1. Find the general solution of the ODE (1-x²) d'y dx² - x dx = 2, -1

Q: e diagram below shows the function f(x) drawn to scale. 10 į -3 -2 -1 8 6 4 2 -2 -4 -6 -8 0 1 3 5

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Q: Solve the following quadratic equations (hint use the quadratic formula) 6x² + x = 12 Find the…

A: The first part of the question asks to solve the quadratic equation 6x² + x - 12 = 0. The quadratic…

Q: if our initial condition for (z,y) is (20,20), what should we expect to happen to z and y in the…

A: The objective of this question is to solve the given system of differential equations and predict…

Q: A and C only

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Q: (b) Find a prime p> 5 such that 2 and 3 are both primitive roots modulo P.

A: We test all the primes p>5 and see which prime works.

Q: 4. After exposure to certain live pathogens, the body develops long-term immunity. The evolution…

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Q: 5° Consider the equation Lu are of the form def - called Helmoltz or reduced wave equation. (a) Show…

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Q: It took amari2 bhours to paint 14ft of a 70 foot long fence.  What percent of the fence have they…

A: It took Amari 2 hours to paint 14ft of a 70 foot long fence. What percent of the fence have they…

Q: 2. Two problems: (a) Prove the formula for integration by parts: if F and G are C¹ functions on [a,…

A: Given,  and  are  functions on  and  and .To Prove: Integration by parts formula,

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS FOR BETTER UNDERSTANDING. x f(x) 0 0…

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Q: 21. s(s+ 1)

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Q: dz de 02 -13 where dz dt 11 Z + [] 2 2 %3*م and Z [2]

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Q: Write a set of parametric equations for the surface of revolution obtained by revolving the graph of…

A: Parametric equation: Let f and g be continuous functions on an interval I. Then, and , where t is a…

Q: The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal…

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Q: 4. (i) Show that 2 is a primitive root mod 11² = 121. Hint: Use the criterion given by Lemma 6.4 and…

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Q: (a) Let G be a simple graph with n vertices and m edges where m ≥ (^₂¹) + 2. (i) Let vand w be any…

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Q: Use the adjoint method to find the inverse: 4 3 2014 5 -37 15 1 -19 15

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Q: Rewrite the given expression as a sum of whose general term involves x". a) b) 00 Σn(n – 1)anxn-2 -…

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Q: Problem 0.4 diverge: (4) Σ=1 (5) Ex-1(-1/2-1/2) n=1\n Determine whether the following series…

A: We have to determine whether the following series converges or diverges.4) 5) We know thati) Cauchy…

Q: Az = 6, where A = --0-0 = 5 12 1 (D) y=1+x (A) y = Using that â = 1/4 the line that best fits the…

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Q: The weight of football players is normally distributed with a mean of 200 pounds and a standard…

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Q: □ x² + y² = 9 2 y = x + 3

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Q: Let V sp({(1, 1, 1, 1), (1, 1, 2, 4), (0, -1, 6, 7)T}) CR¹. = ) Find an orthonormal basis {u₁, U2,…

A: Given that .(a) We need to find an orthonormal basis of .(b) We need to write the vector  as a…

Q: Set up integrals to find the area between the loops of one petal of the function r = 2 cos(59) - 1.…

A: Given the function r=2cos⁡(5θ)−1. To draw the complete 5 petal flower with a loop inside each petal,…

Q: Find series solutions centered at x = 0 for the differential equation 2xy" y' +2y=0

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Q: Find the Laplace transform of e-at u(t) O 1/(s-a) O 1/s O 1/(sa) O 1/(s+a)

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Q: Evaluate R y sin (y² x) dA using the substitutions

A: Clearly, one may find that in the original region Now one may put It will change .And one may also…

Q: The solution to the differential equation f(t) is y(t) = f(t) = g(t)us(t), where = y'' – 5y' + 6y…

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Q: Consider the given function. f(x) = c +8 Evaluate the Riemann sum for 0 ≤ x ≤ 2, with n = 4, correct…

A: The given function..The aim is to find the Midpoint Riemann sum of  in the interval  with…

Q: 1. Find the maximum and minimum values of f(x, y) = x² + 3y + 7 on the set R, where R is the region…

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Q: If fis integrable on [a, b], the following equation is correct. f(x) dx = limf (r.) Ar, where Ar=!…

A: Consider definite integral .To illustrate the value for integral.If  is integrable on  then .Here…

Q: Solve the Linear 1st Order O.D.Es:

A: Given that the differential equation is

Q: Find the general Solution For D-E y + y tan x = [cos²x] y¹ प्रे

A: Given, differential equationMultiplying above equation by y on both sides, thenFrom equation (ii)

Q: Consider the following linear optimization model: (P) max s.t. x1 + 2x₂ -x1+x₂ ≤ 6 x12x2 ≤ 4 X1, X2…

A: Given Information:The Linear programming model is given as follows:Subject to the…

Q: A1. Milk or meat production Y per day is best explained by the inputs: feed needed per day in kg,…

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Q: S is defined by R(u, v) = (2u + v, u - 3v, u + 4v),0 ≤u≤ 2,1 ≤v≤ 3. Determine the surface integral…

A: We have to determine the surface integral .

Q: 8. In solving the DE 2x²y"−xy'+(x² +1)y=0 about the ordinary singular point x = 0, it is found that…

A: The differential equation can be written asy″−12xy′+x2+12x2y=0Here the functions P(x)=−1x and…

Q: Use the power reducing formulas to rewrite cot23x sin 3x in terms of the first power of cosine.…

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Q: Show that p (p(n)) ≤n/2, for n ≥ 2.

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Q: Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = x4 +…

A: We have to find write the polynomial as a product of linear factors.

Q: 8. Determine, algebraically, if y= cos 3x and y = sin 3x intersect on the interval x € [0, π]. If…

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Q: What information about a root of the function can be determined from the graph? 300 250 200 150 100…

A: We want to tell about the root of function using given graph.If f(x)=0, then we say function haa a…

Q: 6. Prove the following version of the Fundamental Theorem of Calculus: Theorem 1. Let F [a, b] → R…

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Q: If A = then det(A) Thus, -7 -91 3 A-1 -102 and det(A1) O is Nonzero 3 -34 34 [图] 3 7 -34 -102 x

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Q: Use Descartes's method to find the slope of the tangent line to y = method as well. x³ at x =a.…

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Q: 1. Find the first five nonzero terms of the taylor series solution, centered at 0, for the initial…

A: The initial value problem,  To find: the first five nonzero terms of the Taylor series solution.

Q: 2 1 A 2 1 2 2 2 1, Find an orthogonal matrix P and a diagonal matrix D such that A = PDPt.

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Q: Can you answer part c, d and e of the question?

A: As salesman offers to deposit 30% followed by 12 monthly payments of $1150 for Bruce to purchase car…

Q: Diagonalize the given matrix A and hence find A². 10 -2 -5] 2 3 3 5 A = -2 -5

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Q: Find a least-squares -1 2 2-3 -1 2 A= solution of Ax = b by (a) constructing the normal equations…

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