Answer:
a. L{t} = 1/s² b. L{1} = 1/s
Step-by-step explanation:
Here is the complete question
The The Laplace Transform of a function ft), which is defined for all t2 0, is denoted by Lf(t)) and is defined by the improper integral Lf))s)J" e-st . f(C)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of s as a fixed constant) 1. Find Lft) (hint: remember integration by parts) A. None of these. B. O C. D. 1 E. F. -s2 2. Find L(1) A. 1 B. None of these. C. 1 D.-s E. 0
Solution
a. L{t}
L{t} = ∫₀⁰⁰[tex]e^{-st}t[/tex]
Integrating by parts ∫udv/dt = uv - ∫vdu/dt where u = t and dv/dt = [tex]e^{-st}[/tex] and v = [tex]\frac{e^{-st}}{-s}[/tex] and du/dt = dt/dt = 1
So, ∫₀⁰⁰udv/dt = uv - ∫₀⁰⁰vdu/dt w
So, ∫₀⁰⁰[tex]e^{-st}t[/tex] = [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ - ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]
∫₀⁰⁰[tex]e^{-st}t[/tex] = [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ - ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]
= -1/s(∞exp(-∞s) - 0 × exp(-0s)) + [tex]\frac{1}{s}[/tex] [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰
= -1/s[(∞exp(-∞) - 0 × exp(0)] - 1/s²[exp(-∞s) - exp(-0s)]
= -1/s[(∞ × 0 - 0 × 1] - 1/s²[exp(-∞) - exp(-0)]
= -1/s[(0 - 0] - 1/s²[0 - 1]
= -1/s[(0] - 1/s²[- 1]
= 0 + 1/s²
= 1/s²
L{t} = 1/s²
b. L{1}
L{1} = ∫₀⁰⁰[tex]e^{-st}1[/tex]
= [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰
= -1/s[exp(-∞s) - exp(-0s)]
= -1/s[exp(-∞) - exp(-0)]
= -1/s[0 - 1]
= -1/s(-1)
= 1/s
L{1} = 1/s
One ballispicked at random from a box containing 3redballs and 1green balls. If X is the number of redballs picked, find the probability distribution of X.
Answer:
P(X = 0) = 0.25
P(X = 1) = 0.75
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The probability distribution of X.
3 red balls out of 4, one picked, so we can have either 0 red balls or 1 red ball. The probability disitribution is the probability of each outcome.
[tex]P(X = 0) = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 1) = \frac{3}{4} = 0.75[/tex]
In this problem, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions. x(π/4) = 2 2 , x'(π/4) = 0
Differentiate the given solution:
[tex]x=C_1\cos(t)+C_2\sin(t) \implies x'=-C_1\sin(t)+C_2\cos(t)[/tex]
Now, given that x (π/4) = √2/2 … (I'm assuming there are symbols missing somewhere) … you have
[tex]\dfrac{\sqrt2}2=C_1\cos\left(\dfrac\pi4\right)+C_2\sin\left(\dfrac\pi4\right)[/tex]
[tex]\implies\dfrac1{\sqrt2} = \dfrac{C_1}{\sqrt2}+\dfrac{C_2}{\sqrt2}[/tex]
[tex]\implies C_1+C_2=1[/tex]
Similarly, given that x' (p/4) = 0, you have
[tex]0=-C_1\sin\left(\dfrac\pi4\right)+C_2\cos\left(\dfrac\pi4\right)[/tex]
[tex]\implies 0=-\dfrac{C_1}{\sqrt2}+\dfrac{C_2}{\sqrt2}[/tex]
[tex]\implies C_1=C_2[/tex]
From this result, it follows that
[tex]C_1+C_2=2C_1=1 \implies C_1=C_2=\dfrac12[/tex]
So the particular solution to the DE that satisfies the given conditions is
[tex]\boxed{x=\dfrac12\cos(t)+\dfrac12\sin(t)}[/tex]
Which of these statements is true for f(x) = 2 · 3x?
Answer:
the statement number D okay!
The y-intercept of the function will be at (0, 2). Then the correct option is A.
What is an exponent?Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as
y = a(b)ˣ
The function is given below.
y = 2·(3)ˣ
The value of y at x = 0, we have
y = 2·3⁰
y = 2·1
y = 2
The y-intercept of the function will be at (0, 2).
Then the correct option is A.
More about the exponent link is given below.
https://brainly.com/question/5497425
#SPJ5
What is the probability that the sample mean would differ from the true mean by greater than 1.9 dollars if a sample of 92 5-gallon pails is randomly selected
Answer:
The correct solution is "0.0226".
Step-by-step explanation:
The given question seems to be incomplete. Please find below the attachment of the complete query.
According to the question,
Mean
= 29
Standard deviation (s),
= 8
For sample size pf 92,
The standard error will be:
[tex]SE=\frac{s}{\sqrt{N} }[/tex]
[tex]=\frac{8}{\sqrt{92} }[/tex]
[tex]=0.834[/tex]
now,
⇒ [tex]1-P(\frac{-1.9}{0.834} < z < \frac{1.9}{0.834} )[/tex] = [tex]1-P(-2.28<z<2.28)[/tex]
or,
= [tex]1-(2\times P(z<2.28)-1)[/tex]
= [tex]2-2\times P(z<2.28)[/tex]
With the help of table, the normal distribution will be:
= [tex]2-2\times 0.9887[/tex]
= [tex]0.0226[/tex]
Javier jogs 3/4 of a mile in 8/1/2 minutes.
If he keeps the same pace, how many minutes will it take him to jog 1 mile?
Answer:
11 1/3 minutes per mile.
Step-by-step explanation:
3/4 miles jogged in 8 1/2 minutes.
So 1 mile jogged in: 8 1/2 divided by 3/4 = 8 1/2 x 4/3 = (17 x 4) / (2 x 3) = 11 1/3 minutes per mile
Answer:
x = 11 1/3 minutes
Step-by-step explanation:
We can write a ratio to solve
3/4 mile 1 mile
----------------- = --------------
8 1/2 minutes x minutes
Using cross products
3/4 *x = 8 1/2
Multiply each side by 4/3
4/3 * 3/4x = 8 1/2 * 4/3
x = 17/2 * 4/3
x = 34/3
x = 11 1/3
If Tevin has 2 times as many dimes as nickels and they have a combined value of 100 cents, how many of each coin does he have?
dimes____
nickels____
Answer:
dimes- 8
nickels- 4
Step-by-step explanation:
dime=10 cents
nickels=5 cents
5 x 4 = 20
10 x 8 = 80
80 + 20 = 100
... please give brainliest ...
need help with this please
Answer:
(-2,4)
Step-by-step explanation:
The solution to the system is where the two lines intersect
The lines intersect at x = -2 and y = 4
(-2,4)
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
(-2,4)Explanation:-
in this above attachment(in questions) the two lines are intersected in a point.
The point are in the quadrant (ii)
x=-2y=4So,
The solution to this system of equation is (-2,4)
A pollster obtains a list of all the residential addresses in a certain town, and uses a computer random number generator to choose 150 of them. The pollster visits each of the 150 households and interviews all the adults in each of the household about their television viewing habits. What kind of sampling is this
Answer:
Cluster sampling.
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
People divided into groups, by households.
Each member of the households(group) is surveyed, so cluster sampling.
Function that goes through (-5,14)(1,-16)
Answer:
y = -5x - 11
Step-by-step explanation:
First we are going to find the slope of the function using the formula attached below as an image:
(-5, 14)
(1, -16)
x_1 = -5
x_2 = 1
y_1 = 14
y_2 = -16
Now plug in the values and start simplifying:
(-16 - 14)/(1 - (-5))
(-30)/(6)
-5
The slope is -5.
Now we're going to use the point-slope formula to find the final function:
(point-slope formula has been attached as an image as well)
I'm going to use the point (-5, 14) for this formula:
y - 14 = -5(x + 5)
y - 14 = -5x - 25
y = -5x - 11
That's your answer! Hope this helps (●'◡'●)
A baseball team plays in a stadium that holds 60000 spectators. With the ticket price at $11 the average
attendance has been 26000. When the price dropped to $8, the average attendance rose to 30000. Find a
demand function D(q), where q is the quantity/number of the spectators. (Assume D(q) is linear)
D(q)
(For best results, keep answers in fraction form, not decimals)
Answer:
D(q) = -(3)/(4,000)q+19.5
Step-by-step explanation:
Given:
overall capacity = 60000
price in point one = 11
spectators in first point = 26000
second point - price = 8
spectators = 30000
solution:
The demand of a product as a function of its price and other factors such as the prices of the substitutes and complementary goods, income is the expression known as demand function. It is represented by D(q)
we have two points in our line for given ques:
first point of line = (26,000, 11)
second point of line = (30,000, 8)
Slope = (11 - 8)/(26,000 - 30,000)
= (3)/(-4,000)
y = mx + b
here, b = factors influencing demand besides price
m = slope
x = price
10 = (3)/(-4,000) )(26,000) + b
b = 19.5
y = -(3)/(4,000)+19.5
D(q) = -(3)/(4,000)q+19.5
as an example, suppose the universal set U is the set of all whole numbers. Let A be the set of all multiples of, B the set of all multiples of 4, and C is the set of all multiples of 8. Detertmine if the Venn diagram at the right represents sets A, B, and C correctly. Explain your reasoning.
PLEASE ANSWER PART A AND B
Answer:
i think if you read it you should get an awnser
Step-by-step explanation: just keep trying bro
Consider Line 1 with the equation: x = − 17 Give the equation of the line parallel to Line 1 which passes through ( 3 , 8 ) :
Answer:
what is thisssss
Step-by-step explanation:
If f(x) = 3x + 2, what is f(5)?
Answer:
17
Step-by-step explanation:
1. 3(5) + 2
2. 15 + 2
3. 17
Answer:
17
Step-by-step explanation:
f(x) = 3x + 2
Let x = 5
f(5) = 3*5+2
= 15+2
= 17
A. Given that K = {x: x ≤ -2}, Y = { x: 1 < x < 6} and z = {x: x < 3}
where x is an integer, find
i. K n (Y u Z)
ii. (K n Y) u (K n Z)
III. What property of operations on sets is shown by your answers in i and ii?
Since x is an integer, we have
K = {…, -6, -5, -4, -3, -2}
Y = {2, 3, 4, 5}
Z = {…, -1, 0, 1, 2, 3}
Then
(i)
Y U Z = {…, -1, 0, 1, 2, 3, 4, 5}
==> K ∩ (Y U Z) = {…, -6, -5, -4, -3, -2} = K
(ii)
K ∩ Y = { } (empty set)
K ∩ Z = {…, -6, -5, -4, -3, -2} = K
==> (K ∩ Y) U (K ∩ Z) = { } U K = K
(iii) This is a demonstration of the distributive property. That is, the intersection distributes over a union:
K ∩ (Y U Z) = (K ∩ Y) U (K ∩ Z)
Will mark BRAINLIEST!:)
Answer:
I got 336 units...not sure if im right tho
Step-by-step explanation:
I added all the sides together and got it. (its much more complicated than that tho)
Which expressions are equivalent to -7+3(-4e-3)
Choose all answers that apply:
A. -4(3e+4)
B. 12e
C. None of the above
Answer: A
-4(3e+4)=
-12e-16
Step-by-step explanation:
-7+3(-4e-3)=
-7-12e-9=
-12e-16
Camilla and Aisha are sisters and go to same school.Camilla bikes to school and Aisha walks. Camilla’s speed is 6.5 mph and Aisha’s is 2 mph. When Camilla reached school, Aisha was 1.5 miles behind. How far away from their house is the school?
Answer:
2 1/6
Step-by-step explanation:
6.5x=2x+1.6=1/3
1/3*6.5=2 1/6
Determine the difference. 3/4 – 5/16 =?
Answer:
[tex]\frac{3}{4} -\frac{5}{16} =\frac{3(4)}{4(4)} =\frac{5}{16} =\frac{12}{16} -\frac{5}{16} =\frac{7}{16}[/tex]
Answer:
7/16
Step-by-step explanation:
3/4 - 5/16
Get a common denominator of 16
3/4 *4/4 -5/16
12/16 - 5/16
7/16
1. One half of a number added to a second
number equals 4. One half of the first
number decreased by the second number
equals zero. Find the two numbers.
Answer:
(4, 2)
Step-by-step explanation:
½x + y = 4
y = 4 - ½x
½x - y = 0
½x - (4 - ½x) = 0
½x - 4 + ½x = 0
x = 4
y = 4 - ½(4)
y = 2
please help, it’s urgent !
Answer:
f(-10) = 2 times -10 + 1
= -19
f(2) = 2^2
= 4
f(-5) = 2 times -5 + 1
= -9
f(-1) = (-1)^2
= 1
f(8) = 3-8
= -5
Step-by-step explanation:
The figure below consists of a rectangle and a
semicircle. Find the perimeter of the figure. Use π =
3.14.
Step 1: Find the perimeter of the rectangle
The rectangle has two lengths and one width that we need to add together. The width of the rectangle is equal to 2 times the radius (or the diameter) of the circle, which is 16.
25 + 25 + 16 = 66
Step 2: Find the perimeter of the semicircle
The perimeter of a semicircle is equal to half of the circumference.
C = pi x diameter
1/2 (3.14) x (16) = 25.12
Step 3: Find the perimeter of the figure
All that's left to do is add the two perimeters together.
66 + 25.12 = 91.12 m
Hope this helps!
A roller coaster descended 32.3 ft in one minute. How would you show this using an integer?
A. -32.3
B. +32.3
C. 32.3-
D. 32.3+\
Answer:
Step-by-step explanation:
a
Sixty out of every 100 pieces of candy is red. Which Indicates the
proportion of red candies? **
60
60/100
60/40
40/100
Answer:
The proportion of red candies is 60/100.
Step-by-step explanation:
Given that sixty out of every 100 pieces of candy is red, to determine which indicates the proportion of red candies, the following calculation must be performed:
60 red candies out of 100 total candies
60/100
Therefore, the ratio of red candies is 60/100.
I need help answering this question
Answer:
I'm pretty sure it's D, sorry if I'm wrong
Step-by-step explanation:
Answer:
I think D
Step-by-step explanation:
Because an experiment is defined as a scientific procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact. This example is testing to see if the mouthwash is effective.
I need help with this question please
Answer:
Average rate of change is - 1/6 or -0.166…
Step-by-step explanation:
[tex]{ \tt{f(x) = \frac{1}{x - 5} }}[/tex]
f(-1):
[tex]{ \tt{f( - 1) = \frac{1}{( - 1 - 5)} }} \\ = { \tt{ - \frac{1}{6} }}[/tex]
f(3):
[tex]{ \tt{f(3) = \frac{1}{3 - 5} }} \\ = { \tt{ - \frac{1}{2} }}[/tex]
Average rate of change:
[tex] = { \bf{ \frac{f(3) - f(-1)}{2} }}[/tex]
[tex]{ \tt{ = \frac{ - \frac{1}{2} - ( - \frac{1}{6} ) }{ 2 } }} \\ \\ = { \tt{ - \frac{1}{6} }}[/tex]
Answer:
- [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ - 1, 3 ] , then
f(3) = [tex]\frac{1}{3-5}[/tex] = - [tex]\frac{1}{2}[/tex]
f(- 1) = [tex]\frac{1}{-1-5}[/tex] = - [tex]\frac{1}{6}[/tex]
average rate of change
= [tex]\frac{-\frac{1}{2}-(-\frac{1}{6}) }{3-(-1)}[/tex]
= [tex]\frac{-\frac{1}{2}+\frac{1}{6} }{3+1}[/tex]
= [tex]\frac{-\frac{1}{3} }{4}[/tex]
= - [tex]\frac{1}{12}[/tex]
I need help answering this question thank you
pleas help
given parallelogram ABCD find m<ADB
Answer:
∠ ADB = 19°
Step-by-step explanation:
Consecutive angles in a parallelogram are supplementary, sum to 180° , so
∠ CDA = 180° - ∠ DAB = 180° - 138° = 42°
Then
∠ ADB + ∠ CDB = 42° , that is
∠ ADB + 23° = 42° ( subtract 23° from both sides )
∠ ADB = 19°
PLEASE HELP ME NOW PLEASE
9514 1404 393
Answer:
x = 12
Step-by-step explanation:
Angle U is supplementary to the arc intercepted by the tangents.
5x +10 = 180 -110
5x = 60 . . . . . . subtract 10 and simplify
x = 12 . . . . . . . . divide by 5
Given the function, calculate the following values:
Answer:
Step-by-step explanation:
The side length of an equilateral triangle is x + 3. Write an expression for the perimeter of the triangle. *
Answer:
Perimeter = (x+3) * 3 = 3x+9
Step-by-step explanation:
(x+3) would be multiplied by 3 in order to account for each of the three sides of the equilateral triangle-
The expression for the perimeter of the triangle is 3x+9.To find the expression for the perimeter of the triangle.
What is the perimeter?Perimeter is the distance around the edge of a shape. The continuous line forms the boundary of a closed geometrical figure.In an equilateral triangle, all 3 sides are the same length, so the equation would look something like this:
P=the perimeter of the triangle
(x+3)=length of each side
P=3(x+3)
To simplify further, distribute the 3 to both the x and the 3 inside of the parentheses, getting
P=3x+9.
So, the expression for the perimeter of the triangle is 3x+9.
Learn more about perimeter here:
https://brainly.com/question/6465134
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