This is a separable differential equation, so let's start of there. Let's separate the variables to their own side with the respective differentials:
![\frac{dy}{dx} = xy^2](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20xy%5E2%20)
![dy = (xy^2) dx](https://tex.z-dn.net/?f=dy%20%3D%20%28xy%5E2%29%20dx)
![\frac{1}{y^2} dy = x dx](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7By%5E2%7D%20dy%20%3D%20x%20dx)
Let's integrate both sides (it's separable, so we can do this):
![\int\ { \frac{1}{y^2} } \, dy = \int\ {x} \, dx](https://tex.z-dn.net/?f=%20%5Cint%5C%20%7B%20%5Cfrac%7B1%7D%7By%5E2%7D%20%7D%20%5C%2C%20dy%20%3D%20%20%5Cint%5C%20%7Bx%7D%20%5C%2C%20dx%20%20)
![- \frac{1}{y} = \frac{x^2}{2} + C](https://tex.z-dn.net/?f=-%20%5Cfrac%7B1%7D%7By%7D%20%3D%20%20%5Cfrac%7Bx%5E2%7D%7B2%7D%20%2B%20C)
Now, let's plug in the values we are given to find the constant "C":
![- \frac{1}{1} =\frac{0^2}{2}+C](https://tex.z-dn.net/?f=-%20%5Cfrac%7B1%7D%7B1%7D%20%20%3D%5Cfrac%7B0%5E2%7D%7B2%7D%2BC%20)
![-1 = C](https://tex.z-dn.net/?f=-1%20%3D%20C)
Let's rewrite the equation, with C in it, then solve for x because we need to ultimately find x:
![- \frac{1}{y} = \frac{x^2}{2} - 1](https://tex.z-dn.net/?f=-%20%5Cfrac%7B1%7D%7By%7D%20%20%3D%20%5Cfrac%7Bx%5E2%7D%7B2%7D%20-%201)
![x = \sqrt{2(- \frac{1}{y}+1)}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%7B2%28-%20%5Cfrac%7B1%7D%7By%7D%2B1%29%7D)
Let's plug in y = 3 and solve for x:
![x = \sqrt{2(- \frac{1}{3}+1)} = \sqrt{ 2( \frac{2}{3}) } = \sqrt{ \frac{4}{3} }](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B2%28-%20%5Cfrac%7B1%7D%7B3%7D%2B1%29%7D%20%3D%20%5Csqrt%7B%202%28%20%5Cfrac%7B2%7D%7B3%7D%29%20%7D%20%3D%20%5Csqrt%7B%20%5Cfrac%7B4%7D%7B3%7D%20%7D)
Let's simplify and rationalize the denominator:
![x = \sqrt{ \frac{4}{3}} = 2 \sqrt{ \frac{1}{3}} = 2 \frac{ \sqrt{3} }{3}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B4%7D%7B3%7D%7D%20%3D%202%20%5Csqrt%7B%20%5Cfrac%7B1%7D%7B3%7D%7D%20%3D%202%20%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B3%7D%20)
So, your answer is
D.
Answer:
the answer is c
Step-by-step explanation:
i just finished the question
Use y = mx + b where m= slope, b = y - intercept
y = mx + b
10 = 3*1 + b
b = 7
y = 3x + 7
Answer:
I think it's a SAS
Step-by-step explanation:
The stamens is false for any value of x