Answer:
So for the first one the first ting u have to do is FLIP the equation so---> X-12=y
Then you have to add 12 to BOTH sides----> x-12+12=y+12
<u><em>So your answer for X ----> x=y+12</em></u>
<u><em>For Y on the first equation it is--->y=x-12</em></u> (Just flipped and the sign changed)
For the second equation we are gonna solve for Y first.
The first thing u want to do is divide both sides by -3 so it will look like this
-3y/-3 = 2x/+36/-3
<u><em>So Y will equal-----> -2/3x- 12</em></u>
Now we are going to do the X part
So fist FLIP the equation----> 2x+36= -3y
The add -36 to both sides-----> 2x+36+-36=-3y+-36
Last step you have to divide both sides by 2
So that would be----> 2x/2= -3y-3
<u><em>Your final result will be----> x=-3/2y-18</em></u>
I hope this helped you out (:::::::
Answer:
x(t) = 5000*( 1 - e^-kt)
Step-by-step explanation:
Given:
- Total number of students n = 5000
Find:
Differential equation governing the number of students x(t) who have contracted the flu.
Solution:
- Number of non-affected students = (5000 - x)
Hence,
- Rate at which students are infected:
dx / dt = k*(5000 - x )
- separate variables:
dx / (5000 - x ) = k*dt
- Integrate both sides:
- Ln(5000 - x) = kt + C
- Evaluate C for x = 0 @ t = 0
- Ln(5000 - 0) = k*0 + C
C = - Ln(5000)
- The solution to ODE is:
Ln(5000 - x) = -k*t + Ln(5000)
5000 - x = 5000*e^-kt
x(t) = 5000*( 1 - e^-kt)
<h3>
Answer: g(x) = (-2/3)*x^2</h3>
============================================
Work Shown:
f(x) = x^2
g(x) = a*f(x) for some constant 'a' since g(x) is a scaled version of f(x).
The value of 'a' vertically stretches f(x) upward if a > 0
If 'a' is negative, then we have a reflection going on as shown in the diagram.
We want (x,y) = (3,-6) to be on the graph of g(x). This means g(3) = -6
If we plugged x = 3 into f(x), we get
f(x) = x^2
f(3) = 3^2
f(3) = 9
So,
g(x) = a*f(x)
g(3) = a*f(3) ... replace x with 3
g(3) = a*9 ... replace f(3) with 9 since f(3) = 9
-6 = a*9 ... replace g(3) with -6 since g(-3) = -6
9a = -6
a = -6/9
a = -2/3
Therefore, this means
g(x) = a*f(x)
g(x) = (-2/3)*f(x)
g(x) = (-2/3)*x^2
