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2 years ago

Find the general solution of y''' + 6y'' + y' − 34y = 0 if it is known that y1 = e−4x cos(x) is one solution.

Mathematics

1 answer:

SashulF [63]2 years ago

3 0

Answer:

Step-by-step explanation:

Given is a differential equation of III order,

$y''' + 6y'' + y' - 34y = 0$

The characteristic equation would be cubic as

$m^3+6m^2+m-34=0$

By trial and error, we find that

$f(2) = 2^3+6(2^2)+2-34 =0\\$

Thus m=2 is one solution

Since given that $e^{-4x} cos x$ is one solution we get

m = -4+i and hence other root is conjugate $m=-4-i$

Hence general solution would be

$y=Ae^{2x} +e^{-4x} (Bcosx +C sinx)$

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A manufacturer is designing a flashlight. For the flashlight to emit a focused beam, the bulb needs to be on the central axis of

aalyn [17]

From the problem, the vertex = (0, 0) and the focus = (0, 3)
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12

Source:
http://www.1728.org/quadr4.htm

5 0

2 years ago

A rectangular floor tile is shown it dimensions are given to the nearest 0.1 metres the tile is only able to sustain maximum pre

egoroff_w [7]

Answer:

736 N

Step-by-step explanation:

The dimensions of the rectangular tile are:

Length = 2.3m

Width = 1.6m

The pressure exerted on a surface is given by the formula

$p=\frac{F}{A}$

where

p is the pressure

F is the force exerted

A is the area on which the force is exerted

In this problem, we have:

$p=200 N/m^2$ is the maximum pressure that the tile is able to sustain

A is the area of the tile, which can be calculated as the product between length and width, so:

$A=L\cdot w =(2.3)(1.6)=3.68 m^2$

Re-arranging the formula for F, we can find the maximum force that can be safely applied to the tile:

$F=pA=(200)(3.68)=736 N$

4 0

2 years ago

What is the value of b and the missing symbol in Jamilla’s inequality?

Sindrei [870]

Answer:

$b=1, \geq$

Step-by-step explanation:

we know that

The absolute value function has two solutions

Observing the graph

the solutions are

$x\geq 1$ and $x\leq -3$

First solution (case positive)

assume the symbol of the first solution and then compare the results

$\left|x+b\right|\ge2$

$(x+b)\ge2$

$x\ge2-b$

$2-b=1\\b=2-1\\ b=1$

Second solution (case negative)

$-(x+b)\ge2$

Multiply by -1 both sides

$(x+b)\leq-2$

substitute the value of b and compare the results

$(x+1)\leq-2$

$x\leq-2-1$

$x\leq-3$ -------> is correct

4 0

2 years ago

Read 2 more answers

Jill is standing at the base of her apartment building. She measures the angle of elevation to the top of a nearby tower to be 4

almond37 [142]

1) From the measure of 40°, you can write:

tan(40°) = 100/x, where x is the base from the building to the tower

⇒x=100/tan(40°) = 119,18 m

2) From the measure of 30°, you can write

tan(30°) = y / 119,18, where y is the height from the roof of Jill's building to the top of the tower.

Then, y = tan(30°) * 119,18 = 68,81 m

3) The height of Jill's building is 100 - 68,81 = 31,19 m

4 0

2 years ago

Read 2 more answers

The given equation has been solved in the table. In which step was the subtraction property of equality applied?

atroni [7]

Answer:

Option (D)

Step-by-step explanation:

Subtraction property of equality tells that whatever subtracted from one side of the equation must be subtracted from the other side.

If x + 2 = 2,

By the property of subtraction of equality,

x + 2 - 2 = 2 - 2

x = 0

But in the given question,

$\frac{x}{2}-7=-7$

$\frac{x}{2}-7+7=-7+7$

shows the addition property of equality in step (2)

Therefore, subtraction property of equality was not applied.

Option (D) will be the answer.

5 0

1 year ago