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2 years ago

6

Type the equations and values needed to compute the difference between the market value of the car and its maintenance and repai

r costs for the eighth year.

1 answer:

Alina [70]2 years ago

7 0

Answer:

ajfksitdkfitgirkyfkeriajfe

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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 ethical issues have been raised by the scientific community's commitment to ensuring that experimental treatments are not

e-lub [12.9K]

Answer:

They include;

1. Fewer chances of determining how effective the treatment plan would be.

2. Inability of every patient to access the experimental treatment.

3. Difficulties in making knowledgeable decisions on the treatment plan.

4. Determining that the experimental treatments are offered with the right motive.

Step-by-step explanation:

In medical treatment administration, it is standard practice that drugs undergo clinical trials on test animals before they are administered to patients. However, some sicknesses are without known drugs for treatment or may have drugs that are still undergoing experiments and trials. In such cases, patients may want to be treated with experimental drugs.

Ethical issues such as the above-listed can arise from this. The foremost of them all is the fact that the treatment might prove ineffective thus causing more problems to the patient.

8 0

2 years ago

Aaron, Bonny and Connor are playing a game with cards.

professor190 [17]

Let the number of cards Aaron has : A

Given :

⊕ Bonny has twice as many cards as Aaron

⊕ Connor has 6 cards more than Bonny

⊕ Total cards : 101

⇒ Number of cards Bonny has : 2A

⇒ Number of cards Connor has : 2A + 6

⇒ Aaron cards + Bonny cards + Connor cards = 101

⇒ A + 2A + 2A + 6 = 101

⇒ 5A = 101 - 6

⇒ 5A = 95

⇒ A = 19

<u>Answer</u> : Aaron has 19 Cards

6 0

2 years ago

What is the solution to this system of linear equations? 12q+3r=15 -4q-4r=-44

PIT_PIT [208]

12q+3r=15
-4q-4r=-44
-4q=-44+4r
q=11-r
12(11-r)+3r=15
132-12r+3r=15
132-9r=15
117=9r
r=13
-4q-4(13)=-44
-4q-52=-44
-4q=8
q=-2

5 0

2 years ago

• The labor and material for renovating a building

Nimfa-mama [501]

Answer:

$17,832.5

Step-by-step explanation:

just multiply 25,475 by 0.70.

7 0

2 years ago