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3 years ago

13

What is the measure of angle A'OB'?

1 answer:

Morgarella [4.7K]3 years ago

6 0

Answer:

79° is the measure of the required angle

since it is the vertically opposite angle of AOB.

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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

3 years ago

What is<br> -15 times the square root of 10 divided by 9? And whats the square root of that answer?

morpeh [17]

Ans: About 2.30

-15 x 3.16 / 9 = x sqrt

-15 x 3.16 = - 47.4

-47.4 / 9 = -5.27

-5.27 sqrt = About 2.30

Hope this helped :)

6 0

3 years ago

What is a standard form equation of a circle

Gre4nikov [31]

Answer:

360 degrees

Step-by-step explanation:

Its Easy Geometry

7 0

2 years ago

Someone please help and make sure the answer is right :)

Yuki888 [10]

Answer:

A - 7

Step-by-step explanation:

These angles are corresponding, meaning they are congruent. Therefore it is simple algebra.

16x - 7 = 105

16x = 112

112/16 = 7

x=7

3 0

2 years ago

Read 2 more answers

Advocard [28]

(6k + 2) - (3k - 2)= 6k + 2 - 3k + 2 = 3k + 4

5 0

3 years ago

Read 2 more answers