Answer: Option (C) is the correct answer.
Explanation:
When atoms which are chemically combining tend to share electrons with each other, that is, forming covalent bonds with each other then the compound formed is known as a molecular compound.
For example,
is a molecular compound.
This is because hydrogen atom has only one electron in its valence shell and an oxygen atom needs two electrons to complete its octet.
Therefore, sharing of electrons take place between the hydrogen and oxygen atom. As a result, it is a molecular compound.
Whereas NaCl, CaO, and MgS compounds are formed due to transfer of electron from one atom to another.
Thus, we can conclude that out of the given options
formula is a molecular compound.
f(x)=10x to the power of two +4
Answer:
36n + 18
Step-by-step explanation:
6 * 6n = 36n
6 * 3 = 18
36n + 18 = 36n + 18
Answer:
100
Step-by-step explanation:
Answer:
See explanation
Step-by-step explanation:
Given the equation:
![2x\sin (2y)dx-(x^2+12)\cos ydy=0](https://tex.z-dn.net/?f=2x%5Csin%20%282y%29dx-%28x%5E2%2B12%29%5Ccos%20ydy%3D0)
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,
![\int \dfrac{2x}{x^2+12}dx=\int \dfrac{1}{2\sin y}dy\\ \\\int \dfrac{d(x^2)}{x^2+12}=\dfrac{1}{2}\int \dfrac{\sin y}{\sin^2 y}dy\\ \\\int \dfrac{d(x^2+12)}{x^2+12}=-\dfrac{1}{2}\int \dfrac{d(\cos y)}{1-\cos^2 y}\\ \\\ln (x^2+12)+C=-\dfrac{1}{2}\int \left(\dfrac{1}{2(1-\cos y)}+\dfrac{1}{2(1+\cos y)}\right)d(\cos y)\\ \\\ln (x^2+12)+C=-\dfrac{1}{4}\int \dfrac{d(\cos y)}{1-\cos y}-\dfrac{1}{4}\int \dfrac{d(\cos y)}{1+\cos y}\\ \\\ln (x^2+12)+C=\dfrac{1}{4}\ln (1-\cos y)-\dfrac{1}{4}\ln (1+\cos y)](https://tex.z-dn.net/?f=%5Cint%20%5Cdfrac%7B2x%7D%7Bx%5E2%2B12%7Ddx%3D%5Cint%20%5Cdfrac%7B1%7D%7B2%5Csin%20y%7Ddy%5C%5C%20%5C%5C%5Cint%20%5Cdfrac%7Bd%28x%5E2%29%7D%7Bx%5E2%2B12%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Cint%20%5Cdfrac%7B%5Csin%20y%7D%7B%5Csin%5E2%20y%7Ddy%5C%5C%20%5C%5C%5Cint%20%5Cdfrac%7Bd%28x%5E2%2B12%29%7D%7Bx%5E2%2B12%7D%3D-%5Cdfrac%7B1%7D%7B2%7D%5Cint%20%5Cdfrac%7Bd%28%5Ccos%20y%29%7D%7B1-%5Ccos%5E2%20y%7D%5C%5C%20%5C%5C%5Cln%20%28x%5E2%2B12%29%2BC%3D-%5Cdfrac%7B1%7D%7B2%7D%5Cint%20%5Cleft%28%5Cdfrac%7B1%7D%7B2%281-%5Ccos%20y%29%7D%2B%5Cdfrac%7B1%7D%7B2%281%2B%5Ccos%20y%29%7D%5Cright%29d%28%5Ccos%20y%29%5C%5C%20%5C%5C%5Cln%20%28x%5E2%2B12%29%2BC%3D-%5Cdfrac%7B1%7D%7B4%7D%5Cint%20%5Cdfrac%7Bd%28%5Ccos%20y%29%7D%7B1-%5Ccos%20y%7D-%5Cdfrac%7B1%7D%7B4%7D%5Cint%20%5Cdfrac%7Bd%28%5Ccos%20y%29%7D%7B1%2B%5Ccos%20y%7D%5C%5C%20%5C%5C%5Cln%20%28x%5E2%2B12%29%2BC%3D%5Cdfrac%7B1%7D%7B4%7D%5Cln%20%281-%5Ccos%20y%29-%5Cdfrac%7B1%7D%7B4%7D%5Cln%20%281%2B%5Ccos%20y%29)
![\ln (x^2+12)+C=\dfrac{1}{4}\ln \dfrac{1-\cos y}{1+\cos y}](https://tex.z-dn.net/?f=%5Cln%20%28x%5E2%2B12%29%2BC%3D%5Cdfrac%7B1%7D%7B4%7D%5Cln%20%5Cdfrac%7B1-%5Ccos%20y%7D%7B1%2B%5Ccos%20y%7D)
Find the constant solutions, if any, that were lost in the solution of the differential equation:
When
![\cos y=0,](https://tex.z-dn.net/?f=%5Ccos%20y%3D0%2C)
then
![y=\dfrac{\pi }{2}+\pi k,\ k\in Z](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B%5Cpi%20%7D%7B2%7D%2B%5Cpi%20k%2C%5C%20k%5Cin%20Z)