Answer:
Step-by-step explanation:
This problem is very simple, since they give the solution for the differential equation from the start. So basically, you need to evaluate the initial conditions into the solution, and the derivative of the solution in order to find the value of the constants 
and 
.
So, first of all, let's find the derivative of 
:
Now, let's evaluate the first initial condition:
Now, the second initial condition:
Combining (1) and (2) we have a 2x2 System of Equations. Let's use elimination method in order to solve it:
Replacing into (1)
Therefore the solution of the second-order IVP is:
Answer:
y= -x+6
Step-by-step explanation:
G1xG2= -1
G2= -1
-1 = (y-8)
-------
(x+2)
-1 (x+2)=y-8
-x-2=y-8
-y=x+2-8
y= -x+6
Answer:
Step-by-step explanation:
If y is directly proportional to x, then the formula for that is a linear one:
y = kx, where k is the constant of proportionality. In our situation, if the pressure is directly proportional to the temp, then our formula is
P = kT. We need to find that value of k. Plug in what we have:
6 = k(440) so
k = .01363636 or as an equivalent fraction,
Now that have that value of k, we can use it in the formula again, this time with a different value for T to solve for P.
so
P = 5.181818 or as an equivalent fraction,
Answer:
<em>x = 4 / 3, y = 7 / 3</em>
Step-by-step explanation:
We are given the following system of equations;
{ 7x - y = 7, ⇒ Let us multiply the first equation by 2,
x + 2y = 6 }
2 * ( 7x - y = 7 ) ⇒ 14x - 2y = 14 ⇒ Now add the two equations
+ x + 2y = 6 + x + 2y = 6
14x + x = 14 + 6 ⇒ Simplify
15x = 20,
<em>x = 4 / 3</em> ⇒ Now substitute this value of x into the first equation to solve for the value of y,
7 * ( 4 / 3 ) - y = 7 ⇒ Simplify,
28 / 3 - y = 7,
y = 7 / 3
<em>Solution; x = 4 / 3, y = 7 / 3</em>
Answer:
Step-by-step explanation:
Subtracting b and c from both sides.
Simplifying both sides.
