t) Consider the initial value problem y

+3y= ⎩




0 if 0≤t<1
11 if 1≤t<5
0 if 5≤t<[infinity], y(0)=7 a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). = help (formulas) b. Solve your equation for Y(s). Y(s)=□{y(t)}= c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t)=






Answers

Answer 1

The laplace transform of y(t) by Y(s) is  7/s. the solution to the initial value problem is  y(t) = 7 - 7e^(-3t) for 0 ≤ t < 1,  y(t) = 11e^(-3(t-1)) for 1 ≤ t < 5, and

y(t) = 0 for t ≥ 5.

a) To find the Laplace transform of the given differential equation, we apply the transform to each term separately.

Let Y(s) denote the Laplace transform of y(t).

Using the linearity property of the Laplace transform, we have

sY(s) + 3Y(s) = 0 for 0 ≤ t < 1, and sY(s) + 3Y(s) = 11 for 1 ≤ t < 5.

The initial condition y(0) = 7 implies Y(s) = 7/s.

b) Solving the algebraic equations, we obtain

Y(s) = 7/s(s + 3) for 0 ≤ t < 1, and Y(s) = 11/(s + 3) for 1 ≤ t < 5.

c) Taking the inverse Laplace transform of Y(s), we find

y(t) = 7 - 7e^(-3t) for 0 ≤ t < 1, and

y(t) = 11e^(-3(t-1)) for 1 ≤ t < 5.

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Related Questions

Find the volume of the cylinder height 10 in base radius 3 in

Answers

Answer: 282.60in³

Step-by-step explanation:

When calculating the volume of a cylinder, the formula to use is:

= πr²h

where,

π = 3.14

r = radius = 3 in

h = height = 10 in

Volume = πr²h

= 3.14 × 3² × 10

= 282.60

Therefore, the volume of the cylinder is 282.60in³

Let f:R" + R" be a linear transformation. Prove that f is injective if and only if the only vector v ERM for which f(v) = 0 is v = 0.

Answers

If  f(u1) = f(u2), then u1 = u2, demonstrating that f is injective.

To prove that a linear transformation f: R^n -> R^m is injective if and only if the only vector v in R^n for which f(v) = 0 is v = 0, we need to establish both directions of the statement.

Direction 1: f is injective implies the only vector v such that f(v) = 0 is v = 0.

Assume that f is injective. We want to show that if f(v) = 0 for some vector v in R^n, then v must be the zero vector, v = 0.

Suppose there exists a non-zero vector v in R^n such that f(v) = 0. Since f is a linear transformation, it satisfies the property that f(0) = 0, where 0 represents the zero vector in R^n.

Now, consider the vector u = v - 0 = v. Since f is linear, it must satisfy the property that f(u) = f(v - 0) = f(v) - f(0) = 0 - 0 = 0.

Since f(u) = 0, and f is injective, it implies that u = 0. However, we initially assumed that v is a non-zero vector. Therefore, we have reached a contradiction.

Hence, if f(v) = 0 for some vector v in R^n, then v must be the zero vector, v = 0.

Direction 2: The only vector v such that f(v) = 0 is v = 0 implies that f is injective.

Now, assume that the only vector v in R^n such that f(v) = 0 is v = 0. We want to show that f is injective.

Let u1 and u2 be two arbitrary vectors in R^n such that f(u1) = f(u2). We need to prove that u1 = u2.

Consider the vector u = u1 - u2. Since f is linear, we have:

f(u) = f(u1 - u2) = f(u1) - f(u2) = 0.

Since f(u) = 0, and the only vector v such that f(v) = 0 is v = 0, it follows that u = 0. This implies that u1 - u2 = 0, which means u1 = u2.

Therefore, if f(u1) = f(u2), then u1 = u2, demonstrating that f is injective.

By proving both directions, we have established that f is injective if and only if the only vector v  in R^n for which f(v) = 0 is v = 0.

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For each set of points below, determine the distance between them using the distance formula. If necessary express your answer in simplest radical form OR rounded to the nearest tenth.

Answers

where are the points below? i cant do anything if there isnt numbers or anything to work with

Since you didn’t give any points I’ll just give an example, and hope you answer using it

With a set of points (x1, y1) and (x2, y2) you can find the distance by d = [ (x2 - x1)2 + (y2 - y1)2 ]1/2.

Let (x1, y1) be (-4, 5) and (x2, y2) be (-1, -1)

d = [ (-1 - -4)2 + (-1 - 5)2 ]1/2 = [ (3)2 + (-6)2 ]1/2 = [ 9 + 36 ]1/2 = [ 45 ]1/2 = 3*[5]1/2 = 6.7

Help me please!!!!!!!!!!!!!!!

Answers

Answer:

reflection over y axis

Step-by-step explanation:

Find the slope of the graph.

Answers

Answer:

The slope is -1.3

Step-by-step explanation:

Plug it in stat, but Ill try to explain it. y2-y1/x2-x1

(-3,4)(3,-4)

-4-4/3-(-3) = -1.3

Find the value of x. Round to the nearest tenth

Answers

Answer:

36.869 or 36.87

Step-by-step explanation:

first, you find which trig function you are using. in this case, tangent.

then, you put calculate the arctan(3/4) which is 36.96989765

The measure of angle x = 36.9°

What is right triangle?

"It is a triangle in which one of the angle measures 90° "

What is hypotenuse?

"It is the longest side of the right triangle."

What is Pythagoras theorem?

"In a right triangle [tex]a^{2}+ b^{2}= c^{2}[/tex] where c is the hypotenuse and a, b are other two sides of the right triangle."

What is sine angle?

"In a right triangle, sine of angle [tex]\theta[/tex] is the ratio of the opposite side of angle [tex]\theta[/tex] to the hypotenuse."

For given question

First we find the hypotenuse of the right triangle.

Let 'h' be the hypotenuse of the right triangle.

Using Pythagoras theorem,

[tex]h^{2} =3^{2} +4^{2} \\\\h^{2} =9+16\\\\h^{2} =25\\\\h=5[/tex]

We find the sine of angle 'x'

[tex]\Rightarrow sin(x)=\frac{opposite~side~of~x}{hypotenuses} \\\\\Rightarrow sin(x)=\frac{3}{5}\\\\ \Rightarrow sin(x)=0.6\\\\\Rightarrow x=sin^{-1}(0.6)\\\\\Rightarrow x=36.9^{\circ}[/tex]

Therefore, x = 36.9°

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HELPPPPPPPPPP!!!!!!!!!!!!

Answers

The answer would be A. C stands for color and the (h) stands for height. The h is in parentheses because it is what changes and is then multiplied to the C. The C can only change when the h changes.
Goodluck with the quiz! :)

PLEASE HELP WITH MY HOMEWORK SCREEN SHOT ATTACTCHED

Answers

Answer:

first, second and fourth are all correct

Step-by-step explanation:

what is the area of the circle to the nearest square foot?

Answers

Answer:

G. 113

Step-by-step explanation:

We know that the diameter = 12, so the radius = 6.

area of circle = πr²

                       = π (6²)

                       = 36π

                       = 113.0973355 . . .

                        ≈ 113 ft²

do perpendicular lines intersect at a 60 degree angle?

Answers

No, they intersect at a 90 degree angle.

Answer:

Perpendicular angles create a 90 degree angle

Step-by-step explanation:

Which equation matches the table?

X 4 5 6 7 8
Y 8 10 12 14 16


y = x - 4
y = x ÷ 2
y = x + 4
y = 2 x

Answers

Answer:

y=2x

Step-by-step explanation








Solve the exponential equation: 529 = 20 O = log 20 2 log 5 O = log 20 5 log 2 Oz C = log 4 2 O None of the above.

Answers

The exponential equation [tex]5^{(2x)[/tex] = 20 has no solution among the given options (a, b, c). Option D is the correct answer.

To solve the exponential equation [tex]5^{(2x)[/tex] = 20, we can take the logarithm of both sides of the equation. The logarithm with base 5 seems appropriate since the base of the exponential term is also 5. So, we have:

[tex]log_5(5^{(2x))[/tex] = [tex]log_5(20)[/tex]

Using the logarithm property [tex]log_a(a^b)[/tex] = b, we can simplify the left side of the equation:

2x = [tex]log_5(20)[/tex]

Next, we need to isolate x. Dividing both sides of the equation by 2 gives us:

x = (1/2) × [tex]log_5(20)[/tex]

Now, we can focus on simplifying the right side of the equation. Using the change of base formula for logarithms, we can express [tex]log_5(20)[/tex] in terms of common logarithms (log base 10) or natural logarithms (log base e). Let's use the common logarithm:

x = (1/2) × [tex]log_5(20)[/tex]

x = (1/2) × (log(20) / log(5))

Simplifying further:

x = (1/2) × (log(20) / log(5))

We can rewrite log(20) and log(5) using their prime factorizations:

x = (1/2) × (log(2² × 5) / log(5))

x = (1/2) × (2 × log(2) + log(5)) / log(5))

Now, we can distribute the (1/2) factor and simplify:

x = (log(2) + (1/2) × log(5)) / log(5)

x = log(2)/log(5) + (1/2) × log(5)/log(5)

x = log(2)/log(5) + (1/2)

Therefore, the correct answer is d. None of these.

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The question is -

Solve the exponential equation:

5^{2x} = 20

a. x = log20/2 log 5

b. x = log20/5 log 2

c. x = log 4/ 2

d. None of these

The lengths of new pencils are normally distributed with mean 11 cm and standard deviation 0.10 cm. Find the probability that a new pencil picked at random has a length that is: a) Less than 11.15 cm [3 marks] b) Greater than 10.85 cm Between 10.9 cm and 11.1 cm II. The mean number of oil tankers at a port city is eight per day. Find the probability that the number of oil tankers on any given day is: a) Exactly 8 b) At most 3 c) More than 3

Answers

Given data: The lengths of new pencils are normally distributed with mean 11 cm and standard deviation 0.10 cm

.a) Find the probability that a new pencil picked at random has a length that is less than 11.15 cm: Formula used: `Z = (X - μ) / σ`Where,Z = Standard score X = Random Variableμ = Meanσ = Standard Deviation Calculating the value of Z, `Z = (X - μ) / σ = (11.15 - 11) / 0.10 = 1.5`

Now, look up the probability corresponding to the value 1.5 from the Z-Table. P(Z < 1.5) = 0.9332 Hence, the probability that a new pencil picked at random has a length that is less than 11.15 cm is `0.9332` approximately.

b) Find the probability that a new pencil picked at random has a length that is greater than 10.85 cm: Calculating the value of Z, `Z = (X - μ) / σ = (10.85 - 11) / 0.10 = -1.5`Now, look up the probability corresponding to the value -1.5 from the Z-Table. P(Z > -1.5) = P(Z < 1.5) = 0.9332Hence, the probability that a new pencil picked at random has a length that is greater than 10.85 cm is `0.9332` approximately.

c) Find the probability that a new pencil picked at random has a length between 10.9 cm and 11.1 cm:

Calculating the value of Z, Z1 = (X1 - μ) / σ = (10.9 - 11) / 0.10 = -1 and Z2 = (X2 - μ) / σ = (11.1 - 11) / 0.10 = 1Hence, the probability that a new pencil picked at random has a length between 10.9 cm and 11.1 cm is P( -1 < Z < 1 ) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 approximately. II. The mean number of oil tankers at a port city is eight per day.

a) Find the probability that the number of oil tankers on any given day is exactly 8:P(X = 8)Formula used: `P(X = x) = (e^(-μ) * μ^x) / x!`

Where, X = Random Variableμ = Mean x = Value of Random Variable P(X = 8) = (e^(-8) * 8^8) / 8! = 0.106Hence, the probability that the number of oil tankers on any given day is exactly 8 is `0.106` approximately.

b) Find the probability that the number of oil tankers on any given day is at most 3:

Formula used: `P(X ≤ x) = Σ P(X = i) i=0 to where, X = Random Variable(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = (e^(-8) * 8^0) / 0! + (e^(-8) * 8^1) / 1! + (e^(-8) * 8^2) / 2! + (e^(-8) * 8^3) / 3! = 0.0003Hence, the probability that the number of oil tankers on any given day is at most 3 is `0.0003` approximately.c) Find the probability that the number of oil tankers on any given day is more than 3:Formula used: `P(X > x) = 1 - P(X ≤ x)`Where,X = Random VariableP(X > 3) = 1 - P(X ≤ 3) = 1 - ( P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ) = 1 - (e^(-8) * 8^0) / 0! + (e^(-8) * 8^1) / 1! + (e^(-8) * 8^2) / 2! + (e^(-8) * 8^3) / 3! = 0.9997Hence, the probability that the number of oil tankers on any given day is more than 3 is `0.9997` approximately.

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Min read 1/8 of his book before lunch and 1/4 of his book after lunch. He says he has read 2/12 ​of his book.

Which statement is most accurate?

Answers

Answer:

neither

Step-by-step explanation:

he has read 3/6 of his book

Given the figure below, find the values of x and z.

Answers

Answer:

Value of :x = 12°z = 101°

By using the Vertically Opposite Angles property

79 = 6x + 7 where value we get is x = 12

By using Linear pair property

79 + z = 180 where we get the value of z = 101

Helppppp me pls asp plssss

Answers

8 pt = 4 qt
1 qt = 4 c? I think it’s asking for cups
8qt = 2 gal
4 qt = 8 pt
5 pts = 10 c
2 pts = 4 c

Find the volume of the following. Round to nearest hundredths place:
Use 3.14 for II
+
7 mi
2 mi

Answers

Answer:

volume of cone=1/3×pi×r²×h

volume of cone =1/3×22/7×(2mi)²×7mi

volume of cone =29.32mi³

Myrtle needs to borrow $200 and is hoping to get a paid day loan with an annual percentage rate (ARP) of less than 50%. if a company charges her $30 in fee for the loan, what is the minimum loan term needed that would give Myrtle her desired APR?

A. 90 DAYS
B. 100 DAYS
C. 110 DAYS
D. 120 DAYS ​

Answers

Answer:

110 days :)

hope it help!

nadine+mixes+a+juice+solution+that+is+made+from+3+gallons+of+an+80%+juice+solution+and+1+gallon+of+a+20%+juice+solution.+what+is+the+percent+concentration+of+the+final+solution?+25%+50%+65%+70%

Answers

The percent concentration of the final juice solution is 65%. The final solution is composed of 65% pure juice.

To compute the percent concentration of the final juice solution, we can calculate the weighted average of the two individual solutions based on their percentages and volumes.

The 80% juice solution is 3 gallons, which means it contains 0.8 * 3 = 2.4 gallons of pure juice.

The 20% juice solution is 1 gallon, which means it contains 0.2 * 1 = 0.2 gallons of pure juice.

The total volume of the final solution is 3 + 1 = 4 gallons.

The total amount of pure juice in the final solution is 2.4 + 0.2 = 2.6 gallons.

To calculate the percent concentration, we divide the amount of pure juice by the total volume and multiply by 100:

Percent concentration = (Pure juice / Total volume) * 100

Percent concentration = (2.6 / 4) * 100

Percent concentration = 65%

Therefore, the percent concentration of the final juice solution is 65%.

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I need help please, anyone will to help?

Answers

Answer:you just add the numbers to get answer

Step-by-step explanation:

i think you would add up all the numbers? if not you should try out calculator soup!! it’s helped me many times with this type of math back then!!<33

whats 24/3 but not 8?

Answers

Answer: well, it =8 and it doesn’t have different answer so that all I have to tell you.

Step-by-step explanation: Hope this help I guess :^ sorry if you don’t want this kind of answer.

Use the distributive property to simplify the following expression: 3 (2 + 5z.)​

Answers

3(2+5z)
3 x 2 = 6 and 3 x 5z = 15z
6+15z

Answer:

6+15z

Step-by-step explanation:

We multiply 3 to 2+5z. So, (3x2)+(3x5z)

What is the volume of a hemisphere with a diameter of 7.6 m, rounded to the nearest tenth of a cubic meter?

Answers

Answer:114.9m^3

Step-by-step explanation:

fyou plant tomato plants in your garden and divide them into four plots. all of the plants are the same variety, and receive the same amount of water and sunlight. you add a different fertilizer to each plot. one plot receives no fertilizer at all. at the end of the month you count how many tomatoes were produced by each plant. the independent variable is the

Answers

The independent variable in this scenario is the type of fertilizer added to each plot.

The independent variable is the factor that the researcher deliberately manipulates or changes in order to observe its effect on the dependent variable, which is the number of tomatoes produced by each plant in this case.

In the experiment, the researcher is interested in investigating how different fertilizers affect the growth and yield of tomato plants. To determine this, four plots are created, with each plot receiving a different type of fertilizer. This allows for a comparison of the effects of the different fertilizers on the dependent variable, which is the number of tomatoes produced.

By controlling other factors such as the tomato variety, amount of water, and sunlight, the researcher ensures that any differences observed in tomato production can be attributed to the independent variable, which is the type of fertilizer.

This setup allows for a systematic investigation of the relationship between the independent variable and the dependent variable in order to draw meaningful conclusions about the impact of fertilizers on tomato plant growth.

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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.
y=-16x^+272x+110

Answers

Answer:

17.40 seconds

Step-by-step explanation:

You would you the quadratic formula to get 17.40 seconds

Differentiate Concavity
Upward and Downward.

Answers

If the second derivative is positive, the function is concave upward, and if the second derivative is negative, the function is concave downward.

To determine the concavity of a function, we look at its second derivative. If the second derivative is positive, the function is concave upward. If the second derivative is negative, the function is concave downward.

To understand concavity, we start with the first derivative of a function. If the first derivative is positive over an interval, it means that the function is increasing within that interval. Similarly, if the first derivative is negative, the function is decreasing.

Now, let's consider the second derivative. If the second derivative is positive over an interval, it means that the first derivative is increasing within that interval. This implies that the function is becoming steeper as x increases, indicating concave upward curvature.

On the other hand, if the second derivative is negative over an interval, it means that the first derivative is decreasing within that interval. This indicates that the function is becoming less steep as x increases, indicating concave downward curvature.

In summary, the sign of the second derivative determines the concavity of a function. If the second derivative is positive, the function is concave upward, and if the second derivative is negative, the function is concave downward. This understanding of concavity helps us analyze the shape and behavior of functions in calculus.

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You are randomly selecting cards from a deck of cards. What is the probability of pulling a king, replacing it, and then pulling a queen?

Answers

Answer:

1/52 since there are usually 52 cards in a deck

Step-by-step explanation:

Please brainliest

Answer:

1/52 since there are usually 52 cards in a deck

Step-by-step explanation:

I need some help with this, just like Rocky, ASAP!

Answers

Answer:

12 possible roots

Step-by-step explanation:

we can use the rational zeros theorem which says that in order to find the possible roots for a polynomial we need to divide the factors of the constant by the factors of the coefficient of the leading term

which in this case is:

±(1, 2, 3, 4, 6, 12)/(1)

±1, 2, 3, 4, 6, 12

so we have 12 possible roots

1 - m∠QRU = _____ °.
2 - m∠VUW = _____ °.
3 - m∠TUW = _____ °.

Answers

Answer:

Step-by-step explanation:

74

Find sin(a) in the triangle.
Choose 1 answer:

Answers

Answer:

5/13

Step-by-step explanation:

Find the diagram to the question attached

Given the following considering angle A

Hypotenuse = 13 = AB

Opposite = 5 (side facing the angle A) = BC

Adjacent = 12

According to SOH CAH TOA;

Sin theta = opposite/hypotenuse

Sin(a) = BC/AB

Sin(a) = 5/13

Hence the value of sin(a) is 5/13

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Calentamiento - warm-up Which sentence below contains an incorrect verb form? O A. He pointed out to Detective Walsh that the lock to the jewelry store had been tampered with. B. The officer in charge was puzzled, so he taking a closer look at the evidence. O C. When Detective Walsh relieved the officer, she noticed that the officer was reluctant to go. OD. She asked Officer Goodman to talk with her briefly at the crime scene. Help me plz!! I need help and NO FILES PLZZZZZZZ! Richard Grasso, and the NYSE, Inc. (a) Harvard Business SchoolFirst, for context, this is a complex, nuanced case without clear answers. It is unclear who is at fault and there is plenty of blame to go around.1a. Is Grasso a victim of an irresponsible board that turned on him, or did he create his own demise? Explain your answer. 1b. As an NYSE board member, would you vote to affirm Grasso or to force his resignation? What factors determined your decision?2. As chair and CEO of the NYSE, to who is Grasso responsible? Is it 1) NYSE board; 2) NYSE members (or seat holders); 3) Specialists; 4) SEC (as a regulator); or 5) the American people (in his assumed post-September 11, 2001 role). Explain your answer.3. What are the root causes of this unfortunate situation?4a. What factors in Grasso's life story, his personality or his character led him into this situation?4b. What's really driving Grasso? How are his motivations impacting his behavior?4c. Can you envision something like this happening to you?5a. What could Grasso have done to prevent this situation? 5b. What should the NYSE board have done to prevent this situation?5c. Now that we have reviewed the case, as a member of the NYSE board, would you vote to A) retain Grasso as chair and CEO or B) force him to resign? The firm's total cost after the rent increase is $2,000, and its new total fixed cost is $1,600. It is producing 20 units of output. Calculate the firm's average variable cost. Show your work. The following information is for the 5% XYZ bondSettlement date 3 April 2019Coupon rate 5%Redemption date 10 December 2020Coupon dates 10 June and 10 DecemberBasis for accrued interest Actual/ActualYTM 4%a. Calculate:i. Days accrued interest (1 mark)ii. Accrued interest (1 mark)iii. Dirty (Gross) price of the bond (5 marks)iv. Clean price of the bond (1 mark)v. Current yield (1 mark)vi. $Duration (5 marks)vii. $Convexity (5 marks)b. What do the modified duration and convexity of a bondrepresent? (4 marks)c. The price change estimated using modified duration andconvexity may be a poor approximation of actual bond pricechange even for small changes in required yield. Discuss.par value is a 100. you are on the settlement date. What is the surface area of the cylinder shown below? Use 3.14 for . 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Given the opportunity cost of a similar bond in the current market is 7.50%, calculate the current market price of Campbell Corporations bond. (Round to the nearest dollar).a. $515 b. $604 c. $692 d. $860 With the beginning of the Space Shuttle program in the 1980s, it became vital to improve the food and methods of eating and drinking in space since astronauts could spend 30 days aboard. The new food system included hot and cold water dispensers, a pantry, and an oven. Astronauts are able to choose meals in advance, though meals are repeated about every week. In addition, the space shuttle includes individual-sized packets of mustard, ketchup, mayonnaise, and hot sauce for seasoning. The space food system has improved drastically since its beginning days of tubes and bite-sized, dehydrated foods. As space missions become longer, the program will undoubtedly make new advances.Which of the following best describes how this paragraph Is organized. 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