You have to divide the number by the denominator of the fraction. For example, if you want to find 1/5 of 20, you have to divide 20 by 5 and that tells you that 1/5 of 20 is 4.
Answer:
![y(x)=tan(-log(cos(x))+\frac{\pi }{3} )](https://tex.z-dn.net/?f=y%28x%29%3Dtan%28-log%28cos%28x%29%29%2B%5Cfrac%7B%5Cpi%20%7D%7B3%7D%20%29)
Step-by-step explanation:
Rewrite the equation as:
![\frac{dy(x)}{dx}-tan(x)=y(x)^{2} *tan(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%28x%29%7D%7Bdx%7D-tan%28x%29%3Dy%28x%29%5E%7B2%7D%20%2Atan%28x%29)
Isolating ![\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D)
![\frac{dy}{dx} =tan(x)+tan(x)*y^{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3Dtan%28x%29%2Btan%28x%29%2Ay%5E%7B2%7D)
Factor:
![\frac{dy}{dx} =tan(x)*(1+y^{2} )](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3Dtan%28x%29%2A%281%2By%5E%7B2%7D%20%29)
Dividing both sides by
and multiplying them by ![dx](https://tex.z-dn.net/?f=dx)
![\frac{dy}{1+y^{2} } =tan(x)dx](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7B1%2By%5E%7B2%7D%20%7D%20%3Dtan%28x%29dx)
Integrate both sides:
![\int\ \frac{dy}{1+y^{2} } = \int\ tan(x) dx](https://tex.z-dn.net/?f=%5Cint%5C%20%5Cfrac%7Bdy%7D%7B1%2By%5E%7B2%7D%20%7D%20%3D%20%5Cint%5C%20tan%28x%29%20%20dx)
Evaluate the integrals:
![arctan(y)=-log(cos(x))+C_1](https://tex.z-dn.net/?f=arctan%28y%29%3D-log%28cos%28x%29%29%2BC_1)
Solving for y:
![y(x)=tan(-log(cos(x))+C_1)](https://tex.z-dn.net/?f=y%28x%29%3Dtan%28-log%28cos%28x%29%29%2BC_1%29)
Evaluating the initial condition:
![y(0)=\sqrt{3} =tan(-log(cos(0))+C_1)=tan(-log(1)+C_1)=tan(0+C_1)](https://tex.z-dn.net/?f=y%280%29%3D%5Csqrt%7B3%7D%20%3Dtan%28-log%28cos%280%29%29%2BC_1%29%3Dtan%28-log%281%29%2BC_1%29%3Dtan%280%2BC_1%29)
![\sqrt{3} =tan(C_1)\\arctan(\sqrt{3} )=C_1\\60=C_1](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%20%3Dtan%28C_1%29%5C%5Carctan%28%5Csqrt%7B3%7D%20%29%3DC_1%5C%5C60%3DC_1)
Converting 60 degrees to radians:
![60degrees*\frac{\pi }{180degrees} =\frac{\pi }{3}](https://tex.z-dn.net/?f=60degrees%2A%5Cfrac%7B%5Cpi%20%7D%7B180degrees%7D%20%3D%5Cfrac%7B%5Cpi%20%7D%7B3%7D)
Replacing
in the diferential equation solution:
![y(x)=tan(-log(cos(x))+\frac{\pi }{3} )](https://tex.z-dn.net/?f=y%28x%29%3Dtan%28-log%28cos%28x%29%29%2B%5Cfrac%7B%5Cpi%20%7D%7B3%7D%20%29)
Answer:
Step-by-step explanation:
this picture has a blue circle with a line through it i dont know what to help you with if you could tell me the equation then i can help you but i cant if there is a blue circle in it.
The answer is: - 6 .
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Evaluate the value INSIDE the "bars".
b - a = -2 - 4 = -6 . The absolute value of the value inside inside the bars is the "positive" number of that value. The value is negative 6; so, the absolute value, or "magnitude", of "-6", is "6"; Then, then "-" (6) = -6. So the answer is: -6 .
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Answer:
11-2x=x+2
-3x=9
x=-3
Step-by-step explanation:
y=11-2x
y=x+2
So we use the first equation to plug in for the second equation.
Then we solve for x and get the answer. Hope this helps. Thank you.