Answer:
8
Step-by-step explanation:
Answer:
See explanation
Step-by-step explanation:
Given the equation:

Separate variables
and
:
![2x\sin (2y)dx=(x^2+12)\cos y dy\\ \\\dfrac{2x\sin (2y)dx}{x^2+12}=\cos ydy\ [\text{Divided by non-zero expression }x^2+12]\\ \\\dfrac{2x}{x^2+12}dx=\dfrac{\cos y}{\sin (2y)}dy\ [\text{Divided by }\sin (2y)]\\ \\\dfrac{2x}{x^2+12}dx=\dfrac{\cos y}{2\sin y\cos y}dy\ [\text{Use formula }\sin (2y)=2\sin y\cos y]\\ \\\dfrac{2x}{x^2+12}dx=\dfrac{1}{2\sin y}dy\ [\text{Simplify when }\cos y\neq 0]](https://tex.z-dn.net/?f=2x%5Csin%20%282y%29dx%3D%28x%5E2%2B12%29%5Ccos%20y%20dy%5C%5C%20%5C%5C%5Cdfrac%7B2x%5Csin%20%282y%29dx%7D%7Bx%5E2%2B12%7D%3D%5Ccos%20ydy%5C%20%5B%5Ctext%7BDivided%20by%20non-zero%20expression%20%7Dx%5E2%2B12%5D%5C%5C%20%5C%5C%5Cdfrac%7B2x%7D%7Bx%5E2%2B12%7Ddx%3D%5Cdfrac%7B%5Ccos%20y%7D%7B%5Csin%20%282y%29%7Ddy%5C%20%5B%5Ctext%7BDivided%20by%20%7D%5Csin%20%282y%29%5D%5C%5C%20%5C%5C%5Cdfrac%7B2x%7D%7Bx%5E2%2B12%7Ddx%3D%5Cdfrac%7B%5Ccos%20y%7D%7B2%5Csin%20y%5Ccos%20y%7Ddy%5C%20%5B%5Ctext%7BUse%20formula%20%7D%5Csin%20%282y%29%3D2%5Csin%20y%5Ccos%20y%5D%5C%5C%20%5C%5C%5Cdfrac%7B2x%7D%7Bx%5E2%2B12%7Ddx%3D%5Cdfrac%7B1%7D%7B2%5Csin%20y%7Ddy%5C%20%5B%5Ctext%7BSimplify%20when%20%7D%5Ccos%20y%5Cneq%200%5D)
Now,


Find the constant solutions, if any, that were lost in the solution of the differential equation:
When

then

Answer:
B
Step-by-step explanation: 68+x+x=180. subtract 68 from both sides, and simplify the x's. so 2x=112. than divide by 2. x=56
Answer:
C
Step-by-step explanation:
The triangle inequality theorem tells us that if two sides of a triangle are known (let it be side a and b), we can know the length of range of third side (side c). By:
a-b< c < a+b
So sides are given 29 and 40.
Sum is 29 + 40 = 69
Difference is 40 - 29 = 11
Hence, the third side would be BETWEEN 11 and 69
C is the correct choice.