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timofeeve [1]
3 years ago
5

Can you help the picture is in the file provided

Mathematics
1 answer:
Reika [66]3 years ago
4 0
Answer:5/half’s
I don’t have an explanation but I think it’s that
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Set up but do not solve for the appropriate particular solution yp for the differential equation y′′+4y=5xcos(2x) using the Meth
taurus [48]

Answer:

So, solution of  the differential equation is

y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x+c_1e^{-2it}+c_2e^{2it}\\

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.

y''+4y=0\\\\r^2+4=0\\\\r=\pm2i\\\\

It is a homogeneous solution:

y_h(t)=c_1e^{-2i t}+c_2e^{2i t}

Now, we finding a particular solution.

y_p(t)=A5x\cos 2x\\\\y'_p(t)=A5\cos 2x-A10x\sin 2x\\\\y''_p(t)=-A20\sin 2x-A20x\cos 2x\\\\\\\implies y''+4y=5x\cos 2x\\\\-A20\sin 2x-A20x\cos 2x+4\cdot A5x\cos 2x=5x\cos 2x\\\\-A20\sin 2x=5x\cos 2x\\\\A=-\frac{x}{4} \cot 2x\\

we get

y_p(t)=A5\cos 2x\\\\y_p(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x\\\\\\y(t)=y_p(t)+y_h(t)\\\\y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x+c_1e^{-2it}+c_2e^{2it}\\

So, solution of  the differential equation is

y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos  2x+c_1e^{-2it}+c_2e^{2it}\\

7 0
3 years ago
Twelve more than the product of a number and four is fewer than 60.
valina [46]
Product of a number and four is 4x 
<span>12 more than that is 12+4x </span>
<span>fewer than 60  </span>

<span>12 + 4x < 60</span>
7 0
3 years ago
A local maximum of the function f(x) occurs for which x-value?
My name is Ann [436]

Answer:

-4

Step-by-step explanation:

the highest f(x) value on the table is at -4 on the x column

3 0
2 years ago
Please help me!!! Will get brainliest!!!
ratelena [41]
1. You already did it.
2. Table
3. t (years since 1990)
4. n (# of cigarettes sold)
5. (t, n)
6. You can see the distribution of the data pretty neatly. There are also many more advantages including it's easier to calculate standard deviation, easier to see the mean, mode and median, and it's also much easier to just tell the extrema of the dataset by just looking at the scattergram.
5 0
3 years ago
NEED HELP ASAP:
zepelin [54]

Answer:

2035.8  (approximately)

6 0
3 years ago
Read 2 more answers
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