Follow the instructions below: a. Use Laplace transforms to solve the following Differential Equations with initial conditions. 1. .) d² + y = et dy - x = 3e-t dt given : x(0) = 0, y(0) : 0, y(0) = 1. dy dt - x = 0 da+y=1 dt given : x -1, y(0) = 2. (0) = =1.

Q: 4. Let f : X → Y define a relation on the set X by „Ry if and only if (x) = fy). Is f an equivalence…

A: f is an equivalence relation if f satisfies three properties. 1. if f is a reflexive relation  2. if…

Q: Find the product of the two complex numbers. 21 = 3 (cos 10 +i sin 10") and zg=-2(cos 35" +i sin…

A: Given: x1=3(cos 10°+i sin10°) and x2=-2(cos 35°+i sin 35°)

Q: Find the value of the variables 20. Kite 21. Parallelogram 3x-8 22. Isosceles Trapezoid 5x+4 22+5…

A:

Q: The cumulative distribution function for a random variable T is given as (0, t7, Find (а)Р(Т %3D 5).…

A: a PT=5=34-12=14=0.25 b PT>3=14+14=12= 0.5

Q: 20 of 20 You can calculate the width of the lake using a surveying technique, as shown in the…

A: Solution:GivenWV=105,     YZ=6     XZ=4To find Width of the lake=XW=?From this two triangles VWX and…

Q: 5/10 Ho math REVIEW 1- Date: Determine whether each number is prime or composite. Explain how you…

A:

Q: 8. When log y is graphed as a function of log x, a straight line results. Graph the straight line…

A: Given: The graph of log x as a function of log y is a straight line.  The points are x1,y1=1,20 and…

Q: Graph 4x - 5y = 20 and identify the x-intercept as an ordered pair. O x-int:

A:

Q: The table to the right lists probabilities for the corresponding numbers of girls in three births.…

A: Given Information :  The table to the right lists probabilities for the corresponding numbers of…

Q: Card Sort for lesson 4.6 Factors, Intercepts, and Graphs Card 3 Factors, Intercepts, and Graphs Card…

A: We have to match the give cards. It will be done by putting y=0. As we haave to find x- intercepts.

Q: Use the Cayley-Hamilton theorem to find A1, A°, and A“ for the given matrix A. 10 -8 - 4

A:

Q: 8. ACand BD are perpendicular bisectors of each other.Find BC,AE,DB, and DC. BC %3D 13 AE 12 DB DC…

A:

Q: Solve for x. Each figure is a parallelogram. 8) 9) U 10 -4 2x- 16 3x -2 K 10) 11) -12+ 2x -12 + 2x…

A: Since you have asked multiple subpart,as per our guidelines we are supposed to answer only first 3…

Q: The table shows recent population data for a major city. Population of a major city Population Age…

A: From the given table it is observed that the population under 5 years is 35,038 and 5 to 9 years is…

Q: The graph shows the altitude of a car as a driver descends down a mountain. Which of these best…

A: Consider

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A: The random variable x is defined as the number of women ted approaches before encountering one who…

Q: A group of scientists studied the amount of erosion at a beach. The scientists determined that the…

A: Given equation which models amount of shoreline is  y=-0.5x+26where x is in decades ,means multiple…

Q: 2) Maria gets a monthly electric bill that has a fixed base charge of $5.35 and for each kilowatt…

A: Given: Fixed charge or intercept α=5.35 Change in charge per kilowatt hour or slope β=0.07

Q: Plz explain properly.

A: The objective of this question is to find the Cartesian product of sets A and B, the relations R and…

Q: -40 20 Plot 1 What type of pattern exists in the data? S Quarter 2 forecast Quarter 3 forecast…

A: QuarterYear 1Year 2Year 31716862249415135860534827871

Q: 5. You have a sample with a mean of 46 and a standard deviation of 8. What is the probability of…

A: Hey there.! thank you for posting your question. Hope you’re doing well. Since you have posted…

Q: (a) Explain both mathematically and graphically what makes a function odd or even. (b) Use the limit…

A:

Q: Solve the compound inequality. 2w- 2> -14 and 4w+3 >7 Write the solution in interval notation. If…

A: Given query is to find the soly for the compound inequality.

Q: State the most specific name for each figure. 1) 2) 3) 5) 7)

A: We can name them as below

Q: Find the value of x in each parallelogram. 7. 9. IK = 35 4x + 3 8. 10 2x - 4 6x - 22

A: Solution:GivenA parellelograms are givenTo find the value of x:In a parellelogram the segement…

Q: The annual earnings (in dollars) of 35 randomly selected microbiologists are shown in the data…

A: The formula of the sample mean is,The formula of the sample standard deviation is,The formula of…