Compute the Laplace transform Luz(t) + uş(t)i'e c{) tucave'st use
Answers
The Laplace transform of the function,\(L[u(t)cos(t)]\) is \(1/(s^2+1)\)where L[.] denotes the Laplace transform and u(t) represents the unit step function.
To compute the Laplace transform of the given function L[u(t)cos(t)], we apply the linearity property and the transform of the unit step function. The Laplace transform of u(t)cos(t) can be written as:
\(L[u(t)cos(t)] = L[cos(t)] = 1/(s^2+1)\),
where s is the complex frequency variable.
The unit step function u(t) is defined as u(t) = 1 for t ≥ 0 and u(t) = 0 for t < 0. In this case, u(t) ensures that the function cos(t) is activated (has a value of 1) only for t ≥ 0.
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Related Questions
Name: Date: 6. A biased four-sided die is rolled. The following table gives the probability of each score. Score 1 21 3 Probability 0.28 k 0.15 0.3 a. Find the value of k. (2 marks) b. Calculate the e
Answers
The expected value of the die roll is 2.47. Finding the value of kProbability is the measure of the likelihood of an event taking place. The sum of the probability of all events occurring must equal one, otherwise, the set of events would be incomplete, which is not possible.
Therefore, we have 0.28 + k + 0.15 + 0.3 = 1 where k is the probability of getting 2 on the die.Solving for k:k = 1 - 0.28 - 0.15 - 0.3k = 0.27Therefore, the value of k is 0.27. b. Calculating the expected valueThe expected value of the die roll is the sum of each score multiplied by its probability of occurrence. This is also called the mean of the probability distribution, given by: E(X) = ΣxP(x)where X is the random variable and P(x) is the probability of X being equal to x.Using the given table of probabilities:E(X) = 1(0.28) + 2(0.27) + 3(0.15) + 4(0.3)E(X) = 0.28 + 0.54 + 0.45 + 1.2E(X) = 2.47Therefore, the expected value of the die roll is 2.47.
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Calvin earns $108.50 for working 7 hours. How much will he earn for working 24 hours
Answers
Answer:
$372
Step-by-step explanation:
108.50 / 7 = 15.50
he earns $15.50 each hour
24 x 15.50 = 372
he would earn $372 in 24 hours
Answer:
$372
Explaination :
7 hour $108.50
1 hour - (180.50 ÷ 7) = $15.5
24 hours - (15.5x24) = $372
What is the minimum value of the function, f(x)=x2+8x+4
Answers
Answer:
The minimum value of the function is 12
Terrence and Teresa both work for a bookstore. Terrence earns $450 per week. Teresa earns $300 per week plus a 6% commission on the total sales of books she sells. In one week, if Teresa sells $2000 worth of books, who make more money and buy how much?
Answers
Answer:
Terrence made $30 more than Teresa.
Step-by-step explanation:
Giving the following information:
Terrence earns $450 per week.
Teresa earns $300 per week plus a 6% commission on the total sales of books she sells.
First, we need to structure the total income formula for each:
Terrence= 450
Teresa= 300 + 0.06*x
x= sales
Now, for $2,000 sales of books:
Terrence= $450
Teresa= 300 + 0.06*2,000= $420
HELPPPPP !!!!!!! Please answer correctly Will mark Brianliest !!!!!!!!!!
Answers
HELP ASAP DUE TOMORRROW
Answers
Based on the box plot, the number of students that gained more than 48 marks is 80 students.
What is a box and whisker plot?In Mathematics, the five-number summary of any box and whisker plot include the following:
MinimumFirst quartileMedianThird quartileMaximumBy critically observing the box and whisker plots which represent the scores of students in a test, we can reasonably and logically deduce that the third quartile (75%) is 70 and the median score is 48. Therefore, we would calculate the total number of students as follows:
Total number of students = 75/100 × T
120 = 0.75T
T = 120/0.75
T = 160 students.
From the median score of 48, the number of students that gained more than 48 marks is given by:
Students = 50/100 × 160
Students = 50/100 × 160
Students = 80 students.
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its urgent please. my assignment is due in like 30 minutes
Answers
Answer:
( iii)
a-x/a+x =b
a-x=b(a+x)
a-x=ab+ax
a-ab=ax+x
a-ab=x(a+1)
a-ab/a+1=x(a+1)/a+1
x=a-ab/a+1
x=a(1-b)/a+1
what is logarithmic differentiation calculator online
Answers
A logarithmic differentiation calculator is an online tool used to calculate the derivative of a function using logarithmic differentiation.
A logarithmic separation mini-computer is a web-based instrument that utilizes logarithmic separation to work out the subordinate of a capability. Logarithmic separation is a procedure used to separate capabilities that are challenging to separate utilizing customary techniques. The cycle includes taking the normal logarithm of the two sides of the capability, then separating utilizing the principles of logarithms and the chain rule. The subsequent articulation can be streamlined to give the subsidiary of the first capability. An internet based logarithmic separation number cruncher robotizes this interaction, permitting clients to enter a capability and accept its subsidiary. This can be helpful for understudies and experts in fields like math, physical science, and designing, who need to rapidly and precisely work out subsidiaries of perplexing capabilities. There are numerous logarithmic separation number crunchers accessible on the web, some of which additionally give bit by bit clarifications of the interaction used to compute the subsidiary.
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A parabola has x-intercepts -2 and -8, and has vertex (-5,-18). Determine the equation of this parabola in the form y=a(x-r)(x-s) Consider the function f(x)=4x^3+1. a) Find the derivativo of f. Answer f’(x)= b) Compute the derivative of f at x=1. Answer f’(1)=
c) Deterine the equation of the tangent line to the curve y=f(x) at the point (1,5).
Answers
a) The derivative f'(x) is 12x².
b) The amount of f'(1) is 12.
c) The equation of the tangent line is 12x - 7.
a) To find the derivative of f(x), we can use the power rule for each term. The power rule states that for any function f(x) = xⁿ, the derivative f'(x) = nx^(n-1). So for f(x) = 4x³ + 1, Thus, the derivative f'(x) = 12x².
b) To compute the derivative of f at x=1, we simply plug in x=1 into the derivative equation we found in part a. So f'(1) = 12(1)² = 12.
c) To determine the equation of the tangent line to the curve y=f(x) at the point (1,5), we use the point-slope form of a line, which is y-y1 = m(x-x1), where m is the slope of the line and (x1,y1) is the point the line passes through. The slope of the tangent line is the derivative of f at x=1, which we found in part b to be 12. So the equation of the tangent line is y-5 = 12(x-1), or y = 12x - 7.
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Consider two orthonormal energy eigenstates of a system, (1) and (2), where H|1) = E1|1) and H|2) = E2|2). Here, H is the Hamiltonian, and E1 E2 Let [A) and (B) define two different linear combinations of the states (1) and |2>, [1)+i|2) [1)-i|2) A) (i) Compute(A|A),and(B|B (3/20) (ii) Compute(A|B),and (B|A) (3/20) (iii) If initially at time t = 0 the particle is in state |/(t = 0)) = |A), what is the wavefunction |(t)) at a later time t? (4/20) particle is in state A) or state (B). For the above initial condition ((t = 0)) =[A), write the probabilities PA(t) and PB(t) that a measurement at time t > 0 will find the particle in state |A) or in state |B). (4/20) (v) Sketch Pa(t) and P(t) as a function of t on the same graph. Iden- tify the times t in which Pa(t) and P(t) obtain their maximum and minimum. What is PA(t) + PB(t)? (3/20) (vi) In this section, consider a particle that is described by the wavefunction |8A+(e|z+(z|2+(I1) N=((0=7)q| where (n) (n = 1...4) are orthonormal eigenstates of a Hamiltonian, with H|n) = En|n). You know that the wavefunction is normalized. namely (|) = 1. Find the normalization constant N. (3/20)
Answers
This problem involves a variety of concepts in quantum mechanics, including energy eigenstates, linear combinations, time evolution, inner products, probabilities, and normalization.
In this problem, we are given two orthonormal energy eigenstates of a system, and we are asked to compute various quantities related to their linear combinations.
We are also asked to find the wavefunction at a later time if the initial state is one of these linear combinations, and to calculate the probabilities of measuring the particle in each of the two states at a later time. Lastly, we are asked to find the normalization constant of a given wavefunction.
To start with, we compute the inner products of the states (A) and (B) with themselves and with each other, and obtain the probabilities of measuring the particle in each of the states.
We then use the time evolution operator to find the wavefunction at a later time t, given the initial state at t=0. Finally, we calculate the probabilities of measuring the particle in each of the two states at a later time t, and sketch the probabilities as a function of time on the same graph. We also find the normalization constant of a given wavefunction by integrating over all space.
By working through this problem, we can gain a deeper understanding of these concepts and their applications in quantum mechanics.
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EX24) 29 du Use the chain rule to find the indicated derivative. og, where du g(u, v) = f(x(u, v),y(u, v)), f(x,y) = 7x³y³.x(u, v) = ucosv, y(u, v) = usiny = 56u² cos v sin³ v
Answers
∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).
To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:
Given:
g(u, v) = f(x(u, v), y(u, v))
f(x, y) = 7x³y³
x(u, v) = ucos(v)
y(u, v) = usin(v)
To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:
∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)
To find ∂f/∂x, we differentiate f(x, y) with respect to x:
∂f/∂x = 21x²y³
To find ∂x/∂u, we differentiate x(u, v) with respect to u:
∂x/∂u = cos(v)
To find ∂f/∂y, we differentiate f(x, y) with respect to y:
∂f/∂y = 21x³y²
To find ∂y/∂u, we differentiate y(u, v) with respect to u:
∂y/∂u = sin(v)
Now, we can substitute these partial derivatives into the equation for ∂g/∂u:
∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))
To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:
x(u, v) = ucos(v) = u * cos(v)
y(u, v) = usin(v) = u * sin(v)
∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))
Simplifying further, we get:
∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))
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why am i failing my LIFE ?
Answers
Answer:
I dont know cause I am too
the life of an electric component has an exponential distribution with a mean of 10 years. what is the probability that a randomly selected one such component has a life more than 7 years?
Answers
The probability is 0.4647.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or the likelihood of a statement being true.The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty. The higher the probability of an event, the more likely the event will occur. A simple example is tossing a fair coin. Both outcomes are equally likely because the coin is fair. The probability of heads or tails is 1/2. These concepts are an axiomatic mathematical formalization of probability theory that is widely used in research fields such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy. Infer the expected frequency from the event. Probability theory is also used to explain the underlying dynamics and laws of complex systems.To learn more about probability from the given link :
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Helppppp me please I need help please
Answers
Answer:
bruh. this wat im working on too and need help also
Answer:
x = 3.6, the measure of the largest angle is 86.4
Step-by-step explanation:
15x + 24x + 21x = 180
50x = 180
180/50 = 3.6
x = 3.6
-------------------------
24x = 24(3.6)
24 * 3.6
86.4
15 = 2x – 10 step and solution
Answers
Answer:
12.5 =x
Step-by-step explanation:
15 = 2x – 10
Add 10 to each side
15+10 = 2x – 10+10
25 = 2x
Divide by 2
25/2 = 2x/2
12.5 =x
Answer:
25/2
Step-by-step explanation:
2x-10=15
+10 +10
2x=25
divide both sides by 2 to get 25/2
Seven more than twice a number x is forty-seven
Answers
Step-by-step explanation:
Seven more than twice a number is 47. Let's break down this sentence into numbers so you can see what's going on.
"Seven more than twice a number" - This tells you that there is a number, let's call it y, that is 7 more than twice a different number, lets call this x. So in equation form this is y = 7 + 2x. Hmm this seems a little tricky, how do we find the answer? Well if we keep reading, it tells you that the number that is 7 more than twice another number is 47, so we now know that y = 47. So let's redo our equation by substituting y for the number 47:
47 = 7 + 2x
Now we have a workable equation. We need to solve for x. So let's rewrite this equation without changing it, just putting it in different order. Now we have 2x + 7 = 47. So how do we solve for x? First, we subtract 7 from both sides. Remember, when solving for x, anything you do to one side you must do to the other. So now we get this:
2x + 7 = 47 simplifies to 2x = 40
Now if we divide both sides by 2 to get x all by itself, we get x = 20. That is your answer. You can check it by substituting 20 for s in your original equation of 2x + 7 = 47, then you get 2(20) + 7 = 47. It works! Hope this helps!
what does the highest point on a bell-shaped curve represent?
Answers
The highest point on a bell-shaped curve represents the peak or maximum value of the distribution. This point is known as the mode of the distribution.
In a bell-shaped curve, also known as a normal distribution or Gaussian distribution, the data is symmetrically distributed around the mean. The curve is characterized by a central peak, and the highest point on this peak corresponds to the mode.
The mode represents the most frequently occurring value or the value that has the highest frequency in the dataset. It is the point of highest density in the distribution.
The bell-shaped curve is often used to model naturally occurring phenomena and is widely applied in statistics and probability theory. The mode provides information about the most common or typical value in the dataset and is useful for understanding the central tendency of the distribution.
While the mean and median also have significance in a normal distribution, the highest point on the bell-shaped curve specifically represents the mode, indicating the value with the highest occurrence in the dataset.
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How would the one-step equation x/5 = 5 be solved?
Multiply both sides by 1/5
Multiply both sides by the reciprocal of 1/5
Divide 5 by both sides
Divide one side by 5
Answers
Answer:
2nd option
Step-by-step explanation:
Given
\(\frac{x}{5}\) = 5 ( multiply both sides by 5, the reciprocal of \(\frac{1}{5}\) to clear the fraction )
x = 25
How do I solve 8k-9(4K+4)
Answers
Answer:
-28k - 36
Step-by-step explanation:
8k - 9(4k+4)
distribute -9 into the ( )
8k - 36k -36
combine 8k and - 36k to get - 28k
-28k-36
hope this helps!!!
16 + 28 + (-42)=? Need help
Answers
☽------------❀-------------☾
Hi there!
~
Answer:
\(16 + 28 + -42\)
\(= 44 - 42\)
\(= 2\)
❀Hope this helped you!❀
☽------------❀-------------☾
Answer:
2
Step-by-step explanation:
This is the answer because:
1) First, we have to add 16 and 28 which is 44
16 + 28 = 44
2) Next, we have to add 44 and -42, which will be 2 because whenever we have to add or subtract integers, we are supposed to multiply the signs, and then we have to put the sign of the greater number. In this case, it would be:
44 + (-42) = 44 - 42 = 2
Hope this helps! :D
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing, and variable costs
(such as printing). The one-time fixed costs will total $49,500. The variable costs will be $12 per book. The publisher will sell the finished product to
bookstores at a price of $23.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from
sales?
OD
Answers
Answer:
Break-even point in units= 4,400
Step-by-step explanation:
Giving the following information:
Fixed costs= $49,500
Unitary variable cost= $12
Selling price= $23.25
We need to calculate the level of sales that will result in a net profit of zero. We need to use the break-even formula:
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 49,500 / (23.25 - 12)
Break-even point in units= 4,400
please please help. Will give brainliest
Answers
If I have 6 packs of Christmas lights and it only covers half of the roof how many more do I need?(The roof is 15ft long)
Answers
Answer:
6 more packs are needed
Step-by-step explanation:
if 6 covers half you will need 6 to.cover the other half
a particle P moves in a straight line such that, t s after leaving a point O, its velocity v ms^-1 is given by v=36t - 3t^2 for t>_ 0
1) find the value of t when the velocity of P stops increasing
2)find the value of t when P comes to instaneous rest
3) find the distance of P from O when P is at instaneous rest
4) find the speed of P when P is again at O
Answers
Answer:
jajjskslslskjsjxjj k k
Guided Practice
Fill in the blank.
(z−4)(2z+1)=\(2z^{2}\)− ___ z−4
A.
7z
B.
9
C.
7
Answers
Answer: Gradpoint answer
C.
7
Step-by-step explanation: Math.way answer
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Exact Form:
z = 0 , 7/ 4
Decimal Form:
z = 0 , 1.75
Mixed Number Form:
z = 0 , 1 3/ 4
Answer:
7
Step-by-step explanation:
(z – 4)(2z + 1) = z(2z + 1) – 4(2z + 1) = 2z2 + z – 8z – 4 = 2z2 – 7z – 4
The second term is –7z, so 7 fills in the blank.
Select all the equations that are true when x = 6. 6x = 12 17 – x = 11 x ÷ 2 = 3 19 ÷ 3 = x 5 + x = 11
Answers
6x = 12
17 – x = 11
x ÷ 2 = 3
5 + x = 11
We are given –
x = 6In case of 1st equation –
\(\qquad\) \(\twoheadrightarrow\bf 6 \times x = 6 × 6 \)
\(\qquad\) \(\twoheadrightarrow\sf 6\times x = 12 \)
\(\qquad\) \(\purple{\twoheadrightarrow\bf L.H.S = R.H.S}\)
Hence, 6x = 12 is true! ☑In case of 2nd equation –
\(\qquad\) \(\twoheadrightarrow\bf 17 – x = 11 \)
\(\qquad\) \(\twoheadrightarrow\sf 17-x = 17-6 \)
\(\qquad\) \(\twoheadrightarrow\sf 17-x = 11 \)
\(\qquad\) \(\purple{\twoheadrightarrow\bf L.H.S = R.H. S} \)
Hence, 17 – x = 11 is true! ☑In case of 3rd equation –
\(\qquad\) \(\twoheadrightarrow\bf\dfrac{x }{2} = 3\)
\(\qquad\) \(\twoheadrightarrow\sf \dfrac{x}{2}=\cancel{ \dfrac{6}{2}}\)
\(\qquad\) \(\twoheadrightarrow\sf \dfrac{x} {2}=3\)
\(\qquad\) \(\purple{\twoheadrightarrow\bf L.H.S=R.H.S}\)
Hence, x/2 = 3 is true! ☑In case of 4th equation –
\(\qquad\) \(\twoheadrightarrow\bf \dfrac{19}{ 3} = x\)
\(\qquad\) \(\twoheadrightarrow\sf \cancel{\dfrac{19}{ 3} }= x\)
\(\qquad\) \(\twoheadrightarrow\sf 6.33= x\)
\(\qquad\) \(\purple{\twoheadrightarrow\bf L.H.S≠R.H.S}\)
Hence, 19/3 = x is false ✖In case of 5th equation –
\(\qquad\) \(\twoheadrightarrow\bf 5 + x = 11\)
\(\qquad\) \(\twoheadrightarrow\sf 5+ x = 6 +5 \)
\(\qquad\) \(\twoheadrightarrow\sf 5+x= 11\)
\(\qquad\) \(\purple{\twoheadrightarrow\bf L.H.S=R.H.S}\)
Hence, 5+x = 6 is true! ☑reiko drove from point a to point b at a constant speed, and then returned to a along the same route at a different constant speed. did reiko travel from a to b at a speed greater than 40 miles per hour?
Answers
Answer:
Step-by-step explanation:
Unfortunately, I cannot answer this question without additional information about the distances traveled and the time taken by Reiko to travel from point A to point B and back to point A.
The speed at which Reiko traveled is calculated as distance divided by time. Therefore, we need to know both the distance and time for each leg of the journey to determine the speed.
Without this information, it is not possible to determine whether Reiko traveled from A to B at a speed greater than 40 miles per hour.
PLEASE HELP!! WILL GIVE BRAINLEST!!
Find the value of x
Answers
what is the future value of $800 one year from today if the interest rate is 7 percent?
Answers
Answer:
800(1+7/100)
800(1.7)
1360
Step-by-step explanation:
formula isp(1+r/100)power t
The exponential or the future value with interest is A = $ 856
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the future value be represented as A
To calculate the future value of $800 after one year with an interest rate of 7%, we can use the formula for simple interest:
The future value = present value x (1 + (interest rate x time))
So , the exponential equation is
x ( t ) = x₀ × ( 1 + r )ⁿ
Plugging in the values we have:
The future value = $800 * (1 + (0.07 * 1))
The future value = $800 * 1.07
The future value = $856
Hence , the future value of $800 one year from today with a 7% interest rate would be $ 856
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true or false The slope of a least squares regression line tells us about the strength of the relationship between x and y.
Answers
The slope of a least squares regression line tells us about the direction and magnitude of the relationship between x and y, but not the strength of the relationship. Given statement is False.
The slope of the regression line represents the amount by which the dependent variable (y) changes for a one-unit increase in the independent variable (x). A positive slope indicates a positive relationship, where an increase in x is associated with an increase in y, while a negative slope indicates a negative relationship, where an increase in x is associated with a decrease in y.
However, the strength of the relationship between x and y is determined by the degree of association between the two variables, which is typically measured using correlation coefficients. Correlation coefficients provide information about the strength and direction of the linear relationship between two variables, with values ranging from -1 to 1. A correlation coefficient of 1 or -1 indicates a perfect positive or negative linear relationship, respectively, while a correlation coefficient of 0 indicates no linear relationship.
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