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3 years ago

6

Plz help me !!!!!!!.........

2 answers:

Andreas93 [3]3 years ago

8 0

I believe the correct answer is a hope this helps

Blababa [14]3 years ago

3 0

The answer is a because each input (x) has to have one output (y) to be a function

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Solve y ' ' + 4 y = 0 , y ( 0 ) = 2 , y ' ( 0 ) = 2 The resulting oscillation will have Amplitude: Period: If your solution is A

Vlad [161]

Answer:

$y(x)=sin(2x)+2cos(2x)$

Step-by-step explanation:

$y''+4y=0$

This is a homogeneous linear equation. So, assume a solution will be proportional to:

$e^{\lambda x} \\\\for\hspace{3}some\hspace{3}constant\hspace{3}\lambda$

Now, substitute $y(x)=e^{\lambda x}$ into the differential equation:

$\frac{d^2}{dx^2} (e^{\lambda x} ) +4e^{\lambda x} =0$

Using the characteristic equation:

$\lambda ^2 e^{\lambda x} + 4e^{\lambda x} =0$

Factor out $e^{\lambda x}$

$e^{\lambda x}(\lambda ^2 +4) =0$

Where:

$e^{\lambda x} \neq 0\\\\for\hspace{3}any\hspace{3}\lambda$

Therefore the zeros must come from the polynomial:

$\lambda^2+4 =0$

Solving for $\lambda$ :

$\lambda =\pm2i$

These roots give the next solutions:

$y_1(x)=c_1 e^{2ix} \\\\and\\\\y_2(x)=c_2 e^{-2ix}$

Where $c_1$ and $c_2$ are arbitrary constants. Now, the general solution is the sum of the previous solutions:

$y(x)=c_1 e^{2ix} +c_2 e^{-2ix}$

Using Euler's identity:

$e^{\alpha +i\beta} =e^{\alpha} cos(\beta)+ie^{\alpha} sin(\beta)$

$y(x)=c_1 (cos(2x)+isin(2x))+c_2(cos(2x)-isin(2x))\\\\Regroup\\\\y(x)=(c_1+c_2)cos(2x) +i(c_1-c_2)sin(2x)\\$

Redefine:

$i(c_1-c_2)=c_1\\\\c_1+c_2=c_2$

Since these are arbitrary constants

$y(x)=c_1sin(2x)+c_2cos(2x)$

Now, let's find its derivative in order to find $c_1$ and $c_2$

$y'(x)=2c_1 cos(2x)-2c_2sin(2x)$

Evaluating $y(0)=2$ :

$y(0)=2=c_1sin(0)+c_2cos(0)\\\\2=c_2$

Evaluating $y'(0)=2$ :

$y'(0)=2=2c_1cos(0)-2c_2sin(0)\\\\2=2c_1\\\\c_1=1$

Finally, the solution is given by:

$y(x)=sin(2x)+2cos(2x)$

5 0

4 years ago

In a class of students, the following data table summarizes

Ksenya-84 [330]

Answer:

Step-by-step explanation:

you have t as a total amount of the whole class.

f= did not pass and you place the total number next to it like this; f/t represents that group. You continue this in your workings.

f/t = probability failed.

p/t = probability passed

c/t = probability completed

dc/t = probability did not complete

and draw a tree.

The random would be either of these, we know there s a possibility of 1/4 but the odds stay central. We look for a new way after this data is converted as a fraction and show these fractions as your answer.

4 0

3 years ago

If a student pours 19 1/4 cups of lemonade into containers that hold 3 1/2 cups each, how many containers can the student fill

hodyreva [135]

Answer:

The student will be able to fill 5 1/2 cups of lemonade.

Step-by-step explanation:

can i get brainliest plz

5 0

3 years ago

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Neena has 54 smiley faces stickers and 36 glittery stickers. She wants to divide the stickers evenly among her friends

Ilia_Sergeevich [38]

90 divided by X (x is the number of friends which the question did not provide)

4 0

3 years ago

Read 2 more answers

What is the square number for 10

guajiro [1.7K]

10^2 equals 100

10 x 10=100

4 0

3 years ago