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3 years ago

15

9/6 as an equivalent fraction

1 answer:

svet-max [94.6K]3 years ago

3 0

3/2 We look for a number that goes into both 9 and 6 without leaving a remainder, and that number is 3

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Find a homogeneous linear differential equation with constant coefficients whose general solution is given by

frez [133]

Answer:

$y" + 2y' + 2y = 0$

Step-by-step explanation:

Given

$y=c_1e^{-x}cosx+c_2e^{-x}sinx$

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

$y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)$

Where

$\alpha = -1$ and $\beta = 1$

For a homogeneous linear differential equation, the repeated value m is given as:

$m = \alpha \± \beta i$

Substitute values for $\alpha$ and $\beta$

$m = -1 \± 1*i$

$m = -1 \± i$

Add 1 to both sides

$m +1= 1 -1 \± i$

$m +1= \± i$

Square both sides

$(m +1)^2= (\± i)^2$

$m^2 + m + m + 1 = i^2$

$m^2 + 2m + 1 = i^2$

In complex numbers:

$i^2 = -1$

So, the expression becomes:

$m^2 + 2m + 1 = -1$

Add 1 to both sides

$m^2 + 2m + 1 +1= -1+1$

$m^2 + 2m + 2= 0$

This corresponds to the homogeneous linear differential equation

$y" + 2y' + 2y = 0$

6 0

3 years ago

What is the volume of C? (The Triangular Prism)

Sloan [31]

according to the pictures I have sent you can solve it! be successful

4 0

3 years ago

What is u^+6u-27 factoring

MissTica

U² + 6u - 27
u² + 9u - 3u - 27
(u - 3)(u + 9)

7 0

3 years ago

The length of a rectangle is 3cm more than twice the width. The perimeter of the rectangle is 42 cm. Find the dimensions of the

bogdanovich [222]

The width is 6cm
And the length is two times + 3 of the width
6 X 2 + 3 = 15
Add all 4 sides for the perimeter 6+6+15+15=42
The the dimensions are a rectangle that is 6cm wide and 15cm tall

5 0

3 years ago

Does the equation −2x + y = 0 represent a direct variation? If so, identify the constant of variation.

Vikentia [17]

Adding 2x to both sides we get

y = 2x

This is direct variation where the constant is 2.

3 0

3 years ago