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4 years ago

14

The blue and orange lines represent a system. Use the sliders to manipulate the orange line to determine which equations would c

reate a system that has no solution.

1 answer:

yarga [219]4 years ago

7 0

The answer is:

2x + y = -5

-2x = y

2x = 4 - y

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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

Can someone please help me with this question?

Basile [38]

Answer:

B ( gabby)

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

WHEN LOGARITHMIC FUNCTIONS ARE GRAPHED WHICH TRANSFORMATION WILL RESULT IN A Y INTERCEPT?

VikaD [51]

The graph of the function LOG has no y-intercept, but has an x-intercept.
However, if we apply a symmetry toward the line y=x, then the graph
will result in an y-intercept.
Check that by drawing

8 0

3 years ago

Read 2 more answers

Hey can you please help me posted picture of question :)

notka56 [123]

The given trinomial can be factored using factorization as

x²-x-12
=x²-4x+3x-12
=x(x-4)+3(x-4)
=(x-4)(x+3)

Thus x-4 and x+3 are the factors of the given trinomial. From these we can see x+3 is listed in option A

So the answer to this question is Option A

6 0

3 years ago

Solving Quadratic Equations posttest <br><br> A.<br> B.<br> C.<br> D.

beks73 [17]

Answer:

D. $x = 3 \pm \sqrt{10}$

Step-by-step explanation:

$x^2 - 6x - 1 = 0$

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

a = 1; b = -6; c = -1

$x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(-1)}}{2(1)}$

$x = \dfrac{6 \pm \sqrt{36 + 4}}{2}$

$x = \dfrac{6 \pm \sqrt{40}}{2}$

$x = \dfrac{6 \pm \sqrt{4 \times 10}}{2}$

$x = \dfrac{6 \pm 2 \sqrt{10}}{2}$

$x = 3 \pm \sqrt{10}$

8 0

3 years ago