First we solve this equation:
x = cos^-1(0) = pi/2 and 3pi/2
Now, this is the answer for angles between 0 and 2pi
but there are "negative angles" and angles larger than 2pi
so the general solution that includes all of these cases is:
x = pi/2 + n*pi
here n is any integer.
the Given data
*The given point is (-1, -5)
*The given scale factor is 5
The image of -1 - 5 after dilation by a scale factor of 5 centered at the origin is given as
Thus, the image after dilation by a scale factor of 5 centered at origin is (-5, -25)
This answer would have to be snakskeewhsof ndxjssoaanshew
Answer:
Step-by-step explanation:
Applying the Laplace transform:
![\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%2B5%5Cmathcal%7BL%7D%5By%27%5D%2B4%5Cmathcal%7BL%7D%5By%27%5D%3D0)
With the formulas:
![\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%3Ds%5E2%5Cmathcal%7BL%7D%5By%5D-y%280%29s-y%27%280%29)
![\mathcal{L}[y']=s\mathcal{L}[y]-y(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%5D%3Ds%5Cmathcal%7BL%7D%5By%5D-y%280%29)
![\mathcal{L}[x]=L](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5Bx%5D%3DL)
Solving for 
Apply the inverse Laplace transform with this formula:
![\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs-a%7D%5D%3De%5E%7Bat%7D)
![y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}](https://tex.z-dn.net/?f=y%3D3%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs%2B4%7D%5D%3D3e%5E%7B-4t%7D)
Answer:
x = 7
Step-by-step explanation:
Because this is a right triangle, one angle is a right angle (90°). All triangles have all three angle measures adding up to 180°, so the other two angles' measures add up to 90° (90 + 90 = 180).
Combine like terms of the angle measures.
6x + 9x = 15x
-3 + (-12) = -15
15x - 15
Because the sum of the measures of the two angles have to equal 90,
15x - 15 = 90
Add 15 from both sides.
15x = 105
Divide both sides by 15.
x = 7
To check, substitute 7 in both expressions.
6(7) - 3 = 39
9(7) - 12 = 51
39 + 51 + 90 (the measure of the right angle) = 180, so the value of x is 7.
I hope this helped :)
