Answer:
x = 0°
Step-by-step explanation:
![\cos x = 3 \cos x - 2 \\ 2 = 3 \cos x - \cos x \\ 2 = 2\cos x \\ \cos x = \frac{2}{2} \\ \cos x =1 \\ \cos x =\cos 0 \degree \\ \huge \red{ \boxed{x = 0 \degree}} \\](https://tex.z-dn.net/?f=%20%5Ccos%20x%20%3D%203%20%5Ccos%20x%20-%202%20%5C%5C%202%20%3D%203%20%5Ccos%20x%20-%20%5Ccos%20x%20%5C%5C%202%20%3D%20%202%5Ccos%20x%20%5C%5C%20%20%5Ccos%20x%20%3D%20%20%5Cfrac%7B2%7D%7B2%7D%20%20%5C%5C%20%5Ccos%20x%20%3D1%20%5C%5C%20%5Ccos%20x%20%3D%5Ccos%200%20%5Cdegree%20%20%5C%5C%20%20%5Chuge%20%5Cred%7B%20%5Cboxed%7Bx%20%3D%200%20%5Cdegree%7D%7D%20%5C%5C%20)
Answer:
5. 6
7. 12
I'm not sure for the last two, sorry :(
Answer:
405 cycles
Step-by-step explanation:
We have the equation:
y = 6*sin(324*π*t)
For the properties of the sin function, we know that the period is 2π.
So between:
Sin(x) and Sin(x + 2*pi)
we have a cycle.
between:
Sin(x) and Sin(x + 6*pi)
we have 3 cycles.
and so on.
Now we want to find how many cycles will occur between t = 3 s, and t = 5.5 seconds
Between these times, the difference in the argument of the sin function is:
324*π*5.5 - 324*π*3 = 324*π*(5.5 - 3) = 324*π*2.5
Now, the number of cycles that we will have between these times is equal to the number of times that "2*π" is in 324*π*2.5
That number is just the quotient between 324*π*2.5 and 2*π
N = (324*π*2.5)/(2*π) = (324*2.5)/(2) = 405
There are 405 cycles between 3 seconds and 5.5 seconds.
Answer:
![\frac{1}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B15%7D)
Step-by-step explanation:
as said in the question that the triangle has three equal sides. i.e. this is an equilateral triangle. So,
let us consider one side of the triangle to be x . and 3x( x+x+x) should be equal to 1/5
![x+x+x = \frac{1}{5}\\3x=\frac{1}{5}\\x = \frac{1}{5} / 3\\x = \frac{1}{5} * \frac{1}{3}\\x = \frac{1}{15}](https://tex.z-dn.net/?f=x%2Bx%2Bx%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5C%5C3x%3D%5Cfrac%7B1%7D%7B5%7D%5C%5Cx%20%3D%20%5Cfrac%7B1%7D%7B5%7D%20%2F%203%5C%5Cx%20%3D%20%5Cfrac%7B1%7D%7B5%7D%20%2A%20%5Cfrac%7B1%7D%7B3%7D%5C%5Cx%20%3D%20%5Cfrac%7B1%7D%7B15%7D)