
Using the identity
<h3>
![\frac{x}{y} = \frac{1}{ \frac{y}{x} }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7By%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7By%7D%7Bx%7D%20%7D%20)
</h3>
<u>Rewrite the expression</u>
We have
<h3>
![- \frac{1}{ \frac{ \tan(2A) - \tan(6A) }{1 + \tan(6A) \tan(2A) } }](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7B%20%5Ctan%282A%29%20%20-%20%20%5Ctan%286A%29%20%7D%7B1%20%2B%20%20%5Ctan%286A%29%20%5Ctan%282A%29%20%20%7D%20%7D%20)
</h3>
<u>Using the trigonometric identity</u>
<h3>
![\frac{ \tan(x) - \tan(y) }{1 + \tan(x) \tan(y) } = \tan(x - y)](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Ctan%28x%29%20-%20%20%5Ctan%28y%29%20%20%7D%7B1%20%2B%20%20%5Ctan%28x%29%20%20%5Ctan%28y%29%20%7D%20%20%3D%20%20%5Ctan%28x%20-%20y%29%20)
</h3>
<u>Rewrite the expression</u>
That's
<h3>
![- \frac{1}{ \tan(2A -6A) }](https://tex.z-dn.net/?f=%20%20-%20%5Cfrac%7B1%7D%7B%20%5Ctan%282A%20-6A%29%20%7D%20)
</h3>
Which is
<h3>
![- \frac{1}{ \tan( - 4A) }](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B1%7D%7B%20%5Ctan%28%20-%204A%29%20%7D%20)
</h3>
<u>Using the trigonometric identity</u>
<h3>
![\frac{1}{ \tan(x) } = \cot(x)](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Ctan%28x%29%20%7D%20%20%3D%20%20%5Ccot%28x%29%20)
</h3>
Rewrite the expression
That's
<h3>
![- \cot( - 4A)](https://tex.z-dn.net/?f=%20-%20%20%5Ccot%28%20-%204A%29%20)
</h3>
<u>Simplify the expression using symmetry of trigonometric functions</u>
That's
<h3>
![- ( - \cot(4A) )](https://tex.z-dn.net/?f=%20-%20%28%20-%20%20%5Ccot%284A%29%20%29)
</h3>
<u>Remove the parenthesis </u>
We have the final answer as
<h2>
![\cot(4A)](https://tex.z-dn.net/?f=%20%5Ccot%284A%29%20)
</h2>
As proven
Hope this helps you
Answer:
Step-by-step explanation:
Triangle GEF is a right angle triangle.
From the given right angle triangle
GE represents the hypotenuse of the right angle triangle.
With ∠E as the reference angle,
FE represents the adjacent side of the right angle triangle.
FG represents the opposite side of the right angle triangle.
To determine tan E, we would apply the tangent trigonometric ratio
Tan θ = opposite side/adjacent side. Therefore,
Tan E = 56/33
Tan E = 1.69697
It becomes 1.70 to the nearest hundredth.