Answer:
So, solution of the differential equation is

Step-by-step explanation:
We have the given differential equation: y′′+4y=5xcos(2x)
We use the Method of Undetermined Coefficients.
We first solve the homogeneous differential equation y′′+4y=0.

It is a homogeneous solution:

Now, we finding a particular solution.

we get

So, solution of the differential equation is

What you don't want is the value of r(t) becoming negative. Surely that would represent water escaping the reservoir.
How big can (t) get before water actually starts escaping the reservoir?
Essentially, to figure this out r(t) would have to be equal to 0.
700 - 40t = 0
40t=700
t=700/40=17.5
So the first answer is 17.5 seconds. After this amount of time has elapsed the reservoir will start to lose water as r(t) would become negative.
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The reservoir had the least amount of water in it before it was being filled. That was when t=0. The volume of water in the reservoir wasn't negatively impacted as not enough water had escaped it during the 17.5 to 30 second period.
Answer:
y=mx + b
the slope is -3,2
y= -0.67x + 5
this is what. i got i could be wrong, sorry if i am
Step-by-step explanation:
Let the number of orders Eric served be x
Eric = x
Mai = x+ 8 [Mai served 8 more than Eric]
Dean = 3x [Dean served 3 times as many as Eric]
Given that the total is 103
x + x + 8 + 3x = 103
5x + 8 = 103
5x = 103 - 8
5x = 95
x = 19
x = 19
x + 8 = 19 + 8 = 27
3x = 19 x 3 = 57
Eric served 19
Mai served 27
Dean served 57