Answer:
6t - 3
Step-by-step explanation:
9t - 3t + 2
Combine like terms: 9t - 3t = 6t
so
9t - 3t + 2
= 6t - 3
The volume of a right rectangular prism is length x height x width
4.7 x 6.2 x 3.1 = 90.334
Answer:
A. x = -2,500.
Step-by-step explanation:
sqrt(-4x) = 100
(sqrt(-4x)^2 = (100)^2
-4x = 10,000
4x = -10,000
x = -2,500
Check your work...
sqrt(-4(-2,500))
= sqrt(4 * 2,500)
= sqrt(10,000)
= plus or minus 100
A. x = -2,500 is your answer.
Hope this helps!
Answer:
<em>102°</em>
Step-by-step explanation:
(3x - 12)° + (2x + 2)° = 180°
5x - 10 = 180 ⇒ x = 38
m∠A = (3x - 12)°
<em>m∠A</em> = (3×38 - 12)° = <em>102°</em>
We have:
![\cos 2x = 1 - 2 \sin^2 x](https://tex.z-dn.net/?f=%5Ccos%202x%20%3D%201%20-%202%20%5Csin%5E2%20x)
Thus:
![1 - 2 \sin^2 x = \sin x](https://tex.z-dn.net/?f=1%20-%202%20%5Csin%5E2%20x%20%3D%20%5Csin%20x)
Adding
![2 \sin^2 x - 1](https://tex.z-dn.net/?f=2%20%5Csin%5E2%20x%20-%201)
gives:
![2 \sin^2 x + \sin x - 1 = 0](https://tex.z-dn.net/?f=2%20%5Csin%5E2%20x%20%2B%20%5Csin%20x%20-%201%20%3D%200)
Factoring gives:
![(2 \sin x + 1)(\sin x - 1) = 0](https://tex.z-dn.net/?f=%282%20%5Csin%20x%20%2B%201%29%28%5Csin%20x%20-%201%29%20%3D%200)
Thus, we have:
![\sin x = \frac{-1}{2}](https://tex.z-dn.net/?f=%5Csin%20x%20%3D%20%5Cfrac%7B-1%7D%7B2%7D)
or
![\sin x = 1](https://tex.z-dn.net/?f=%5Csin%20x%20%3D%201)
.
Note that because
![2 \pi > 2](https://tex.z-dn.net/?f=2%20%5Cpi%20%3E%202)
, there will be no solutions
![y](https://tex.z-dn.net/?f=y)
of the form
![2n\pi + z](https://tex.z-dn.net/?f=2n%5Cpi%20%2B%20z)
for positive integer
![n](https://tex.z-dn.net/?f=n)
and solution
![z](https://tex.z-dn.net/?f=z)
. So we find the basic values of
![x](https://tex.z-dn.net/?f=x)
giving
![\sin x \in (\frac{-1}{2}, 1)](https://tex.z-dn.net/?f=%5Csin%20x%20%5Cin%20%28%5Cfrac%7B-1%7D%7B2%7D%2C%201%29)
.
For
![\sin x = \frac{-1}{2}](https://tex.z-dn.net/?f=%5Csin%20x%20%3D%20%5Cfrac%7B-1%7D%7B2%7D)
with positive
![x](https://tex.z-dn.net/?f=x)
,
![x > \pi > 2](https://tex.z-dn.net/?f=x%20%3E%20%5Cpi%20%3E%202)
(this can be seen easily from the unit circle. But
![x < 2](https://tex.z-dn.net/?f=x%20%3C%202)
, a contradiction. So we examine the case in which
![\sin x = 1](https://tex.z-dn.net/?f=%5Csin%20x%20%3D%201)
.
In this case,
![x = \frac{\pi}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D)
. So this is the only solution to this equation.
Substituting this back in, we have
![\sin \frac{\pi}{2} = \cos \pi = 1](https://tex.z-dn.net/?f=%5Csin%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%3D%20%5Ccos%20%5Cpi%20%3D%201)
, as desired. So this is a valid solution.
Thus,
![x = \frac{\pi}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B%5Cpi%7D%7B2%7D)
.