Answer: 1775
Step-by-step explanation: a p e x
Answer: The required solution of the given IVP is

Step-by-step explanation: We are given to find the solution of the following initial value problem :

Let
be an auxiliary solution of the given differential equation.
Then, we have

Substituting these values in the given differential equation, we have
![m^2e^{mx}-e^{mx}=0\\\\\Rightarrow (m^2-1)e^{mx}=0\\\\\Rightarrow m^2-1=0~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mx}\neq0]\\\\\Rightarrow m^2=1\\\\\Rightarrow m=\pm1.](https://tex.z-dn.net/?f=m%5E2e%5E%7Bmx%7D-e%5E%7Bmx%7D%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%5E2-1%29e%5E%7Bmx%7D%3D0%5C%5C%5C%5C%5CRightarrow%20m%5E2-1%3D0~~~~~~~~~~~~~~~~~~~~~~~~~~%5B%5Ctextup%7Bsince%20%7De%5E%7Bmx%7D%5Cneq0%5D%5C%5C%5C%5C%5CRightarrow%20m%5E2%3D1%5C%5C%5C%5C%5CRightarrow%20m%3D%5Cpm1.)
So, the general solution of the given equation is
where A and B are constants.
This gives, after differentiating with respect to x that

The given conditions implies that

and

Adding equations (i) and (ii), we get

From equation (i), we get

Substituting the values of A and B in the general solution, we get

Thus, the required solution of the given IVP is

Answer: Third option:
Step-by-step explanation:
The equation in Slope Intercept form of a line that does not pass through the point (0,0), which is known as "Origin, is the following:

Where "m" is the slope of the line and "b" is the y-intercept.
The equation in Slope Intercept form of a line that passes through the Origin, is:

Where "m" is the slope of the line.
In this case you can observe in the picture attached that the line passes through the point (0,0).
You can also notice that "y" would be the Dependent variable and "x" the Independent variable.
Therefore, the equation of this must have this form:

The only equation that matches with that form, is the one given in the Third option. This is:

Answer:
5x + 3y = 2
5x - 3y = -22
Step-by-step explanation:yes
Answer:
24
Step-by-step explanation:
In a deck of 52 cards, there are 4 kings and 4 queens
Selection of 3 kings out of 4 = 4 C 3 = 4
Selection of 2 queens out of 4 = 6
So, total number of selections = 4 x 6 = 24