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2 years ago

15

Which rule explains why these triangles are congruent?

1 answer:

Vinil7 [7]2 years ago

8 0

AAS

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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

George walks to a friend's house. He walks 750 meters North, then realizes he walked too far. He turns around and walks 250 mete

Hunter-Best [27]

Answer:

The velocity in meter per seconds is 76.9m/s

Step-by-step explanation:

The total distance walked is 1000m

Velocity= distance/time

= 1000/13

= 76.9m/s

The speed and velocity is used interchangeably therefore the speed is also 76.9 m/s

8 0

2 years ago

If 1m = 3.3 ft, how many cubic feet is the Kuroshio Sea tank? Volume is 9,450. Show your calculations!

Naddika [18.5K]

Answer:

339604.65 cubic feet

Step-by-step explanation:

We are given that 1 m is equal to 3.3 ft.

1 m = 3.3 ft

This means that if we find the volume of a cube of 1 m, we have its volume as:

$1^3 = 1 m^3$

In the same way, the volume of a cube of 3.3 ft (1 m) is:

$3.3^3 = 35.937 ft^3$

This means that:

$1m^3 = 35.937 ft^3$

The Kuroshio sea tank has volume of $9450 m^3$ . Its volume in cubic feet is therefore:

$1m^3 = 35.937 ft^3\\\\9450 m^3 = 9450 * 35.937 = 339604.65 ft^3$

The volume of the tank is 339604.65 cubic feet.

3 0

2 years ago

Nathan cut a rectangular tile in half for his kitchen floor design. The tile was NOT a square. He made once cut along a diagonal

zhenek [66]

They will both be right, scalene triangles.

6 0

3 years ago

Read 2 more answers

Which table of ordered pairs represents a proportional relationship?

EleoNora [17]

Answer:

second x -1,-3,-5 y 1 3 5 for proportional relation

8 0

2 years ago