Answer:
1. 
2. 
![23. [tex]Assuming t as independent variable:F(r,t)=t+\frac{1}{m} exp(m+r)+\frac{r^{2} }{2} =C\\Step-by-step explanation:1. Separable variables:[tex]\frac{dy}{dt}=\frac{y*cos(t) }{t}\\ \frac{dy}{y}= \frac{cos(t) }{t}dt\\ \int {\frac{dy }{y}} \, dt=\int {\frac{cos(t) }{t}} \, dt \\ln(y)-ln(C)=ln(t)-\frac{t^{2} }{2(2!)} +\frac{t^{4} }{4(4!)} -\frac{t^{6} }{6(6!)}+... \\y=C(t*exp(\frac{t^{2} }{2(2!)} +\frac{t^{4} }{4(4!)} -\frac{t^{6} }{6(6!)}+...))](https://tex.z-dn.net/?f=2%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E3.%20%5Btex%5DAssuming%20t%20as%20independent%20variable%3A%3C%2Fp%3E%3Cp%3EF%28r%2Ct%29%3Dt%2B%5Cfrac%7B1%7D%7Bm%7D%20exp%28m%2Br%29%2B%5Cfrac%7Br%5E%7B2%7D%20%7D%7B2%7D%20%3DC%5C%5C%3C%2Fp%3E%3Cp%3E%3Cstrong%3EStep-by-step%20explanation%3A%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3E1.%20Separable%20variables%3A%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3E%3Cstrong%3E%5Btex%5D%5Cfrac%7Bdy%7D%7Bdt%7D%3D%5Cfrac%7By%2Acos%28t%29%20%7D%7Bt%7D%5C%5C%20%20%5Cfrac%7Bdy%7D%7By%7D%3D%20%5Cfrac%7Bcos%28t%29%20%7D%7Bt%7Ddt%5C%5C%20%5Cint%20%7B%5Cfrac%7Bdy%20%7D%7By%7D%7D%20%5C%2C%20dt%3D%5Cint%20%7B%5Cfrac%7Bcos%28t%29%20%7D%7Bt%7D%7D%20%5C%2C%20dt%20%5C%5Cln%28y%29-ln%28C%29%3Dln%28t%29-%5Cfrac%7Bt%5E%7B2%7D%20%7D%7B2%282%21%29%7D%20%2B%5Cfrac%7Bt%5E%7B4%7D%20%7D%7B4%284%21%29%7D%20-%5Cfrac%7Bt%5E%7B6%7D%20%7D%7B6%286%21%29%7D%2B...%20%5C%5Cy%3DC%28t%2Aexp%28%5Cfrac%7Bt%5E%7B2%7D%20%7D%7B2%282%21%29%7D%20%2B%5Cfrac%7Bt%5E%7B4%7D%20%7D%7B4%284%21%29%7D%20-%5Cfrac%7Bt%5E%7B6%7D%20%7D%7B6%286%21%29%7D%2B...%29%29)
2. Separable variables
\frac{dy}{sin(y)}=dt\\ \int\ \frac{1}{sin(y)}} \, dy = \int\ 1} \, dt\\t+C=ln(csc(y)-cot(y))[/tex]
3. Homogeneous D.E
Rewriting:

Answer:
Coefficient of Q is 36.
Step-by-step explanation:
The coefficient means the constant term with the variable
Here, we need to find the coefficient of Q
We have been given an expression:

The coefficient of Q is the simplified form of the constant terms given:
Multiply the terms to get the simplified form which is:

Hence, the coefficient of Q is 36.
Answer:
114
Step-by-step explanation:
The 5 angles equal 540, so subtract the 4 angles and you are left with 114.
540-111-103-122-90=114
Answer:
It's 3
Step-by-step explanation:
Answer:
42
Step-by-step explanation:
We know that 10x + 6y = 7, and so
6(10x + 6y) = 6(7) = 42