Say that the function f(x) is x for -π < x < 0 and zero for 0 < x < π. Find the a0 coefficient for the Fourier Series.

Q: Scott’s current grades in Algebra II are the following. Use the information to calculate Scott’s…

A: Solution: Average marks in tests = (85 + 75 + 60 + 92) /4= 312/4 = 78 Weightage for tests = 20% So,…

Q: You deposit P dollars into an account that earns a nominal rate of i compounded semiannually. At the…

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Q: n gent

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Q: (b) (c) (d) (e) dy=3x²(y-1) dx dy_y+2 = dx x+1 dy dx -+e*y² = 0 dy dx -= cos x tan y hotnes

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Q: 16. (a) Find the solution of the differential equation cos x dy+ (sin x) y = 1. dx (b) Give the…

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Q: Define some other metric on prove its metric. a Rn and

A: Metric defined below is sum metric that follows three properties.

Q: Question 4 Let a and b be natural numbers. Give all solutions to the following equation: 2ª + 1 = 6²…

A: Solution:    2a + 1 = b2    =&gt; 2a = b2 - 1              = (b - 1)(b + 1)  =&gt; both (b - 1) and…

Q: (f) y-x=3+4y=4 when x = 1 dx dx

A: We have to find the particular solution of the following differential equation:…

Q: 2v 2ycos3

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Q: 0-2 3 Given A= 1 7 4 3 5 9 [10 2 3 B-2 -1 3 6 [4 4 10 9 (1) (a) Find the transpose of B. symbol BT…

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Q: dy dx = y² y² - 1 x² - 1 ´‚y(2) = 2

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Q: p: 10+6=15 Determine the truth value for the statement pv-p. Choose the correct truth value below.…

A: Remember the truth values of the following : pp \neg p¬p True False False True   and…

Q: Let f : A → B be a function. Prove that for any B1, B2, ⊂ B, f -1(B1) ∪ f -1(B2) ⊂ f -1(B1 ∪ B2)

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Q: 15. (a) Find the solution of the differential equation x(x + 1) dy + xy = 1. dx (b) Give the largest…

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Q: lim (x,y) → (0, 0) √x²y² +1 -1 x² + y²

A: We have to show if the given limit exists or not. lim(x,y)→(0,0)x2y2+1-1x2+y2

Q: 5. Find the plane Moment of Inertia of the given plane area y=4-x², x=0, y=0, about the x-axis and…

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Q: An object of mass m moves at a constant speed v in a circular path of radius r. The force required…

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Q: A body moves on a coordinate line such that it has a position s= f(t)=12-5t+4 on the interval 0…

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Q: Let A be an n × n matrix and let B = A − αI for some scalar α. How do the eigenvalues of A and B…

A: To check that (eigenvalue of A- alpha) is an eigenvalue of B.

Q: Given the following state equations and the output equation b. *₁ =−x₁ + 2x₂ +26 x₂ =-3x₁ - x₂ + Su…

A: As per the question we are given a linear dynamic control system with state variables x1 , x2  input…

Q: sinh(t2)

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Q: 7. Use a sum identity to find sin 75 degrees 7x 8. Use a sum identity to find cos 12 I 9. Use an…

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Q: 20. You distribute 25 identical pieces of candy among five children. In how many ways can this be…

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Q: 9. Given an infinite collection An, n=1,2,... of intervals of the real line, their intersection is…

A: Let An : = [ n ,∞)  where  n = 1,2, 3 .....  . So { An } n∈ℕ is an example of infinite collection…

Q: 65. Let f and g be linear functions with equations f(x) = mx + b₁ and g(x) = m₂x + b2. Is fo g also…

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Q: Find the value of k for which the constant function r(t) = k is a solution of the differential…

A: First order differential equation,

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Q: C. Family of Curves 1. Show that with distance from vertex to foci fixed as a, the family of curves…

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Q: If st", find 08/0t, as/Ou.

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Q: В.долие не а) 20x=16 год 64 5) 131× = 21 mod 77 following linear сондчиснете, 1 ?? У

A: (a) Given,            20x≡16(mod 64).

Q: The rate of inflation for 2018 was 2.4%. Did the price of Minnesota Twins tickets exceed the…

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Q: Find the general solution of the given differential equation.  y^(6) +y -0

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Q: 7. Use secant method in finding the root of f(x) = -1 +5.5x - 4x² +0.5x³. Consider the given initial…

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Q: The matrix A 0 4 0 0 -4 -8 has two real eigenvalues, one of multiplicity 1 and one of multiplicity…

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Q: A potato is launched vertically upward with an initial velocity of 170 feet per second from a potato…

A: Solution: (a) s = -16t2 + 170t + 66        Velocity is given by,           v = ds/dt = 170 - 32t…

Q: 1. Find the general solution to the DE ye ²x dx - (4+e ²*) dy = 0 2x 2x using two (2) methods with…

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Q: determine the present value (p) that must be invested to have the future value (A) at a simple…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Given  ∫02ex4+x2dx,  n=10

Q: 1. Let ā=ī-2j+k, b = i +4j-5k, c = 5i + j - 2k & d = -2ī-j+k. Answer each of the following: Sketch…

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Q: 4. When using a numerical method to approximate the value of an integral, we expect there to be some…

A: Note: As per the our guidelines we can anser only three subparts.

Q: Consider the nonhomogeneous differential equation x²y" (x² + 2x)y' + (x+2)y=x³, x>0. 1. Verify that…

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Q: 4. The curve in the following figure is the graph of a function y=f(x). -2 y f(x) 2 Sketch the graph…

A: The details are provided in step 2.

Q: if $24 is is invested at a simple interest rate of 2% per year what was the account balance be after…

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Q: x' = 2x + y, y = 6x + 3y; x(0) = 1, y(0) = -2

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Q: Determine whether the function f is even, odd, or neither. f(x) = x² + 2x² even odd neither Sketch…

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Q: y" - 7y" +7y +15y = 0 Find three linear independent Solutions • write general solution as arbitrary…

A: We have to find the general solution of the following differential equation:…

Q: Step 1 Solution: 2a +1=b² = 2a = b2 - 1 = (b - 1) (b => both (b - 1), form 2k for som i.e, b-1= 2m,…

A: This can be achieved by solving upper two equations in the solution.

Q: fruit grower can use two types of fertilizer in her orange grove, brand A or brand B. The amounts…

A: Let x bags of brand A and y bags of amount B should be added.

Q: 3 days? (Write

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Q: Construct a truth table for the statement q→ (pvr). pqr pvr q→ (pvr) TTT T TF TFT TFF FTT FTF FT FF…

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