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3 years ago

9

Derek wants to practice playing the guitar for 9 hours in 8 days. What is the

1 answer:

bonufazy [111]3 years ago

7 0

Answer:

1 hour and 7.5 minutes or 67.5 per day will help him reach his goal of 9 hours per 8 days.

Step-by-step explanation:

9 hours

- 8 days

________

8 hours

1 hour left

1 hour is 60 minutes and 60/8 is 7.5 so each day will have added to it 7.5 minutes wish makes the answer 1 hour and 7.5 minutes or 67.5 minutes.

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What are vertically opposite angles

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very helpful to know that.

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3 years ago

Read 2 more answers

What is the value of X? <br><br><br> A. 5 <br><br> B. 2.5<br><br> C. 7.5<br><br> D. 10

lawyer [7]

Answer:

12. 5

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8

Step-by-step explanation:

12. 5

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15. 7

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6 0

1 year ago

Please help on this one? :)

kirill [66]

Answer:B,C,D

Step-by-step explanation:B- The point is over 1 off the y-axis

C-They are the points the line crosses the x-axis

D- There is no lower point

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3 years ago

I need help with 12 questions because idk how to do it and it's on metric units of liquid volume someone help quick I need to go

insens350 [35]

Where is the picture for this question

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2 years ago

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