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2 years ago

5

If the diameter of a circle is 12cm, what is the circumference of the circle?

1 answer:

Vera_Pavlovna [14]2 years ago

5 0

Answer:

6cm

Step-by-step explanation:

bc diameter is 12cm the radius is 6 and the area is 36

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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

2 years ago

Diners frequently add a 15% tip when charging a meal to a credit card. What is the total amount charged if the cost of the mea

aksik [14]

Answer:

$40.25

Step-by-step explanation:

.15 x 35 = 5.25

35+ 5.25 = 40.25

Hope this helps!

7 0

2 years ago

What is 37,000 in scientific notation

polet [3.4K]

<span>3.7 x 10^<span>4 that is the answer</span></span>

5 0

2 years ago

Read 2 more answers

Which is equivalent to –8? Choose Yes or No. 8010 No −8010 Yes 80÷(−10) Yes −80÷(−10) No

nexus9112 [7]

Answer: No,Yes,Yes,No

7 0

2 years ago

Each week morning sunshine cafe orders coffee packets that costs $2.50 per packet with a 10.00 shipping fee . If morning sunshin

Anni [7]

Answer:

193 packets

Step-by-step explanation:

Each morning they order with a shipping fee of $10 daily.

Considering they order all 7 days of the week, so the total shipping fee for the week would be:

7 * $10 = $70

Their budget for the week is $554, out of which $70 is for shipping for the week, so remaining balance would be:

554 - 70 = $484

This 484 dollars are for coffee packets that cost $2.50 each, so the number of packets would be:

484/2.50 = 193.6

You can't order fractional packets so 193 packets is the max in this budget

7 0

2 years ago