Find y as a function of t if 100y′′−9y=0100y″−9y=0 with y(0)=3,y′(0)=8.

fourier transform of the following with steps:

x(t) = z(t) + z(t - 30)

x(t) = z(2*t) + z(t + 30)

x(t) = z^(2)(t)

Please use python or matlab. The function e^x −100x^2 =0 has three true solutions.Use secant method to locate the solutions with tolerance 10^(−10).

Summarize the basics of a Laplace equation problem by using conformal mapping.

Explain the Math behind it and define the symbols used and why it is utilized for a problem.

Example: Complex potential of an upward parallel flow. If a sketch is used explain the sketch in detail. How can this problem be done using conformal mapping?

Thank you.

Please provide step by step solution in excel (with formulas) Breaking Even Mountain Cycle specializes in making custom mountain bikes. The company founder, PJ Steffan, is having a hard time making the business profitable. Knowing that you have great business knowledge and solid financial sense, PJ has come to you for advice. Project Focus PJ would like you to determine how many bikes Mountain Cycle needs to sell per year to break even. Using Goal Seek in Excel solve using the following: Fixed cost equals $65,000 Variable cost equals $1,575 Bike price equals $2,500

Use the Stoke’s theorem to evaluate Z Z S (∇×F)·nˆ·dS where F(x, y, z) = (x^2 z^2,y^2 z^2, xyz) and surface S is part of the paraboloid z = x^2 + y^2 that lies inside the cylinder x^2 + y^2 = 4, oriented upwards. Sketch the surface S and label everything.

The following tables list the numbers of home runs hit by the leaders in the National and American Leagues. (A graphing calculator is recommended.) Home Run Leaders National League 70 42 72 35 52 64 45 55 46 63 59 61 63 62 35 66 36 62 36 54 71 31 33 54 58 65 69 52 35 62 71 38 58 52 American League 57 44 41 57 38 56 42 41 50 56 41 23 54 40 53 28 53 27 22 38 48 40 25 35 39 38 40 44 42 41 29 30 30 31 (a) Find the mean and the population standard deviation of the number of home runs hit by the leaders in the National League. Round each result to the nearest tenth. mean home runs population standard deviation home runs (b) Find the mean and the population standard deviation of the number of home runs hit by the leaders in the American League. Round each result to the nearest tenth. mean home runs population standard deviation home runs (c) Which of the two data sets has the larger mean? National League American League Which of the two data sets has the larger standard deviation? National League American League

Prove by contradiction, every real solution of x³+x+3=0 is irrational.

Compute the number of ways to deal each of the following five-card hands in poker. (a) At least one card from each suit. (b) At least one card from each suit, but no two values matching.

1. Use the midpoint of each subinterval for the value of each ck to find the Riemann sum S5S5 for the following information. Round your answer to the nearest hundredth.

f(x)=49−x^2  [a,b]=[−7,3]; n=5

2. Find the Riemann sum S5S5 for the following information. Round your answer to the nearest hundredth.

(x)=sqrt5−x; [a,b]=[−5,5]; n=5, c1=−4.5, c2=−2.5,c3=−0.5, c4=1.5, c5=3.5

The Regal Cycle Company manufactures three types of bicycles—a dirt bike, a mountain bike, and a racing bike. Data on sales and expenses for the past quarter follow: Total Dirt Bikes Mountain Bikes Racing Bikes Sales $ 927,000 $ 269,000 $ 406,000 $ 252,000 Variable manufacturing and selling expenses 473,000 117,000 204,000 152,000 Contribution margin 454,000 152,000 202,000 100,000 Fixed expenses: Advertising, traceable 69,600 8,200 40,500 20,900 Depreciation of special equipment 44,000 20,500 7,500 16,000 Salaries of product-line managers 113,900 40,100 38,700 35,100 Allocated common fixed expenses* 185,400 53,800 81,200 50,400 Total fixed expenses 412,900 122,600 167,900 122,400 Net operating income (loss) $ 41,100 $ 29,400 $ 34,100 $ (22,400) *Allocated on the basis of sales dollars. Management is concerned about the continued losses shown by the racing bikes and wants a recommendation as to whether or not the line should be discontinued. The special equipment used to produce racing bikes has no resale value and does not wear out. Required: 1. What is the financial advantage (disadvantage) per quarter of discontinuing the Racing Bikes? 2. Should the production and sale of racing bikes be discontinued? 3. Prepare a properly formatted segmented income statement that would be more useful to management in assessing the long-run profitability of the various product lines.

Q1. In a class of 50 students, the number of students who offer Accounting is twice as the number who offer Economics. 10 students offer neither of the two students and 5 student offer both subjects.
i.) Illustrate the information on a Venn diagram.
ii.) How many students offer Accounting?
iii.) How many students offer only one subjects?

Q2. In a class of 60 students, the number of students who passed Biology is 6 more than the number who passed chemistry. Every student passed at least one of the two subjects and 8 students passed both subjects.
i.) How many students passed Biology?
ii.) How many students passed Chemistry?
iii.) How many students passed only one subjects?

4)Find the general solution of the following differential equation.

y''+4y=tan(x) -pi

5)A mass of 100 grams stretches a spring 98 cm in equilibrium. A dashpot attached to the spring supplies a damping force of 600 dynes for each cm/sec of speed. The mass is initially displaced 10 cm above the equilibrium point before the mass is attached, and given a downward velocity of 1 m/sec. Find its displacement for t>0.