Answer:
The inverse Laplace transform of [tex]F(s) = \frac{3\cdot s + 9}{s^{2}+9}[/tex] is [tex]f(t) = 3\cdot \cos \omega t + 3\cdot \sin \omega t[/tex].
Step-by-step explanation:
In this case, we should use the following direct and inverse Laplace Transforms:
[tex]F(s) = G(s) + H(s)[/tex] (1)
[tex]\mathcal{L}^{-1} \{\frac{s}{s^{2}+\omega^{2}} \} = \cos \omega t[/tex] (2)
[tex]\mathcal{L}^{-1}\{\frac{\omega}{s^{2}+\omega^{2}} \} = \sin \omega t[/tex] (3)
[tex]\mathcal\{L\}^{-1}\{c\cdot F(s)\} = c\cdot \mathcal\{L\}^{-1}\{F(s)\}[/tex] (4)
Then, we apply all these trasforms:
[tex]F(s) = \frac{3\cdot s + 9}{s^{2}+9}[/tex]
[tex]F(s) = 3\cdot \left(\frac{s}{s^{2}+9} \right)+3\cdot \left(\frac{3}{s^{2}+9} \right)[/tex]
[tex]f(t) = 3\cdot \cos \omega t + 3\cdot \sin \omega t[/tex]
The inverse Laplace transform of [tex]F(s) = \frac{3\cdot s + 9}{s^{2}+9}[/tex] is [tex]f(t) = 3\cdot \cos \omega t + 3\cdot \sin \omega t[/tex].
select the correct anwser from the drop down menu.
what equation has no solution
A. 13y + 2-2y = 10y + 3 - y
B. 9 (3y + 7) - 2 = 3 ( - 9y + 9)
C. 32.1y + 3.1 + 2.4y - 8.2 = 34.5y - 5.1
D. 5 (2.2y + 3.4) = 5 (y - 2) + 6y
Answer:
D. 5(2.2y + 3.4) = 5(y-2) + 6y
This equation has no solution
Marcos is making a pyramid in his wood shop class. The base of the pyramid is a rectangle. 6 What is the surface area of the pyramid? Show your work.
What expression is equivalent to
2/3 X 5
Answer:
1/3
Step-by-step explanation:
1/3 can be used as an expression that is exactly the same as 2/3x5.
When you multiply 2/3 x 5-
Look here if you need help solving 2/3 X 5: (2/3 x 5/1...is the simplest way to multiply the two, make sure to multiply 2 by 5 and 3 by 1 to get your answer.)(5x2=10...3x1=3)
-you get 10/3. This answer simplified is 1/3. So in the end, 1/3 is a great expression or answer to use as an equivalent to the equation 2/3 x 5.
Hoped this helped! :)
A parallelogram has an area of 37.72 m² and a height of 4.6 m.
How long is the base of the parallelogram?
Enter your answer as a decimal in the box
Answer:
8.2m
Step-by-step explanation:
Formula : Area = base x height
rearrange : Base = area ÷ height
37.72÷4.6=8.2m
Answer:
8.2
Step-by-step explanation:
Describe the slope of the line.
The slope is
Find the slope.
m =
step by step explanation
Answer:
The slope is POSITIVE.
The line has a slope of positive 4/3
Step-by-step explanation:
It rises 4 then runs 3.
Benita observed that 28 out of 55 patrons at the public library used the computer. The librarian told Benita that 660 patrons enter the library throughout the day. Based on Benita's observations, how many patrons during the day would be expected to use the computer?
Answer:
336
Step-by-step explanation:
Need help fast please with these 5 questions
Answer:
16.....................................
6⁹*6ⁿ = 6¹²6⁹⁺ⁿ = ¹²9 + n = 12n = 317.....................................
7⁸/7ⁿ = 7³7⁸⁻ⁿ = 7³8 - n = 3n = 518.....................................
15ⁿ = 115ⁿ = 15⁰n = 019.....................................
1/10⁵ = 10ⁿ10⁻⁵ = 10ⁿ-5 = nn = -520.....................................
(8²)ⁿ = 8¹²8²ⁿ = 8¹²2n = 12n = 6An insurance company divides its policy holders into three categories: low risk, moderate risk, and high risk. The low-risk policy holders account for 55% of the total number of people insured by the company. The moderate-risk policy holders account for 25%, and the high-risk policy holders account for 20%. The probabilities that a low-risk, moderate-risk, and high-risk policy holder will file a claim within a given year are respectively 5%, 15% and 60%. Given that a policy holder files a claim this year, what is the probability that the person is a moderate-risk policy holder?
Answer:
0.2027 = 20.27% probability that the person is a moderate-risk policy holder
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Policy holder files a claim.
Event B: The person is a moderate-risk policy holder.
Probability of filling a claim:
5% of 55%(low risk)
15% of 25%(moderate risk)
60% of 20%(high risk).
So
[tex]P(A) = 0.05*0.55 + 0.15*0.25 + 0.6*0.2 = 0.185[/tex]
Files a claim and is moderate risk:
15% of 25%(moderate risk)
So
[tex]P(A \cap B) = 0.15*0.25 = 0.0375[/tex]
Given that a policy holder files a claim this year, what is the probability that the person is a moderate-risk policy holder?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0375}{0.185} = 0.2027[/tex]
0.2027 = 20.27% probability that the person is a moderate-risk policy holder
Find m∠4 if m∠1 = 100°
Answer:
m4{=100 is the answer,,,,,,
Plz Work out -1x(6x-8)=
Find the sum of the first six terms of the Geometric Progression (G.P.):
2
1, 2, 4, ....
Step-by-step explanation:
Heueueirjrjkwugoystsitso5wpysoydlusktzlhskgdlysyldj
FREE BRAINLIST NEED HELP ASAP
Answer:
A
Step-by-step explanation:
PLEASE HELP, will get brainliest
Answer:
The answer is the first, hope this helps
Step-by-step explanation:
If lines r and s are parallel, what would be the measurement of angle 6 if angle 1 was 2x+4 and angle 2 was 6x+8?
Answer: 134
Step-by-step explanation:
Angle 1 and 2 are supplementary and Angle 2 is congruent to Angle 6
Thus, first solve for x
8x+12=180
x = 21
Then solve for angle 2 which is congruent to angle 6
6(21) + 8 = 134
One way to recognize a line of symmetry is to look for a line that divides the
original image into:
A. Two congruent parts
B. Three congruent parts
C. Two perpendicular parts
D. Two intersecting parts
A child is standing across the street from his apartment. His mother is on their balcony. The angle of elevation between the child's eyes and his mother's eyes is 28°. If the distance between their eyes is 35 ft, how far is the child standing from his apartment building? Round to the nearest foot.
look at the image below and identify:
what is the same?
what is different? plz help me
Answer:
the difference is number 4
Which three pieces of information contribute the most to your credit score?
Displayed is the ordered data of body temperatures, in degrees Fahrenheit, for 65 healthy adult women: 96.4, 96.7, 96.8, 97.2, 97.2, 97.4, 97.6, 97.7, 97.7, 97.8, 97.8, 97.8, 97.9, 97.9, 97.9, 98.0, 98.0, 98.0, 98.0, 98.0, 98.1, 98.2, 98.2, 98.2, 98.2, 98.2, 98.2, 98.3, 98.3, 98.3, 98.4, 98.4, 98.4, 98.4, 98.4, 98.5, 98.6, 98.6, 98.6, 98.6, 98.7, 98.7, 98.7, 98.7, 98.7, 98.7, 98.8, 98.8, 98.8, 98.8, 98.8, 98.8, 98.8, 98.9, 99.0, 99.0, 99.1, 99.1, 99.2, 99.2, 99.3, 99.4, 99.9, 100.0, 100.8
Which value would need to be exceeded for a data point to be considered an outlier when using the 1.5 X IQ R rule?
a. 99,8
b. 100.0
c. 99.6
d. 100.8
Answer:
54932540-476715.jpeg
A study of stroke patients who survived 6 months after the stroke found that 6/45 men and 22/63 women lived in an institution (e.g., nursing home or assisted living facility). What is the risk difference of living in an institution between men and women (using men as the reference group)?
Data (1=males, 2 =females)
temp sex Heart rate
96.3 1 70
96.7 1 71
96.9 1 74
97 1 80
97.1 1 73
97.1 1 75
97.1 1 82
97.2 1 64
97.3 1 69
97.4 1 70
97.4 1 68
97.4 1 72
97.4 1 78
97.5 1 70
97.5 1 75
97.6 1 74
97.6 1 69
97.6 1 73
97.7 1 77
97.8 1 58
97.8 1 73
97.8 1 65
97.8 1 74
97.9 1 76
97.9 1 72
98 1 78
98 1 71
98 1 74
98 1 67
98 1 64
98 1 78
98.1 1 73
98.1 1 67
98.2 1 66
98.2 1 64
98.2 1 71
98.2 1 72
98.3 1 86
98.3 1 72
98.4 1 68
98.4 1 70
98.4 1 82
98.4 1 84
98.5 1 68
98.5 1 71
98.6 2 77
98.6 1 78
98.6 1 83
98.6 2 66
98.6 1 70
98.6 1 82
98.7 2 73
98.7 1 78
98.8 1 78
98.8 1 81
98.8 2 78
98.9 1 80
99 2 75
99 2 79
99 1 81
99.1 1 71
99.2 1 83
99.3 1 63
99.4 1 70
99.5 1 75
96.4 2 69
96.7 2 62
96.8 1 75
97.2 1 66
97.2 2 68
97.4 2 57
97.6 1 61
97.7 2 84
97.7 1 61
97.8 2 77
97.8 2 62
97.8 2 71
97.9 1 68
97.9 2 69
97.9 2 79
98 2 76
98 1 87
98 2 78
98 2 73
98 2 89
98.1 2 81
98.2 2 73
98.2 2 64
98.2 2 65
98.2 2 73
98.2 2 69
98.2 2 57
98.3 2 79
98.3 2 78
98.3 2 80
98.4 2 79
98.4 2 81
98.4 2 73
98.4 2 74
98.4 2 84
98.5 2 83
98.6 2 82
98.6 2 85
98.6 2 86
98.6 2 77
98.7 2 72
98.7 2 79
98.7 2 59
98.7 2 64
98.7 2 65
98.7 2 82
98.8 2 64
98.8 2 70
98.8 2 83
98.8 2 89
98.8 2 69
98.8 2 73
98.8 2 84
98.9 2 76
99 2 79
99 2 81
99.1 2 80
99.1 2 74
99.2 2 77
99.2 2 66
99.3 2 68
99.4 2 77
99.9 2 79
100 2 78
100.8 2 77
Step-by-step explanation:
The points T(1,5), U(-5,1), and V(4,-2) are the midpoints of the sides of triangle ABC. Graph the three midsegments. Complete the coordinates of each vertex of triangle ABC. Pls answer quick
Answer:
use your instincts
Step-by-step explanation:
trust your gut that is what my idiot dad told me to do
Select the Ratio that is not equivalent to the rest.
25 points
12:25
6:15
14:35
2:5
How do I find the x? Please and thank you!
Answer:
x = 9
Step-by-step explanation:
The two opposite interior angles that are opposite to the exterior angle are congruent as shown in the diagram.
Therefore, based on the exterior angle theorem of a triangle, we have the following equation:
2(7x + 2)° = (17x - 23)
14x + 4 = 17x - 23
Collect like terms
14x - 17x = -4 - 23
-3x = -27
Divide both sides by -3
-3x/-3 = -27/-3
x = 9
PLEASE HELP‼️‼️
A
B
C
D
Answer:
C i think
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
use the side splitter theorem
6/12 = x/18 (replacing AQ with x)
12x = 108 (cross multiply)
x = 9
PLS HELP I ONLY NEED PART B
Kari and Julie are practicing for basketball tryouts. Kari makes 3 less than twice as many baskets as Julie.
Part A Write an expression with two terms for the number of baskets that Kari makes. Explain how you found your expression.
Part B Write an expression with three terms for the number of baskets that Kari and Julie make in all. Explain how you found your expression.
Answer:
X= 2y - 3
Kari makes X tryouts. She also makes 3 less than twice as many as Julie which would be X= 2y - 3
Julie makes y tryouts and twice would be 2y.
Step-by-step explanation: hope this helps!!! :)
Answer:
X= 2y - 3
Kari makes X tryouts. She also makes 3 less than twice as many as Julie which would be X= 2y - 3
Julie makes y tryouts and twice would be 2y.
Step-by-step explanation:
Which of the following is not True.
A. Angle 1 and Angle 8 are alternate exterior angles.
B. Angle 8 and Angle 4 are corresponding angles.
C. Angle 3 and Angle 2 are Vertical Angles.
D. Angle 5 and Angle 3 are Alternate Exterior Angles.
Find the height of the parallelogram shown below, if the area is 2115.
45
?
51
Answer:
47
Step-by-step explanation:
2115/45=47
Can you pls help meSimplify 6+(-11)
basically all you're doing here is subtracting 6 from 11. 11-6=5, add the - sign, so the answer is -5
Find the area under the standard normal curve that lies outside the interval between z = -2.16 and z = 2.14
Answer:
The area is 0.0316
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X
Find the area under the standard normal curve that lies outside the interval between z = -2.16 and z = 2.14
Below z = -2.16 or Above z = 2.14
Below z = -2.16
z = -2.16 has a pvalue of 0.0154, which means that this area is 0.0154
Above z = 2.14
z = 2.14 has a pvalue of 0.9838, which means that this area is 1 - 0.9838 = 0.0162
Total:
0.0154 + 0.0162 = 0.0316
The area is 0.0316
Your friend says that enough information is given to prove that x= 15. Is your friend correct?
please help
Answer:
Yes, it appears so.
Step-by-step explanation:
Based on the fact that angle L and angle P are congruent, the angles at point M are also congruent to their opposites. All of this points to triangles MNP and MLK being the same, which would mean that x does equal 15. Sorry I couldn't state any specific laws or anything.
In ADEF, the measure of ZF=90°, the measure of ZE=53°, and DE = 57 feet. Find the
length of FD to the nearest tenth of a foot.
E
539
57
F
D
X
Answer:
Check pdf
Step-by-step explanation: