Laplace Transform of t ^{2}sin(2t)? ...?
Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.
The Laplace transform of the given function is,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]
What is Laplace transformation?Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.
Given information-
The function given in the problem is,
[tex]t^{2}\sin(2t)[/tex]
By the Laplace transform we can write that,
[tex]L[t^{2}\sin(2t)]=(-1)^2\dfrac{d^2}{ds^2}L(\sin 2t)\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\;\dfrac{d}{ds}\dfrac{2}{s^2+4}\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\left [\dfrac{-4s}{(s^2+4)^2} \right ]\\[/tex]
Solve further to get the final result,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{(s^2+4)^2(-4)+4s(s^2+4)\times2s}{(s^2+4)^2} \right ]\\[/tex]
Simplify the above equation as,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]
Hence, the Laplace transform of the given function is,
[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]
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which mixed number is equal to 7.6
In the diagram, transversal t cuts parallel lines a and b. Which angles form a pair of alternate exterior angles?
∠1 and ∠7
∠1 and ∠8
∠2 and ∠8
∠2 and ∠5
In the diagram, the pair of angles ∠1 and ∠7 form a pair of alternate exterior angles.
Here is the reason:
A transversal is a line where two parallel lines meet. In the diagram, line t is the transversal.Parallel lines: Parallel lines are two lines that never meet, no matter how distant they are amplified. Within the graph, lines a and b are parallel.Interchange exterior angles: When a transversal crosses two parallel lines, it makes eight points. The combination of points that are on the inverse sides of the transversal and exterior of the parallel lines are called substitute outside points.Within the graph, ∠1 and ∠7 are on the inverse sides of transversal t and exterior lines a and b. Subsequently, they are a combination of substitute outside points.
The other answer choices are not correct since:
∠1 and ∠8 are not on inverse sides of the transversal.∠2 and ∠8 are not both exterior parallel lines.∠2 and ∠5 are comparing points, not substituting outside points.2/3, 3/4, 4/5, 5/6, 6/7
Which of the following represents the general term for the sequence given?
n/n+1
n-1/n
n+1/n+2
Answer:
Option C. (n + 1)/(n +2).
Step-by-step explanation:
The given sequence is 2/3, 3/4, 4/5, 5/6, 6/7.
and we have to find the general term of the given sequence.
Since first term of the sequence is 2/3
So numerator can be represented as (n + 1) and the denominator as (n + 2)
Therefore the general term will be (n + 1)/(n + 2)
Option C is the answer.
What is the value of the function y=2x−3ywhen x=−1x=−1 ?
−5
−1
2
3
You made a typo in your question.
The equation should be y = 2x - 3.
y = 2(-1) - 3
y = -2 - 3
y = - 5
During a sale the price of a sweater changed from 20$ to 16$ what was the percent of decrease in the price of the sweater
write the equation in standard form. 8−5y=−2x8−5y=−2x the equation in standard form is .
Benito is selling T-shirts for $8 each for his school fund-raiser. So far, he has sold 16 T-shirts. How many more does he need to sell to reach his goal of $200 in sales?
Three of these equations solve for the number of T-shirts, t, he still needs to sell to reach $200 in sales. Which equation does NOT?
a) t=9
b)8t+128=200
c)8(t+16)=200
d)8t+16=200
Answer:
Its D) 8t + 16 = 200
Answer: The correct option is (d) [tex]8t+16=200.[/tex]
Step-by-step explanation: Given that Benito is selling T-shirts for $8 each for his school fund-raiser and he has sold 16 T-shirts till now.
We are to find the number of T-shirts that he still need to sell to reach his goal of $200 in sales.
The number of T-shirts still he needs to sell is represented by t.
The, according to the given information, we have
[tex]8(t+16)=200\\\\\Rightarrow 8t+128=200\\\\\Rightarrow 8t=200-128\\\\\Rightarrow 8t=72\\\\\Rightarrow t=\dfrac{72}{8}\\\\\Rightarrow t=9.[/tex]
So, the number of T-shirts that he still needs to sell is 9.
Now, we can see from the above steps of solution for t that options (a), (b) and (c) gives the correct value of t, but from option (d), we get
[tex]8t+16=200\\\\\Rightarrow 8t=200-16\\\\\Rightarrow 8t=184\\\\\Rightarrow t=23\neq 9[/tex]
So, option (d) does NOT solve for the correct value of t.
Thus, (d) is the correct option.
What is the simplified form of 12z^2-7z-12/3z^2+2z-8? ...?
If events A and B are independent, and the probability that event A occurs is 83%, what must be true?
c The probability that event A occurs, given that event B occurs, is 83%.
19 Julia is allowed to watch no more than 5 hours of television a week. So far this week, she has watched 1.5 hours. Write and solve an inequality to show how many hours of television Julia can still watch this week.
20 You are a member of your local movie theater’s club. Every time you see a movie at the theater, you earn 2 advantage points. When you earn 100 points, you get a free movie pass. Currently, you have 40 advantage points.
Write an equation to model the number of movies m you have to watch before you earn a free movie pass.
Solve the equation. Show your work. 21 Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.
My answers: 19 T<5 T - 1.5 < 5 - 1.5 T = 3.5 20 40 + 2m = 100 40 + 2m - 40 = 100 - 40 2m = 60 2m ÷ 2 = 60 ÷ 2 m = 30 21. ????????
The solution to the first problem is that Julia can watch up to 3.5 more hours of TV this week. The solution to the second problem is that you need to watch 30 more movies to earn a free movie pass. An example of an equation with infinitely many solutions is x = x.
Explanation:19. To represent this scenario as an inequality, we let T be the amount of television Julia can still watch this week. Since she can watch no more than 5 hours per week and she has already watched 1.5 hours, we subtract 1.5 from 5. So we have the inequality T + 1.5 <= 5. Subtracting 1.5 from both sides gives us the inequality T <= 3.5. So Julia can watch 3.5 more hours of TV this week.
20. Let m be the number of movies you need to watch to get a free movie pass. Each movie gives you 2 advantage points and you currently have 40 points. The equation to model this situation is 2m + 40 = 100. Subtracting 40 from both sides gives 2m = 60. Dividing by 2 gives m = 30. So you need to watch 30 more movies to get a free movie pass.
21. An equation with infinitely many solutions is one where all the terms on one side can be made identical to all the terms on the other side. A simple example is x = x. For every value of x, the equation holds, meaning it has an infinite number of solutions.
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To the nearest tenth of a degree, what is the measure of the central angle that represents 46% in a circle graph?
a.
180.3
c.
156.5
b.
149.7
d.
165.6
Write y = 1/6x + 4 in standard form using integers.
we know that
The standard form of the equation of the line is
[tex] Ax + By = C [/tex]
we have
[tex] y = \frac{1}{6}x + 4 [/tex]
Multiply by [tex] 6 [/tex] both sides
[tex] 6y = x+24 [/tex]
Subtract x both sides
[tex] -x+6y = 24 [/tex]
therefore
the answer is
the equation of the line in standard form is equal to
[tex] -x+6y = 24 [/tex]
what number multiplied by itself 4 times equals 81
Final answer:
The number that, when multiplied by itself 4 times equals 81, is 3, as 3 to the fourth power (3^4) is 81.
Explanation:
To find what number multiplied by itself 4 times equals 81, we need to find the fourth root of 81. The fourth root is the same as raising a number to the 0.25 power. To calculate manually, we may take two square roots in succession, since the square root of a number squared is the original number. The square root of 81 is 9, and the square root of 9 is 3, thus the fourth root of 81 is 3. Indeed, 34 = 3 × 3 × 3 × 3 = 81.
imkim
What is 5 1/4 divided by 1 5/9 ?
Express the answer in simplest form.
A person is standing exactly 36 ft from a telephone pole. There is a 30° angle of elevation from the ground to the top of the pole. What is the height of the pole?
The height of the telephone pole is approximately 20.79 feet, calculated using tangent function with a 30° angle.
To find the height of the telephone pole, we can use trigonometry. We'll use the tangent function since we have the opposite side and the adjacent side of the right triangle formed by the person, the pole, and the ground.
Let [tex]\( h \)[/tex] be the height of the pole.
We have the tangent of the angle:
[tex]\[ \tan(30^\circ) = \frac{h}{36} \][/tex]
Now, we can solve for [tex]\( h \):[/tex]
[tex]\[ h = 36 \times \tan(30^\circ) \][/tex]
Let's calculate:
[tex]\[ h = 36 \times \tan(30^\circ) \]\[ h = 36 \times 0.5774 \] (rounded value of tan(30°))\[ h \approx 20.7864 \][/tex]
So, the height of the telephone pole is approximately 20.79 feet.
Based on the graph shown, which of the following statements is true?
median < mode
median = mode
median > mode
Answer:
Option 2 is correct.
Step-by-step explanation:
In the given graph x-axis represents the numbers and y-axis represent the frequency.
Number Frequency Cumulative frequency
100 14 14
200 6 20 (20<36)
300 18 38 (38>36)
400 12 50
500 2 52
600 12 64
700 8 72
Total 72
Mode is the number which has highest frequency. From the above table it is noticed that the highest frequency is 18 at 300. Therefore mode of the data is 300.
Sum of frequency is 72, which is an even number.
[tex]Median=\frac{n}{2}\text{th term}[/tex]
[tex]Median=\frac{72}{2}\text{th term}[/tex]
[tex]Median=36\text{th term}[/tex]
We have to find the number whose cumulative frequency is more than 36 but preceding cumulative frequency is less than 36.
Median of the graph is 300.
Since the value of median and mode are same, therefore
[tex]median=mode[/tex]
Option 2 is correct.
What is cos 45
A.
B.
C. 1
D.
E.
F.
HELP PYTHAGORAS THEOREM
Answer:
Step-by-step explanation:
Yes
A train leaves New York for Boston, 200 miles away, at 4:00 P.M. and averages 75 mph. Another train leaves Boston for New York on an adjacent set of tracks at 5:00 P.M. and averages 40 mph. At what time will the trains meet? (Round to the nearest minute.)
The trains will meet at 6:40 P.M. after traveling at different speeds towards each other.
The trains will meet at 6:40 P.M.
To calculate the time when the trains will meet, we need to determine the time it takes for the second train to cover the distance that the first train has already covered.
The first train covers the 200-mile distance in 200 / 75 = 2.67 hours, which is 2 hours and 40 minutes.
The second train leaves at 5:00 P.M., so adding 2 hours and 40 minutes gives us 7:40 P.M. as the time the second train reaches the meeting point.
By then, the first train has been traveling for 3 hours and 40 minutes, making the meeting time 6:40 P.M.
What is the rounded number for 0.6?
Answer:
1
Step-by-step explanation:
6 Is rounded to 10 like 0.6 is rounded to 1
4. What kind of triangle is made by connecting the points A(0, –6), B(3, –6), and C(3, –2)?
equilateral
right
isosceles
right and isosceles
5. What type of quadrilateral is formed by connecting the points (0, 9), (3, 6), (0, 1), and (–3, 6)?
rhombus
trapezoid
kite
quadrilateral ...?
Answer:
Part 4) Right triangle
Part 5) Kite
Step-by-step explanation:
Part 4) What kind of triangle is made by connecting the points A(0, –6), B(3, –6), and C(3, –2)?
Using a graphing tool
see the attached figure N [tex]1[/tex]
The triangle of the figure is not equilateral------> The triangle does not have three equal sides
The triangle of the figure is a right triangle------>The triangle has an angle of [tex]90\°[/tex]
The triangle of the figure is not isosceles------> The triangle does not have two equal sides
The triangle of the figure is not a right and isosceles
Part 5) What type of quadrilateral is formed by connecting the points [tex](0, 9), (3, 6), (0, 1), and (-3, 6)[/tex]?
Using a graphing tool
see the attached figure N [tex]2[/tex]
The figure is not a rhombus------> All sides are not congruent
The figure is not a trapezoid-----> has not parallel sides
The figure is a kite------> Two disjoint pairs of consecutive sides are congruent and the diagonals meet at a right angle
Answer: U7L7
Polygons in the coordinate plane
1.D
2.A
3.D
4.B
5.C
Step-by-step explanation:
A triangle has one side that measures x, and the other two sides each measure 4 inches less than x. the perimeter is 19 inches.what is the measure of x?
Grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. Which equation can he use to find n, the number of gallons of water he should remove?
Answer:
its c on edge babes, yw <3
Step-by-step explanation:
Grant should remove approximately 7.33 gallons of water to obtain a 24% ammonia solution from the initial 16% ammonia solution.
Let x be the number of gallons of water that Grant needs to remove.
The equation you can use to represent this situation is based on the principle of maintaining the amount of ammonia in the solution:
The amount of ammonia in the original solution = The amount of ammonia in the final solution
The amount of ammonia in the original solution is the product of the initial concentration (16%) and the initial volume (22 gallons).
The amount of ammonia in the final solution is the product of the desired concentration (24%) and the final volume (22 - x gallons, where x is the amount of water removed).
So, the equation becomes:
0.16 * 22 = 0.24 * (22 - x)
Now, you can solve this equation for "x" (the number of gallons of water to remove) to achieve the desired concentration:
0.16 * 22 = 0.24 * (22 - x)
3.52 = 5.28 - 0.24x
Now, isolate the variable "x" by subtracting 3.52 from both sides:
0.24x = 5.28 - 3.52
0.24x = 1.76
Now, divide both sides by 0.24 to solve for "x":
x = 1.76 / 0.24
x ≈ 7.33
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Find the arithmetic means in the given sequence. 145, , , , 205
a. 160, 175, 190
c. 155, 165, 175
b. 165, 185, 195
d. 190, 175, 160
To find the arithmetic means in the given sequence, we fill in the missing numbers using the average of the numbers before and after them. The arithmetic means in the given sequence are 160, 175, and 190.
Explanation:To find the arithmetic means in the given sequence, we need to fill in the missing numbers.
Given sequence: 145, __, __, __, 205.
The arithmetic mean is the average of two numbers. We can find the missing numbers by taking the average of the numbers before and after them.
First, let's find the missing number between 145 and 205. The average of 145 and 205 is 175. So, the missing numbers are:
145, 175, 175, 175, 205.
To find the last missing number, we can take the average of the two numbers after it: (175 + 205) / 2 = 190.
So, the arithmetic means in the given sequence are 160, 175, and 190.
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Which answer is the explicit rule for the sequence: 13, 10.5, 8, 5.5, 3, 0.5, ...
Answer: The explicit rule for the sequence will be
[tex]a_n=15.5-2.5n[/tex]
Step-by-step explanation:
Since we have given that
[tex]13,10.5,8,5.5,3,0.5.....[/tex]
Here,
a = first term = 13
d = common difference
[tex]a_2-a_1 = 10.5-13=-2.5[/tex]
Since it forms an A.P. ;
[tex]a_n=a+(n-1)d\\\\a_n=13+(n-1)(-2.5)\\\\a_n=13-2.5n+2.5\\\\a_n=15.5-2.5n[/tex]
Hence, the explicit rule for the sequence will be
[tex]a_n=15.5-2.5n[/tex]
Answer:
[tex]a_n[/tex] [tex]= 15.5-2.5n[/tex]
Step-by-step explanation:
(solve for vf) m1v1+m2v2=m1vf+m2vf
The final equation is vf = [tex]\frac{(m1v1 + m2v2)}{(m1 + m2)}[/tex]
The given equation represents the conservation of momentum, which can be written as :
m1v1 + m2v2 = (m1 + m2) vf
To solve for vf, follow these steps :
Start with the equation : m1v1 + m2v2 = m1vf + m2vf.Factor out vf on the right-hand side : m1v1 + m2v2 = vf (m1 + m2).Isolate vf by dividing both sides by the sum of the masses : vf = [tex]\frac{(m1v1 + m2v2)}{(m1 + m2)}[/tex].This formula shows that the final velocity vf is the sum of the individual momenta divided by the total mass.Thus, the final equation is vf = [tex]\frac{(m1v1 + m2v2)}{(m1 + m2)}[/tex].(m-a)(m-b)(m-c)......(m-x)(m-y)(m-z) =?
If there are 6 circles and 42 hearts what is the simplified ratio
Which is the completely factored form of 12x^3 – 60x2 + 4x – 20?
4(3x^2 – 1)(x – 5)
4x(3x^2 + 1)(x – 5)
4x(3x^2 – 1)(x + 5)
4(3x^2 + 1)(x – 5)
The correct option is:
4(3x² + 1)(x – 5)
To find the completely factored form of the expression 12x³ – 60x² + 4x – 20, we can first factor out the greatest common factor, which is 4.
4(3x³ – 15x² + x – 5)
Next, we can factor the quadratic expression 3x³ – 15x² + x – 5 by grouping:
4[3x²(x – 5) + 1(x – 5)]
4(3x² + 1)(x – 5)
Therefore, the completely factored form of 12x³ – 60x² + 4x – 20 is:
4(3x² + 1)(x – 5
So, the correct option is:
4(3x² + 1)(x – 5)