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2 years ago

Which equation goes with the graph

Mathematics

1 answer:

Rus_ich [418]2 years ago

3 0

Link is scam. literally cap. don’t use it or what do ever!

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Solve the following equation with the initial conditions. x¨ + 4 ˙x + 53x = 15 , x(0) = 8, x˙ = −19

Katen [24]

$x''+4x'+53x=15$

has characteristic equation

$r^2+4r+53=0$

with roots at $r=-2\pm7i$ . Then the characteristic solution is

$x_c=C_1e^{(-2+7i)t}+C_2e^{(-2-7i)t}=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)$

For the particular solution, consider the ansatz $x_p=a_0$ , whose first and second derivatives vanish. Substitute $x_p$ and its derivatives into the equation:

$53a_0=15\implies a_0=\dfrac{15}{53}$

Then the general solution to the equation is

$x=e^{-2t}\left(C_1\cos(7t)+C_2\sin(7t)\right)+\dfrac{15}{53}$

With $x(0)=8$ , we have

$8=C_1+\dfrac{15}{53}\implies C_1=\dfrac{409}{53}$

and with $x'(0)=-19$ ,

$-19=-2C_1+7C_2\implies C_2=-\dfrac{27}{53}$

Then the particular solution to the equation is

$\boxed{x(t)=\dfrac1{53}e^{-2t}(409cos(7t)-27\sin(7t)+15)}$

8 0

3 years ago

What are common numbers of the numbers 15 45 90

Alex787 [66]

Answer:

If you are talking about common factors, the common factors of 15 are 15, 5, 3, and 1. The common factors of 45 are 45, 9, 5, 3, and 1. Common factors are numbers that a number can be divided by. Like 35 / 5, 5 is a common factor of 35.

Step-by-step explanation:

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3 years ago

A collector bought a rare coin for $30. The coin is now valued at $37.50. What is the percent increase in value?

AlladinOne [14]

Answer:

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If g(x)=3/4x+2,find g(-12)

Triss [41]

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