The Laplace transform of the given function is [tex]f(s)=\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]
Given,
[tex]f(t)=\left \{ {{t, 0\leq t < 5} \atop {0,t\geq 5}} \right.[/tex]
Write the function in unit step function.
[tex]f(t)=t(u_{0}(t)-u_{5} (t))[/tex]
= [tex]t(1-u_{5}(t))[/tex] ∵[tex]u_{0} (t)=1[/tex]
= [tex]t-tu_{5} (t)[/tex]
[tex]f(t)=t-tu_{5} (t)[/tex]
In order to make it easier to take the Laplace transform of the function, we can follow the steps:
[tex]f(t)=t-tu_{5} (t)[/tex]
= [tex]t-(t-5+5)u_{5} (t)[/tex]
= [tex]t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]
[tex]f(t)=t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]
We need to find the Laplace transform of f(t).
Apply Laplace transform on both sides,
£[tex][f(t)=[/tex]£[tex](t)-[/tex]£[tex](t-5)u_{5} (t))+5[/tex]£[tex](u_{5} (t))[/tex]
= [tex]\frac{1}{s^{2} } -e^{-s}[/tex]£[tex](t)+5(\frac{e^{-5s} }{s} )[/tex]
= [tex]\frac{1}{s^{2} } -e^{-5s} (\frac{1}{s^{2} } )+\frac{5se^{-5s} }{s^{2} }[/tex]
= [tex]\frac{1-e^{-5s}+5se^{-5s} }{s^{2} }[/tex]
= [tex]\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]
[tex]f(s) =\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]
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Sam has 3/4 ton of stones to divide evenly among for sidewalks. how much stone will it be used in each sidewalk
The amount of stone in each sidewalk is 3/16
How to determine the amount of stone in each sidewalk?The given parameters are
Stones = 3/4 tons
Side walks = 4
The amount of stone in each sidewalk is calculated using
Amount = Stones/Side walks
Substitute the known values in the above equation
Amount = 3/4 / 4
Evaluate the quotient
Amount = 3/16
Hence, the amount of stone in each sidewalk is 3/16
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Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle
[tex]5th \: row = 1 \: \: \: 5 \: \: \: 10 \: \: \: 10 \: \: \: 5 \: \: \: 1[/tex]
[tex](x - 4) {}^{5} = x {}^{5} + 5x {}^{4} ( - 4) {}^{1} + 10x {}^{3} ( - 4) {}^{2} + 10x {}^{2} ( - 4) {}^{3} + 5x( - 4) {}^{4} + ( - 4) {}^{5} [/tex]
[tex](x - 4) {}^{5} = x {}^{5} - 20x {}^{4} + 160x {}^{3} - 640x {}^{2} + 1280x - 1024[/tex]
Find the least positive integer N so that the value of 2020 + N
is both
• a perfect cube, and
• a multiple of 56.
Answer:724
Step-by-step explanation: Let us go through trail and error method.
Question: Need to find N, so that 2020+ N should be a perfect cube, as well as a multiple of 56.
2744 is the first number we get after 2020 and it is a cube of 14. ___ equation -01
Let us divide, 2744 with 56.
i.e., 2744/56= 49. ___ equation -02
As per 1st and 2nd equation 2744 meets with the condition. And we can consider it as 2020+ N.
i.e., 2020+N= 2744
N= 2744-2020
Therefore; N= 724.
Answer:
724,
Step-by-step explanation:
14^3 = 2744 is the next perfect cube > 2020.
2744 / 56 = 49.
So that fits the requirements in the question.
So N = 2744 - 2020
= 724,
√(2x+1)
Evaluate the integral
2
(2x + 1) In (2x + 1)
dx.
Substitute [tex]y=\ln(2x+1)[/tex] and [tex]dy=\frac2{2x+1}\,dx[/tex], so that
[tex]\displaystyle \int \frac2{(2x+1) \ln(2x+1)} \, dx = \int \frac{dy}y = \ln|y| + C = \boxed{\ln|\ln(2x+1)| + C}[/tex]
A group of 5 students took 15 days to finish a project. After 9 days, 3 students left the group. How many days did it take the students to finish the project in this case?
Using proportions, it is found that it took 15 days for the students to finish the project.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, we have that:
100% of the project is done by 5 students in 15 days.After the 3 students left, 2 students will have a time of x days to do 100 - (9/15) = 40% of the project.The compound rule of three is given as follows:
1 project - 5 students - 15 days
0.4 project - 2 students - x days
Increasing the number of students, the number of days is reduced, hence the measures are inverse proportional and the rule of three is given by:
[tex]\frac{15}{x} = \frac{2}[5} \times \frac{1}{0.4}[/tex]
[tex]\frac{15}{x} = \frac{2}{2}[/tex]
15/x = 1
x = 15 days.
It took 15 days for the students to finish the project.
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PLS HELP ASAP....i need to finish this soon
A GDP per capita of $13,000 would correspond to the following corruption score of: B. 42.
What is a scatter plot?A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
Based on the information provided in the table above, we can logically deduce that the situation can be modeled by this linear function:
y = 511x - 8540
Where:
x is the corruption score.
y is GDP per capita in dollars.
How to calculate the corruption score?Based on the model, a GDP per capita of $13,000 would correspond to the following corruption score:
y = 511x - 8540
13,000 = 511x - 8540
511x = 13,000 + 8540
511x = 21,540
x = 21,540/511
x = 42.1 ≈ 42.
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18 times the quantity g plus 5
Answer:
Step-by-step explanation:
Comment
The first thing you should notice once you have read it, is there is a plus sign required. That means you are likely to get a binomial (two different things that won't reduce or combined).
So what you get is
18*g + 5
Notice where the place sign is. It is between 18g and 5. The result cannot be simplified any further.
Answer
18g + 5
What do you get when you combine the following numbers? -4-4-4-4
Answer:
-16
Step-by-step explanation:
you just add all of them together
The lines below are perpendicular.
the slope of the solid line iS 4, what is the slope of the dashed line?
Answer:
[tex]\frac{-1}{4}[/tex]
Step-by-step explanation:
Perpendicular lines have opposite reciprocal slopes. This means you change the sign and flip the numerator and denominator.
If the original slope is 4, the perpendicular slope is [tex]\frac{-1}{4}[/tex]
Listed below are systolic blood pressure measurements (in mmHg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05.
The regression equation between the variables is y = 1.03x + 62.12 and the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg is 149.67
How to determine the regression equation?From the table of values, we make use of the following representations:
Represent the Right Arm on the x axisRepresent the Left Arm on the y axisUsing the above representations, we can now plot our data values on a graphing calculator
From the graphing calculator, we have the following summary:
Sum of X = 458Sum of Y = 782Mean X = 91.6Mean Y = 156.4Sum of squares (SSX) = 601.2Sum of products (SP) = 618.8The regression equation is
y = bx + a
Where
b = SP/SSX = 618.8/601.2 = 1.02927
a = MY - bMX = 156.4 - (1.03*91.6) = 62.11843
This gives
y = 1.03x + 62.12
Hence, the regression equation between the variables is y = 1.03x + 62.12
To predict the blood pressure on the left arm given that the systolic blood pressure in the right arm is 85 mm Hg, we have
y = 1.03 * 85 + 62.12
Evaluate
y = 149.67
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The histogram shows the distribution of minting year for a sample of
100
100100 nickels at a bank.
a histogram. the x-axis is labeled minting year and numbered from 1900 to 2020. the y-axis is labeled nickels and numbered from 0 to 25. there are 12 buckets of equal width. the mids and counts for the buckets are mid: 1905, count: 1. mid: 1915, count: 0. mid: 1925, count: 0. mid: 1935, count: 0. mid: 1945, count: 1. mid: 1955, count: 1. mid: 1965, count: 11. mid: 1975, count: 17. mid: 1985, count: 15. mid: 1995, count: 20. mid: 2005, count: 24. mid: 2015, count: 10.
0
0
5
5
10
10
15
15
20
20
25
25
1900
19001900
1910
19101910
1920
19201920
1930
19301930
1940
19401940
1950
19501950
1960
19601960
1970
19701970
1980
19801980
1990
19901990
2000
20002000
2010
20102010
2020
20202020nickelsminting year
describe the distribution of minting year.
shape: the distribution of minting year is
.
center: the median is somewhere between
years.
spread: the range is approximately
years.
outliers: there are
potential outliers.
All the parts of the questions about the given histogram have been answered below.
What is a histogram?A histogram is a graph that depicts the frequency of numerical data using rectangles. The vertical axis of a rectangle represents the distribution frequency of a variable (the amount, or how often that variable appears).(A) The distribution of minting year:
According to the histogram, the distribution of minting years is 1900-1910 and 1940-2020.
(B) The median:
Add the two middle numbers together and divide them by two to get the median.
10 + 15 / 2 = 12.5
So, the median is somewhere between 10-15.
(C) The range:
The range is computed by subtracting the lowest and highest values.
25 - 0 = 25
So, the range is 25.
(D) The potential outliers:
According to the histogram, the potential outliers are 1910-1940.
Therefore, all the parts of the questions have been answered.
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Answer:
Step-by-step explanation:
I got it right on khan
I have been staying up studying all night i and have ming so mich trouble with this will someone help
Answer:
may be like this
its 32cm³
Which equation is represented by the graph below?
The equation of the graph, in slope-intercept form, is: C. y = 2/3x + 6.
How to Write a Linear Equation in Slope-Intercept Form?The linear equation of a graph in slope-intercept form is expressed as y = mx + b. Where the variable in the equation are as follows:
b = y-intercept (this is the point on the y-axis where the line intercepts).m = slope (this is the rise/run along the line = change in y / change in x).Considering the graph given, to write the linear equation it represents, find the slope (m) and the y-intercept (b) of the line.
Slope (m) = rise/run = 2 units/3 units
Slope (m) = 2/3.
The line intercepts the y-axis at y = 6, thus, the y-intercept (b) would be 6. b = 6.
Substitute m = 2/3 and b = 6 into the slope-intercept form equation, y = mx + b:
y = 2/3x + 6
Thus, the equation, in slope-intercept form, that represents the linear graph as shown in the image given is: C. y = 2/3x + 6.
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5. In one game, the final score was Falcons 3, Hawks 1. What fraction and
of the total goals did the Falcons score? Show your work in the space
percent
below. Remember to check
your
solution.
Step-by-step explanation:
Translate the triangle by
(-2 and -4)
Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
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Phillippe wants to drink at least 72 ounces of water every day while at work. He works 6 hours a day. How many ounces of water must Phillippe drink each hour? Write and solve an inequality to answer the question.
Answer:
the answer to this question is 12
Step-by-step explanation:
72÷6=12
What is the slope of the line that passes through the points (6, 2) and
(
-18, 2)? Write your answer in simplest form.
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 2 ) and (x₂, y₂ ) = (- 18, 2 )
m = [tex]\frac{2-2}{-18-6}[/tex] = [tex]\frac{0}{-24}[/tex] = 0
The slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
m = ( y₂ - y₁) / (x₂ - x₁)
It is given that the two points are (6, 2) and (-18, 2).
The two-point can be represented as,
(x₁, y₁ ) = (6, 2)
(x₂, y₂ ) =(-18, 2)
The slope of the line can be obtained as,
m = ( y₂ - y₁) / (x₂ - x₁)
m = (2-2) / (-18-6)
m =0 / -24
m =0
Thus, the slope of the line that passes through the points (6, 2) and (-18, 2) will be 0.
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What is a population parameter? a population parameter is a numerical descriptive measure of a population. give three examples. (select all that apply. )
Examples of population parameter are mentioned below .
According to the question
Population parameter :
A population parameter is a numerical descriptive measure of a population or a number that describes something about an entire group or population.
The examples of population parameter is
1. The average weight of all middle-aged female Americans. The population consists of all middle-aged female Americans, and the parameter is µ.
2. The average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.
3. The average height of a class X. This is a parameter because it is states something about the entire population of class X.
Hence, examples of population parameter will depend on the population .
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If a2 = i, where i is the identity matrix, which matrix correctly represents matrix a?
[tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
We can find the A as shown below:
Given A^2=I
We know that A^2=A×A
And [tex]I=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
So, [tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Let [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right] \left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}9-8&-6+6\\12-12&-8+9\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Hence, [tex]A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right][/tex]
Hence, option C is correct
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Disclaimer: Given question is incomplete. Complete question is attached.
Combine the like terms to create an equivalent expression.
7+4c+2d+3
Answer:
4c+2d+10
Step-by-step explanation:
7+4c+2d+3
4c+2d+(3+7)
4c+2d+10
Answer: 4c+2d+10
Step-by-step explanation:
At an airport screening, every 4th passenger will be selected to have their hands swabbed to screen for traces of explosives. Which sampling method is being used
The sampling method used is classified as Systematic.
How are sampling strategies classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, every 4th element is taken, which is a systematic sample with k = 4.
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Identify the meaning of the variables in the point-slope form of a line.
m
(X1. Y1)
(x,y)
000
the slope of the line
any point on the line
a given point on the line
In the point-slope form of a line, (y-y1)=m(x-x1)
'm' represents the slope of the line.
(x1,y1) represents a given point on the line.
(x,y) represents any point on the line.
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
A straight line is represented using its slope and a point on the line using point slope form. This means that the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1,y1).
The point slope form's equation is (y-y1)=m(x-x1), where (x, y) is a randomly chosen point on the line and m is the slope.
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Answer:
1) (x1,y1)= a given point on the line
2)(x,y) = any given point on the line
3)m= a slope of a line
the sum of three consecutive even integers if the largest is y
Answer: 3y-3
Step-by-step explanation: Largest is y. They are consecutive so the 2nd and 3rd and y-1 and y-2. So, the sum is y+y-1+y-2 which is 3y -3.
Which equations for the line of best fit do not accurately represent the data in the scatter plot? Select all that apply.
Concluding, the equations that do not accurately represent the data in the scatter plot are B, C, and D.
Which equations do not accurately represent the data in the scatter plot?By looking at the scatter plot, we can see that as we read from left to right, the number of shoes sold (y variable) decreases.
Then the linear fit must have a negative slope, from that, we can discard options B and C.
Now, we also can see that the line starts almost at y = 70.
If you look at the option D, you can see that the constant term of that line is -70, so we can also discard that option.
Concluding, the equations that do not accurately represent the data in the scatter plot are B, C, and D.
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The sum of two consecutive even integers is 26. What is the product of the two integers?
A) 168
B) 160
C) 132
D)120
The length of a parallelogram exceeds its breadth by 30 cm. If the perimeter of the parallelogram is 2 m 60 cm, find the length and breadth of the parallelogram.
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
[tex]\longrightarrow \sf{2(1 + b) = 260}[/tex]
[tex]\longrightarrow \sf{2(x+30+x) = 260}[/tex]
[tex]\longrightarrow \sf{ 2x+30 = \dfrac{260}{20} }[/tex]
[tex]\longrightarrow \sf{2x + 30 =130}[/tex]
[tex]\longrightarrow \sf{2x = 130 - 30}[/tex]
[tex]\longrightarrow \sf{2x = 100}[/tex]
[tex]\longrightarrow \sf{x= \dfrac{100}{2} }[/tex]
• [tex]\longrightarrow \sf{b= \underline{50cm}}[/tex]
[tex]\longrightarrow \sf{= x + 30}[/tex]
[tex]\longrightarrow \sf{= 50 + 30}[/tex]
• [tex]\longrightarrow \sf{ \underline{80cm}}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\large\bm{Breadth= \: 50cm}[/tex]
[tex]\large\bm{Length= \: 80cm}[/tex]
Instructions: Find the missing side. Round your answer to the
nearest tenth.
x=
30
38⁰
X
The value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units. This can be obtained by using trigonometric ratios.
Find the value of the missing side:Trigonometric identities,
If in a right triangle ΔABC where A is the right angle
sin A = [tex]\frac{opposite\ side}{hypotenuse}[/tex]cos A =[tex]\frac{adjacent\ side}{hypotenuse}[/tex]tan A = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]
In the question,
x is the adjacent side of the angle 38° and 30 units is the opposite side.
The ratio with opposite side and adjacent side is tan A
Therefore,
⇒ tan 38° = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]
⇒ tan 38° = 30/x
⇒ x = 30/tan 38°
∵ tan 38° = 0.781285627
⇒ x = 30/0.781285627
⇒ x = 38.398249
⇒ x = 38.40
Hence the value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units.
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The idea that group work theories are appropriate for all clients all the time is a(n)? empirical truth professional tenet myth lie
The idea that group work theories are appropriate for all clients all the time is a myth (Third option).
About Group Process:
The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.
Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.
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Triangle Angle Sum Theorem
Answer:
Step-by-step explanation:
Comment
The sum of the remote interior angles = The exterior angle not connected to them
What that means is that
<C + <D = <KEB
Givens
<C = 60
<KED = <C + <D
Solution and answer
<KED = <C + <D Substitute the givens into this equation
100 = 60 + <D Turn this around
<60 + <D = <100 Answer first equation
Subtract 60 from both sides
<60-<60 + <D = <100 - 60
<D = <40 Answer second Equation
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:
▪ [tex]\longrightarrow \sf{KED = 100^\circ}[/tex]
▪ [tex]\longrightarrow \sf{\angle ECD = 60^\circ}[/tex]
[tex]\leadsto[/tex] According to the triangle angle sum theorem, the sum of interior angles of a triangle is 180°.
[tex]\leadsto[/tex] We can find the value of ∠E if we know the sum of two supplementary angles is equal to 180°
[tex]\longrightarrow \sf{m \angle E+ m \angle K=180^\circ}[/tex]
[tex]\longrightarrow \sf{m \angle E+ 100^\circ =180^\circ}[/tex]
[tex]\longrightarrow \sf{m \angle E= 80^\circ}[/tex]
As we find the value of ∠E, we can replace it in the initial formula. [tex]\downarrow[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex]\bm{m \angle C + m \angle \boxed{\bm D} = m \angle \boxed{\bm E}}[/tex]
[tex]\bm{m \angle D= \boxed{\bm{ 40^\circ}}}[/tex]
A cylinder has a radius of 1 inch and height of 1 inch.what is the approximate volume of the cylinder? round to the nearest hundredth. use 3.14 for π.1.05 cubic inches1.57 cubic inches3.14 cubic inches6.28 cubic inches
The volume of the cylinder is [tex]3.14 inch^3[/tex]
Given that
radius = 1 inch
height = inch
we know that volume =[tex]V = \pi \times r^2 \times h[/tex]
now put the value in the above equation we get
[tex]V = 3.14 \times 1 ^2\times 1\\V = 3014inch ^3[/tex]
What is Volume?Volume is a measurement of three-dimensional space that is occupied.Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch).The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes.If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects with dimensions of zero, one, and two have no volume;To know more about volume with the given link
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