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3 years ago

Urgent please help!!!!

Mathematics

1 answer:

34kurt3 years ago

7 0

Answer:

Step-by-step explanation:

Inequality given for Sara,

-4(2x + 4) > 8x + 64

-8x - 16 > 8x + 64

-8x - 8x > 16 + 64

-16x > 80

-x > 5

x < -5

x = -12 will be the answer.

Option (3)

Inequality for Alezandro,

7x + 20 ≥ 2(x - 15)

7x + 20 ≥ 2x - 30

7x - 2x ≥ -30 - 20

5x ≥ -50

x ≥ -10

Therefore, x = 2 is the answer.

Option (2)

For Daria,

3(x - 17) < 9(1 - 3x)

3x - 51 < 9 - 27x

3x + 27x < 51 + 9

30x < 60

x < 2

x = -6 will be the answer.

Option (1)

For Jamal,

5(x + 11) > -4(-x - 12)

5x + 55 > 4x + 48

5x - 4x > 48 - 55

x > -7

x = 10 will be the answer.

Option (4)

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

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Answer:

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

Step-by-step explanation:

Given

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

Required

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Rewrite the expression as:

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

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

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

$m = -1 \± 1*i$

$m = -1 \± i$

Add 1 to both sides

$m +1= 1 -1 \± i$

$m +1= \± i$

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$(m +1)^2= (\± i)^2$

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

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

In complex numbers:

$i^2 = -1$

So, the expression becomes:

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

Add 1 to both sides

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

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This corresponds to the homogeneous linear differential equation

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

6 0

3 years ago

Question 2

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Answer:

The square root of 60

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12-3 (2w+1)=7w-3 (7+w)

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