The Laplace transform of the solution y(t) is Y(s) = (3/s * e^(-2s) - 6/s * e^(-2s) - 3/s * e^(-3s) + 9/s * e^(-3s)) / (s^2 + 16).
To apply the Laplace transform to the given differential equation, we use the linearity property of the Laplace transform and the fact that the Laplace transform of the unit step function is 1/s e^(-as):
L[y'' + 16y] = L[(3t – 6)h(t – 2) – (3t – 9)h(t – 3)]
s^2 Y(s) - s y(0) - y'(0) + 16Y(s) = 3/s * e^(-2s) - 6/s * e^(-2s) - 3/s * e^(-3s) + 9/s * e^(-3s)
Since y(0) = y'(0) = 0, the first two terms on the left-hand side are zero, and we can solve for Y(s):
s^2 Y(s) + 16Y(s) = 3/s * e^(-2s) - 6/s * e^(-2s) - 3/s * e^(-3s) + 9/s * e^(-3s)
Y(s) (s^2 + 16) = 3/s * e^(-2s) - 6/s * e^(-2s) - 3/s * e^(-3s) + 9/s * e^(-3s)
Y(s) = (3/s * e^(-2s) - 6/s * e^(-2s) - 3/s * e^(-3s) + 9/s * e^(-3s)) / (s^2 + 16)
Therefore, the Laplace transform of the solution y(t) is Y(s) = (3/s * e^(-2s) - 6/s * e^(-2s) - 3/s * e^(-3s) + 9/s * e^(-3s)) / (s^2 + 16). Note that we have not solved the differential equation yet; this is just the Laplace transform of the solution.
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Add. (15w - 6x) and (6x + 20w)
Answer:
35w
Step-by-step explanation:
15w-6x+6x+20w
collect like terms
15w+20w-6x+6x
=35w
help me please will mark you brainliests
Answer:
tommorow what time exam you have you help me with answers iil help you back
Step-by-step explanation:
your answer is 180-2x hope it helps u
Harold cut 18 1/2 noches of ropero that was 60 inches long how much is the length of the remaining rope un inches written un decimals f From
Answer:
41.5
Step-by-step explanation:
If you do 60- 18.5 (1/2 = 0.5), you get about 41.5 inches left of the rope
Plz help ASAP with the correct answer plz
Answer:
3rd one
Step-by-step explanation:
its an idiom you are welcome
direction: find the quotiend
Answer:
broo this is easy check the comments the on yo tail
Step-by-step explanation:
I don’t really understand could you help
Answer:
M: (-7, -3)
A: (0, -3)
T: (0, -8)
Step-by-step explanation:
each of the points are associated with a letter. you can find the points by looking at the points it matches up with in the formatting of (x,y)
for example, for M, you can see that the dot on the x axis seems to be hovering below -7, on the y axis, it seems to be hovering next to -3. therefore, its (-7,-3)
A rectangular playground has an area of 3,394 square meters. If the width of the playground is 32 meters, find the length.
Answer:
106 square
Step-by-step explanation:
Area of rectangle = 3,394 square meters
Width = 32 meters
Length = ?
Area of rectangle = Length * Weight
3,394 = 32 * x
x = 3,394 /32
x = 106.0625
x = 106
The Length is 106 square
Expand and combine like terms.
(765 – 46)(765 + 46)
Answer:
587,341
Step-by-step explanation:
(I'm hoping this is what you mean by expand)
(765 – 46)(765 + 46)
First, multiply 765 by 765 = 585,225
Second, multiply 765 by 46 = 35,190
Third, multiply -46 by 765 = -35,190
Fourth, multiply -46 by 46 = -2,116
The second and third answers (35,190 and -35, 190) will cancel each other out. Then, just subtract -2,116 from 585,225.
585,225 - (-2,116) = 585,225 + 2,116 = 587,341
What is the domain of the function graphed below?
Answer:
Positive infinite to negative infinite
Step-by-step explanation:
Find the slope when given (2,3) (3,5) plz
The length, in inches, of a box is 3 inches less than twice its width, in inches. Which of the following gives the length, l inches, in terms of the width, w inches, of the box?
l = w + 3
l = w + 3
l = w – 3
l = 2w + 3
l = 2w – 3
Answer:
l = 2w – 3
Step-by-step explanation:
Answer:
l = 2w – 3
Step-by-step explanation:
Hope this helps!!!
There were 60 students enrolled in Grade 5 last year. If 66 students are enrolled in the same grade level this year, what is the percentage increase in the number of Students?
There is a 10% increase
There are 6 more students this year than there were last year.
If you find what 10% of 60 is and add that to 60, you'll find that it'll equal 66.
//
[tex]60 \times 0.10 = 6[/tex]
[tex]10\% \: of \: 60 \: is \: 6[/tex]
[tex]60 + 6 = 66[/tex]
A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The survey reported a confidence interval that between 16.5% and 25.5% of the residents supports the plan. What is the margin of error on the survey? Do not write \pm± on the margin of error.
Answer:
9
Step-by-step explanation:
The confidence interval is related to margin of error ; according to the relation :
Confidence interval = mean ± margin of error
Margin of Error = (upper boundary value - lower boundary value)
Confidence interval = 16.5% and 25.5%
Margin of Error = (25.5% - 16.5%)
Margin of Error = ±9
The margin of error on the survey is 9.
We know that
Confidence interval = mean ± margin of error
And,
Margin of Error = (upper boundary value - lower boundary value)
We have Confidence interval between 16.5% and 25.5%.
upper boundary value = 25.5%
lower boundary value = 16.5%
So, Margin of Error
= 25.5% - 16.5%
=9
Therefore, Margin of Error is 9.
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If the Federal Reserve buys $40,000 in Treasury bonds from a bank at 6%
interest, what is the immediate effect on the money supply?
A. It is decreased by $40,000
B. It is increased by $40,000
C. It is decreased by $2400
D.it is increased by $2400
Answer:
The answer would be it would increase by 40,000
Yep here we go again:
In the diagram below, the red angle angle YAK and the blue angle angle OAT are both right angles. If angle YAO=23 then what is the measure of angle KAT
If you don't know the answer or not sure, please don't answer it!
Whoever answers it correctly gets brainliest!!
Answer:
23 degrees
Step-by-step explanation:
90+23-90=23
9514 1404 393
Answer:
23°
Step-by-step explanation:
Both angles YAO and KAT are complementary to angle OAK, so are congruent.
∠YAO = ∠KAT = 23°
4. Consider the right triangle below.
If the perimeter is 1,013 units, find the value of x and the area of the
triangle.
16x + 27
14x - 45
25x
The value of x is
The area is
square units.
Answer:
16x+27+14x-45+25x=1013 units
X= 18.75
Area= b × h × (1/2)
A= 1/2 × 327 × 217.5 = 35561.25 units^2
Answers:
x = 1031/55 = 18.74545 approximatelyarea = 35,542.92 square units approximately==============================================================
Explanation:
The perimeter is the sum of the exterior sides. We'll add up these three sides
16x+2714x-4525xand set the sum equal to the perimeter 1013
The equation we need to solve is
(16x+27)+(14x-45)+(25x) = 1013
Solving for x leads to...
(16x+27)+(14x-45)+(25x) = 1013
16x+27+14x-45+25x = 1013
(16x+14x+25x)+(27-45) = 1013
55x-18 = 1013
55x = 1013+18
55x = 1031
x = 1031/55
x = 18.74545 approximately
-----------------------------
Use this x value to find the length of each side. I'll use the decimal form of x. We get the following side lengths:
16x+27 = 16*(18.74545) + 27 = 326.927214x - 45 = 14*(18.74545) - 45 = 217.436325x = 25*(18.74545) = 468.63625Those values are approximate.
We can then find the area of the triangle
area = (1/2)*base*height
area = (1/2)*(326.9272)*(217.4363)
area = 35,542.92036868
area = 35,542.92
The area is approximate as well.
Last year, Diane opened an investment account with S6400. At the end of the year, the amount in the account had increased by 26%.
(a) Fill in the blank to write the year-end amount in terms of the original amount. Write
your answer as a decimal.
Year-end amount =. XOriginal amount
(1) Use your answer in part (ə) to determine the year-end amount in Diane's account
Year-end amount: $
Answer:
Your answer is.....
8064$
Mark it as brainlist answer . follow me for more answer.
Step-by-step explanation:
Find the product.
5
----
8
of
2
----
4
Answer:
5/16
Step-by-step explanation:
10/32=5/16
find the value for x and y (no decimals
Answer:
x=6
y=3r3
Step-by-step explanation:
[tex]\frac{x}{sin90} =\frac{x}{sin60} =\frac{3}{sin3}\\x=6\\y=3\sqrt{3}=3r3[/tex]
If the temperature outside is 60 degrees at 6 pm and then drops by 15% at 10 pm, what is the temperature at 10 pm?
Answer:
51 degrees
Step-by-step explanation:=Given data
Temperature at 6pm = 60 degrees
percent drop= 15%
= 15/100*60
=0.15*60
=9 degrees
Hence the temperature at 10 pm is 60-9= 51 degrees
Express as a trinomial. (x+3)(3x-1)
Answer:
3x^2+8x-3
Step-by-step explanation:
(x+3)(3x-1)
x*3x + x*(-1) + 3x*3 + 3*(-1)
x*3x = 3x^2
x*(-1) + 3x*3 = -x+9x = 8x
3*(-1) = -3
= 3x^2+8x-3
The expression for the trinomial ( x + 3 ) ( 3x - 1 ) is [tex]3x^{2} + 8x - 3[/tex]
Given data:
The expression is represented as (x + 3)(3x - 1)
To express the product of (x + 3)(3x - 1) as a trinomial, perform the multiplication.
Using the FOIL method (First, Outer, Inner, Last), we multiply the terms:
(x + 3)(3x - 1) = x(3x) + x(-1) + 3(3x) + 3(-1)
Simplifying further:
[tex]3x^{2} - x + 9x - 3[/tex]
Combining like terms:
[tex]3x^{2} + 8x - 3[/tex]
Hence, the expression (x + 3)(3x - 1) can be expressed as the trinomial [tex]3x^{2} + 8x - 3[/tex] .
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Having trouble solving this:
Answer:
The answer is 24*(1/5)........
Answer:
the answer is D) 121/500
Step-by-step explanation:
ANSWER ASAP GIVING BRAINLIEST FIVE STARS AND A HEART I ONLY NEED A FEW SENTENCES!
Please answer the following essay question:
An isosceles triangle has two congruent angles. Write an expression to represent the measure of the third angle of the triangle. Explain.
Answer:
third angle =180-two congruent angles. is expression.
What do you notice about the equation y=12?
Answer:
X=0
Step-by-step explanation:
If you look at the graph and follow, the x axis to match up with y=12, then you will see that x is 0
Answer:
M=0
Step-by-step explanation:
I got it right on I-Ready and because there is no change in y
Find the mean then the mean absolute deviation (MAD) of the following data set Round your answer to two decimal places if necessary
3, 1, 5, 4, 8,6
The area of triangle ABC is?
Answer:
[tex] A(\triangle ABC) =17.5 \: {units}^{2} [/tex]
Step-by-step explanation:
AB = 4 - (-3) = 4 + 3 = 7 units
BC = 3 - (-2) = 3 + 2 = 5 units
[tex]A(\triangle ABC) = \frac{1}{2} \times AB\times BC \\ \\ A(\triangle ABC) = \frac{1}{2} \times 7\times 5 \\ \\ A(\triangle ABC) = \frac{1}{2} \times 35 \\ \\ A(\triangle ABC) =17.5 \: {units}^{2} [/tex]
El perímetro de un rombo es igual al de un pentagono regular más 9, y la medida del lado del rombo es el doble de lo que mide un lado del pentagono. ¿Cuánto miden los lados de cada figura?
Answer:
Rombo es 6
Pentágono es 3
Step-by-step explanation:
Formula del perímetro de un rhombus es 4a
Formula del perímetro de un pentágono es 5b
La pregunta dice
4a = 5b + 9
Otra vez, la pregunta dice la medida del lado del rombo es el doble de lo que mide un lado del pentagono. Entonces,
a = 2b
Si
4a = 5b + 9 y
a = 2b, entonces que
4(2b) = 5b + 9
8b = 5b + 9
8b - 5b = 9
3b = 9
b = 9/3
b = 3
si, b = 3, tan
a = 2(3)
a = 6
Entonces, la medida del lado del rombo es 6 y la medida del lado del pentágono es 3
Please help me with this
Answer:
1/5
Step-by-step explanation:
Hi there!
To find the answer, use inverse operations to solve.
Multiply 7/15 by 3/7 to isolate the unknown number.
7/15 * 3/7 is equal to 0.2, which can be simplified into fraction form as 1/5.
I hope this helps!
:)
Evaluate the expression when a=3 and b=-6.
-a +6b
Answer:
Step-by-step explanation:
-a + 6b = -3 + 6 * (-6) = -3 - 36 = -39
Substitute the values in:
-a + 6b
-(3) + 6(-6)
-3 + (-36)
= -39
HELP PELASE ASAPppppp
Answer:
(a)[tex]\frac{d}{a}=\frac{a}{f}[/tex]
(d)[tex]\frac{e}{c}=\frac{c}{f}[/tex]
(b)[tex]\frac{d}{b}=\frac{b}{e}[/tex]
Step-by-step explanation:
All right triangles are similar
When two triangles are similar then the ratio of their corresponding sides are equal.
Using the property
[tex]\triangle ABC\sim \triangle DBA[/tex]
[tex]\frac{BC}{AB}=\frac{AB}{BD}[/tex]
[tex]\frac{e}{c}=\frac{c}{f}[/tex]
[tex]\triangle ACD\sim\triangle BAD[/tex]
[tex]\frac{CD}{AD}=\frac{AD}{BD}[/tex]
[tex]\frac{d}{a}=\frac{a}{f}[/tex]
[tex]\triangle ACD\sim \triangle BCA[/tex]
[tex]\frac{CD}{AC}=\frac{AC}{BC}[/tex]
[tex]\frac{d}{b}=\frac{b}{e}[/tex]
Correct options are
(a)[tex]\frac{d}{a}=\frac{a}{f}[/tex]
(d)[tex]\frac{e}{c}=\frac{c}{f}[/tex]
(b)[tex]\frac{d}{b}=\frac{b}{e}[/tex]