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3 years ago

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A survey of 120 teachers determined the following:

1 answer:

son4ous [18]3 years ago

3 0

Answer:

0%

Step-by-step explanation:

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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

Answer the question below<br><br> 1 - (-4)

tensa zangetsu [6.8K]

Answer:

4

Step-by-step explanation:

7 0

3 years ago

Find the area of the shaded regions. Give your answer as a completely simplified

Snezhnost [94]

Do the area of the circle as a whole minus (72/360 x radius^2) and then minus the other grey area.

8 0

3 years ago

Whats 4/5 as a decmal?

Rashid [163]

Answer:

0.8

Step-by-step explanation:

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3 years ago

Pythagorean Theorem in Cones. Please help

Lady_Fox [76]

3^2 + height^2 = 9^2

9 + height^2 = 81
height ^2 = 72

height = sqrt(72)

5 0

3 years ago