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3 years ago

6

The answer to that algebra 2 equation

1 answer:

IRISSAK [1]3 years ago

3 0

The answer is (2,-5)

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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

The following set of coordinates represents which figure? (0, 4), (0, 7), (1, 5), (1, 2)

Romashka [77]

Answer:

The figure represent a parallelogram

Step-by-step explanation:

we have

$(0, 4), (0, 7), (1, 5), (1, 2)$

using a graphing tool

Plot the points

see the attached figure

The figure has opposite sides parallel and equal in length

6 0

3 years ago

Read 2 more answers

If y=20 when x=8, whats the value of x when y=-2

lisabon 2012 [21]

Answer:

x=-4/5

Step-by-step explanation:

8/20=x/-2

simplify 8/20 into 2/5

2/5=x/-2

cross product

5*x=-2*2

5x=-4

x=-4/5

8 0

3 years ago

The output is eight less than the input

horsena [70]

x | y
——-
-10|-18
-9 |-17
-8 |-16
-7 |-15
-6 |-14
-5 |-13
-4 |-12
-3 |-11
-2|-10
-1 | -9
0 | -8
1 | -7
2 |-6
3 | -5
4 | -4
5 | -3
6 | -2
7 | -1
8 | 0
9 | 1
10| 2

6 0

3 years ago

Read 2 more answers

100 POINTS HELP ASAP Linear Combination

notka56 [123]

Answer:

1) $x=\dfrac12$

2) $n = -3 \ \ \textsf{and} \ \ m = -4$

3) see below

4) A: 0 = 1

Step-by-step explanation:

<u>Question 1</u>

$15-0.5(4x-2)+4x=17$

$\implies 15-2x+1+4x=17$

$\implies 2x+16=17$

$\implies 2x=1$

$\implies x=\dfrac12$

<u>Question 2</u>

$\textsf{rearrange} \ n=m+1 :$

$\implies -m=-n+1$

$\textsf{add equations} \ -m=-n+1 \ \textsf{and} \ m=2n+2:\\$

$\implies0=n+3$

$\implies n=-3$

$\textsf{substitute} \ \ n=-3 \ \ \textsf{into} \ \ m=n-1:$

$\implies m=-3-1$

$\implies m=-4$

<u>Question 3</u>

subtract the second equation from the first

divide both sides by -4

substitute found value for y into first equation

solve for x

<u>Question 4</u>

$3j=k$

$k=3j+1$

$\textsf{rearrange} \ 3j=k :$

$\implies -k=-3j$

$\textsf{add equations}\ -k=-3j \ \ \textsf{and}\ \ k=3j+1:$

$\implies 0=1$

Solution = A

6 0

2 years ago