Answer:
y=(-4/3)x
Step-by-step explanation:
you put the points into this equation to find the slope
(y2-y1)/(x2-x1)
now lets label the points
(6,-8)
x1=6 and y1=-8
(3,-4)
x2=3 and y2=-4
Input into equation
(-4-(-8))/(3-6)=
(-4+8)/(3-6)
4/-3
Answer:
x = -45, y = -40
Step-by-step explanation:
Based on the first clue, we find out that
x + 5 = y
5x = 6y + 15
We can re-write the first equation to x = y - 5.
Therefore, the second equation can also be written as 5(y - 5) = 6y + 15
This can be simplified to 5y - 25 = 6y + 15
We can subtract 6y from each side, and add 25 to each side;
5y - 6y = 15 + 25
Therefore, -y = 40
Therefore y = -40.
Now let's plug this back into the original equation, to get : x + 5 = -40
x=-45
Answer:
Step-by-step explanation:
-5x² - 6 = -4x
-5x² + 4x - 6 = 0
a = -5 ; b = 4 ; c = -6
Discriminant = b² - 4ac
= 4² - 4*(-5)*(-6)
= 16 - 120
= -104
roots = 
![=\dfrac{-4+\sqrt{-104}}{2*(-5)};\dfrac{-4-\sqrt{-104}}{2*(-5)}\\\\=\dfrac{-4+2i\sqrt{26}}{-10} ; \dfrac{-4-2i\sqrt{26}}{-10}\\\\=\dfrac{(-2)[2-i\sqrt{26}]}{-10} \ ; \ \dfrac{(-2)[2+i\sqrt{26}]}{-10}\\\\=\dfrac{2-i\sqrt{26}}{5} \ ; \ \dfrac{2+i\sqrt{26}}{5}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B-4%2B%5Csqrt%7B-104%7D%7D%7B2%2A%28-5%29%7D%3B%5Cdfrac%7B-4-%5Csqrt%7B-104%7D%7D%7B2%2A%28-5%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7B-4%2B2i%5Csqrt%7B26%7D%7D%7B-10%7D%20%3B%20%5Cdfrac%7B-4-2i%5Csqrt%7B26%7D%7D%7B-10%7D%5C%5C%5C%5C%3D%5Cdfrac%7B%28-2%29%5B2-i%5Csqrt%7B26%7D%5D%7D%7B-10%7D%20%5C%20%3B%20%5C%20%5Cdfrac%7B%28-2%29%5B2%2Bi%5Csqrt%7B26%7D%5D%7D%7B-10%7D%5C%5C%5C%5C%3D%5Cdfrac%7B2-i%5Csqrt%7B26%7D%7D%7B5%7D%20%5C%20%3B%20%5C%20%5Cdfrac%7B2%2Bi%5Csqrt%7B26%7D%7D%7B5%7D)
If the given differential equation is
then multiply both sides by 
:
The left side is the derivative of a product,
![\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%5Csin%28x%29y%5Cright%5D%20%3D%20%5Csec%5E2%28x%29)
Integrate both sides with respect to 
, recalling that 
:
![\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%5B%5Csin%28x%29y%5Cright%5D%20%5C%2C%20dx%20%3D%20%5Cint%20%5Csec%5E2%28x%29%20%5C%2C%20dx)
Solve for 
:
![\boxed{y = \sec(x) + C \csc(x)}which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}](https://tex.z-dn.net/?f=%5Cboxed%7By%20%3D%20%5Csec%28x%29%20%2B%20C%20%5Ccsc%28x%29%7D%3C%2Fp%3E%3Cp%3Ewhich%20follows%20from%20%5Btex%5D%5Ctan%28x%29%3D%5Cfrac%7B%5Csin%28x%29%7D%7B%5Ccos%28x%29%7D)
.
