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3 years ago

How do you identify the angle of rotation including the direction

1 answer:

6 0

In rotation, the angle through which the plane figure is rotated is called the point of a figure through a specified angle and direction about a fixed point. Identify the corresponding vertices of the rotation.

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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

Solve for x 14 -2x = \frac{3 + x}{2}

Stels [109]

I think x = 2 is the answer

6 0

3 years ago

A diner asks patrons for their preference for waffles or pancakes and syrup or fruit topping.

prohojiy [21]

Answer:

$P (Waffles | Syrup)\neq P(Waffles)$

Step-by-step explanation:

From the table we have to:

Probability of syrup is 0.96

Probability of waffles and syrup is 0.32

P (Waffles | Syrup) = P (Waffles and syrup) / P (syrup)

So:

If this equality is met, the probabilities are dependent, if on the contrary

P (Wafles | Syrup) = P (Wafles) then are independent probabilities.

$P (Wafles | Syrup) = 0.32 / 0.96 = 0.333 \neq 0.32$

So we have to:

$P (Waffles | Syrup)\neq P(Waffles)$

The probabilities are dependent.

7 0

3 years ago

Read 2 more answers

Can someone please help me .

dusya [7]

Answer:

for 10. a

for 11. f.

Step-by-step explanation:

5 0

3 years ago

Which expression is equivalent to the one below?

FromTheMoon [43]

9 divided by 13 = 9/13

None of the answer above
Should be: 9 • 1/13

7 0

3 years ago