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Sergeeva-Olga [200]
3 years ago
7

Can someone please help me understand

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
7 0
Stop being like that I helped u
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5. Find the general solution to y'''-y''+4y'-4y = 0
CaHeK987 [17]

For any equation,

a_ny^(n)+\dots+a_1y'+a_0y=0

assume solution of a form, e^{yt}

Which leads to,

(e^{yt})'''-(e^{yt})''+4(e^{yt})'-4e^{yt}=0

Simplify to,

e^{yt}(y^3-y^2+4y-4)=0

Then find solutions,

\underline{y_1=1}, \underline{y_2=2i}, \underline{y_3=-2i}

For non repeated real root y, we have a form of,

y_1=c_1e^t

Following up,

For two non repeated complex roots y_2\neq y_3 where,

y_2=a+bi

and,

y_3=a-bi

the general solution has a form of,

y=e^{at}(c_2\cos(bt)+c_3\sin(bt))

Or in this case,

y=e^0(c_2\cos(2t)+c_3\sin(2t))

Now we just refine and get,

\boxed{y=c_1e^t+c_2\cos(2t)+c_3\sin(2t)}

Hope this helps.

r3t40

5 0
4 years ago
Please help!! Will get brainliest! Zoom if can’t see. Correct answer only!!
8090 [49]
Domain = Set of all real numbers, which is choice B
Range = Choice C) y \le 3

The domain is the set of allowed x value inputs of a function. In this case, we can plug in any x value we want. The graph stretches forever in both directions along the x axis. This is shown by the arrows.So that's why the domain is the set of all real numbers.

The range is the set of outputs of a function. It is the set of possible y values. As you can see on the graph, the highest point is at (-1,3) which is the vertex.
The largest y value possible is y = 3. Any other y value smaller than this is possible. So the range is therefore y \le 3 where y is a real number


7 0
3 years ago
3x^2 + 14x<br>how do you factories this​
I am Lyosha [343]

Answer:

x(3x+14)

Step-by-step explanation:

what do those terms share? they share the letter "x"

therefore we multiply x by 3x^2/x + 14x/x

3x^2/x = 3x and 14x/x = 14

8 0
3 years ago
The bottom of a ladder must be placed 3 ft from a wall. the ladder is 12 feet long. how far above the ground does the ladder tou
3241004551 [841]
9 feet above the ground, since it has to be 3 feet away from the wall you would have to subtract those 3 feet from the length of the ladder.
6 0
3 years ago
Mark has 20 pencils he wants to divide his pencils to 5 friends how much will each friend get?
Nookie1986 [14]

Answer: B. 4

Step-by-step explanation: Divide 20 by 5 and get 4.

8 0
3 years ago
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