Answer:
a
Step-by-step explanation:if x=y x number y
Answer:
no you cant
Step-by-step explanation:
= 9.71 Only way I could think of to solve it
Step-by-step explanation:
10x-72=3x-4
7x=68
x=9.71
Answer:
16
Step-by-step explanation:
Set up a proportion: 27/12=36/n
Solve algebraically: 27n=432
n=16
Therefore, 16
Answer:
The solutions on the given interval are :
![0](https://tex.z-dn.net/?f=0)
![\pi](https://tex.z-dn.net/?f=%5Cpi)
![\cos^{-1}(\frac{1}{4})](https://tex.z-dn.net/?f=%5Ccos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29)
![-\cos^{-1}(\frac{1}{4})+2\pi](https://tex.z-dn.net/?f=-%5Ccos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%2B2%5Cpi)
Step-by-step explanation:
We will need the double angle identity
.
Let's begin:
![2\sin(2x)=\sin(x)](https://tex.z-dn.net/?f=2%5Csin%282x%29%3D%5Csin%28x%29)
Use double angle identity mentioned on left hand side:
![2\cdot 2\sin(x)\cos(x)=\sin(x)](https://tex.z-dn.net/?f=2%5Ccdot%202%5Csin%28x%29%5Ccos%28x%29%3D%5Csin%28x%29)
Simplify a little bit on left side:
![4\sin(x)\cos(x)=\sin(x)](https://tex.z-dn.net/?f=4%5Csin%28x%29%5Ccos%28x%29%3D%5Csin%28x%29)
Subtract
on both sides:
![4\sin(x)\cos(x)-\sin(x)=0](https://tex.z-dn.net/?f=4%5Csin%28x%29%5Ccos%28x%29-%5Csin%28x%29%3D0)
Factor left hand side:
![\sin(x)[4\cos(x)-1]=0](https://tex.z-dn.net/?f=%5Csin%28x%29%5B4%5Ccos%28x%29-1%5D%3D0)
Set both factors equal to 0 because at least of them has to be 0 in order for the equation to be true:
![\sin(x)=0 \text{ or } 4\cos(x)-1=0](https://tex.z-dn.net/?f=%5Csin%28x%29%3D0%20%5Ctext%7B%20or%20%7D%204%5Ccos%28x%29-1%3D0)
The first is easy what angles
are
-coordinates on the unit circle 0. That happens at
and
on the given range of
(this
is not be confused with the
-coordinate).
Now let's look at the second equation:
![4\cos(x)-1=0](https://tex.z-dn.net/?f=4%5Ccos%28x%29-1%3D0)
Isolate
.
Add 1 on both sides:
![4 \cos(x)=1](https://tex.z-dn.net/?f=4%20%5Ccos%28x%29%3D1)
Divide both sides by 4:
![\cos(x)=\frac{1}{4}](https://tex.z-dn.net/?f=%5Ccos%28x%29%3D%5Cfrac%7B1%7D%7B4%7D)
This is not as easy as finding on the unit circle.
We know
will render us a value between
and
.
So one solution on the given interval for x is
.
We know cosine function is even.
So an equivalent equation is:
![\cos(-x)=\frac{1}{4}](https://tex.z-dn.net/?f=%5Ccos%28-x%29%3D%5Cfrac%7B1%7D%7B4%7D)
Apply
to both sides:
![-x=\cos^{-1}(\frac{1}{4})](https://tex.z-dn.net/?f=-x%3D%5Ccos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29)
Multiply both sides by -1:
![x=-\cos^{-1}(\frac{1}{4})](https://tex.z-dn.net/?f=x%3D-%5Ccos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29)
This going to be negative in the 4th quadrant but if we wrap around the unit circle,
, we will get an answer between
and
.
So the solutions on the given interval are :
![0](https://tex.z-dn.net/?f=0)
![\pi](https://tex.z-dn.net/?f=%5Cpi)
![\cos^{-1}(\frac{1}{4})](https://tex.z-dn.net/?f=%5Ccos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29)
![-\cos^{-1}(\frac{1}{4})+2\pi](https://tex.z-dn.net/?f=-%5Ccos%5E%7B-1%7D%28%5Cfrac%7B1%7D%7B4%7D%29%2B2%5Cpi)