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3 years ago

Find a particular solution to y" - y' + 9y = 3 sin 3x

Mathematics

1 answer:

Dima020 [189]3 years ago

6 0

Answer:

cos3x

Step-by-step explanation:

y" - y' + 9y = 3 sin 3x

$D^{2}y-Dy+9y=3 sin3x$

$y=\frac{3 sin 3x}{(D^{2} -D+9}=3 sin 3x$

here $D^2$ will be replaced by $\alpha^2$ where $\alpha$ is coefficient of x

$y=\frac{3 sin 3x}{-3^{2} -D+9}$

$y=-3\frac{sin 3x}{D}$

$y=-3\int\ {sin 3x} \, dx$

$y=-3\frac{cos3x}{-3}$

y=cos3x

hence Particular solution is cos3x

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I need help on this problem in math

S_A_V [24]

Answer:

correct answer is C
Haley incorrectly applied the distributive property

Step-by-step explanation:

If you simplify the given equation, you find it matches choice C.

$\dfrac{1}{2}(6-x)+3x=\dfrac{1}{2}x-8\\\\3-\dfrac{1}{2}x+3x=\dfrac{1}{2}x-8\\\\3+\dfrac{5}{2}x=\dfrac{1}{2}x-8\qquad\text{matches choice C}$

Haley's error seems to be failing to distribute the 1/2 properly when she eliminated parentheses. Apparent, she incorrectly decided that ...

1/2(6 -x) ⇒ 3 -x . . . . instead of 3 -1/2x

Then when -x was added to +3x, she got 2x. Had she done it properly, she would have added -1/2x to +3x to get 5/2x.

_____

<em>Additional comment</em>

It is a common error to "distribute" the factor outside parentheses to the first term only, as Haley apparently did. Another common error is to fail to distribute minus signs properly. The distributive property requires you apply the outside factor to <em>all</em> of the terms inside parentheses.

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1 year ago

Point M (-3, 6) and point 'N (1,-1) are located on a coordinate

lisabon 2012 [21]

The distance between point M and point is is about 8.06 units (rounded to nearest hundredth)

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2 years ago

A certain animated movie earned $1.1*10^9 in revenues at the box office. The movie lasts 9.1*10^1 minutes. How much revenue was

Vadim26 [7]

Answer:

$12,087,912.1

Step-by-step explanation:

$1.1*10^9$ is in scientific notation, to get this into normal number, we take the decimal point and move it "9" times to the right [whatever power of 10 we have, we move to right (if positive).] Then we fillup the rest with zeros.

So we have:

$1.1*10^9=1,100,000,000$

This is the revenue.

We do similar process for time:

$9.1*10^1=91$

This is the time , in minutes.

We want revenue PER minute, that means we divide the total revenue by total time, that would be:

$\frac{1,100,000,000}{91}=12,087,912.1$

The revenue earned per minute is $12,087,912.1

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2 years ago

A proportional relationship betweeof potatoes (x) and the price in dollars (y) is graphed, and the ordered pair (4, 3) is on the

CaHeK987 [17]

4/3 = 1/x.....4 lbs potatoes to $3 = 1 lb of potatoes to $x
cross multiply
(4)(x) = (3)(1)
4x = 3
x = 3/4
x = 0.75....so 1 lb of potatoes cost 75 cents

(8,6)...this means 8 lbs of potatoes cost $6

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2 years ago

Waves with an amplitude of 2 feet pass a dock every 30 seconds. Write an equation for a cosine function to model the height of a

kolbaska11 [484]

Answer:

The cosine function to model the height of a water particle above and below the mean water line is h = 2·cos((π/30)·t)

Step-by-step explanation:

The cosine function equation is given as follows h = d + a·cos(b(x - c))

Where:

$\left | a \right |$ = Amplitude

2·π/b = The period

c = The phase shift

d = The vertical shift

h = Height of the function

x = The time duration of motion of the wave, t

The given data are;

The amplitude $\left | a \right |$ = 2 feet

Time for the wave to pass the dock

The number of times the wave passes a point in each cycle = 2 times

Therefore;

The time for each complete cycle = 2 × 30 seconds = 60 seconds

The time for each complete cycle = Period = 2·π/b = 60

b = π/30 =

Taking the phase shift as zero, (moving wave) and the vertical shift as zero (movement about the mean water line), we have

h = 0 + 2·cos(π/30(t - 0)) = 2·cos((π/30)·t)

The cosine function is h = 2·cos((π/30)·t).

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2 years ago