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- #1 Solve the following non-linear equations manually using: c) Simple Fixed Point Iteration (10 iterations)arrow_forward4. Find the first three nonzero terms in each of two linearly independent solutions of the equation. (1+x²)y" + xy = 0arrow_forward4. Suppose the following functions are a general solution of: y(4) + a3y" +a2y" + a1y' + a0y = 0arrow_forward
- The procedure to find the stationary points of a particular function f(x, y) leads to the eq 3x² +18x3y² +27= 0, -6xy +by = 0. The second of these equations has solutions y = 0 or x = 1. Select the option that gives a complete list of the stationary points of the function. Select one: O (-3,0), (1, –4), (1, 4) O (0, -3), (-4, 1), (4, 1) O(1, -3), (-4, 0), (4,0) O(-3, 1), (0, -4), (0, 4)arrow_forwardFind the particular and general solution of y'''-3y''-10y'+24y=48e-2x using Variation of parametersarrow_forward(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.arrow_forward
- Problem #1: Solve the following initial value problem. y = -2y₁ - y2 y = бу1 — 7уг y₁(0) = 5, y₂(0) = 3. Enter the functions y₁(x) and y2(x) (in that order) into the answer box below, separated with a comma. Do not include 'y₁(x) =' or 'y₂(x) =' in your answer. Problem #1: Enter your answer as a symbolic function of x, as in these examples Just Save Problem #1 Your Answer: Your Mark: Submit Problem #1 for Grading Attempt #1 Attempt #2 Attempt #3arrow_forwardplease solve question 2 from (a) to (f)arrow_forwardFind a general solution of y"=(-2+2isqrt(3))yarrow_forward
- Find the values of a, b, c, and d when f (x) = ax³ + bx² + cx + d and the following conditions are true: a, b, c, & d are constants f (0) f(1) = 0 f'(1) = -1 f"(0) = -6 = 2 Hints: Start by taking the derivative of f You might have to solve a system of equationsarrow_forwardSuppose that the cost function C for a chemical lab to produce x liters sanitizer liquid per week is given by C(x)=5000+ Vx-0.001x°(RM). The lab set the price pand amount x liters sold follow the demand equation p(x)= 60–0.0005x° (RM). As an intern in the lab, you are required to find the break-even point, that is, how much it should produce the liquid per week in order to have neither a profit nor a loss. Use the Secant method with error tolerance 5x10² to approximate the break-even point. Begin your search with po-50 and pi=200. Show all the necessary working steps and write your answer in 4 decimal places.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning