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Stels [109]
3 years ago
15

What does the symbol in the image on number 39 mean

Mathematics
1 answer:
anastassius [24]3 years ago
5 0

Answer:

It means direct sum.

Step-by-step explanation:

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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
You hang two strands of decorative lights.
Sphinxa [80]

Answer:

The stands will change color at the same time after 54 seconds.

Step-by-step explanation:

Find the Lcm number of both number (18 and 27)

The answer will be 54

5 0
2 years ago
Given the triangle below, which of the following equations correctly represents the relationship between a, b, and c?
maxonik [38]

Answer:

C. c^2=a^2+b^2-2abcos(90°)

Step-by-step explanation:

This is the law of cosine.

7 0
2 years ago
Read 2 more answers
What is the probability of drawing five face cards?
anastassius [24]
Total number of cards = 52
Total number of face cards = 12

P( 5 face cards) = (12/52)(11/51)(10/50)(9/49)(8/48) = 33/108290


Answer: 33/108290
4 0
3 years ago
Five million divided by fivethousand
Phantasy [73]

Answer:

1000 (one thousand)

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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