Answer:
wer
Step-by-step explanation:
wer
Answer:
52%.
Step-by-step explanation:
There are a total of 50 squares in the shape, and only 26 squares of the shape are shaded. That makes 52% or 0.52.
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)
.
Answer:
0.4x^3 - xy.
Step-by-step explanation:
2/7x(1.4x^2-3.5y) Distributing the2/7x over the parentheses:
= 2/7 * 1.4 x^3 - 2/7 *3.5xy
= 0.4x^3 - xy
Answer:
hi
x+102° =180°[ Being cointerior angle]
x=180°-102°
x=78°
Also,
y=102°[ the opposite angle of parallelogram are equal]
z=78°[ the opposite of parallelogram are equal]
Hence, x=78°,y=102° and z=78°