Stuck on differential equation question, part a) and part b)

Q: The region = square centimeter. The mass of is: mass {(x, y) |0 ≤ y ≤ 4 cos x; 0 ≤ x ≤ π/2} has…

A: Density function

Q: Let's consider the following system of equations: A₁=²+²-2=0 F₂=2²-2²-1=0 Solve the following system…

A: Consider the following system of equations:To Find:

Q: Let f(x) = (x5 + x² + 1)er³+1 and g(x) = ex³ +¹. (a) Draw a rough sketch of the graphs of the…

A: (a)

Q: (a) Is the set S = {1 + x + x2, 1 − x3,  x + x2 + x3,  x3} ⊂ P3 linearly independent? If so, prove…

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Q: Solve the following integral. Where x(t) = t, and T, = 1/2. [ 10 n=0 x(t)8(t-nTs) dt

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(x) S…

A: Given:The given integral is .Also, given that .To Find:We have to approximate the given integral…

Q: Answer the following questions for a game played as an alternate move, single choice game using the…

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Q: a) Draw the Hasse diagram of D90- b) What is the poset interval [3,90] ? c) Compute dist(3, 90). d)…

A: Let's address each part of the question step by step.Here's the Hasse diagram for ​:

Q: Let be a vector field and fbe a scalar point function, then curl (f) is equivalent to (1) 2. (grad…

A:

Q: Q3/ Express in Polar form for the following 2 - 1) z = (²+)*

A: First we reduce the term given inside square. Then we try to write it in Euler's form, i.e.,…

Q: The population of Bradford is increasing at a rate of 5.1% per year. The city council predicts to…

A: Since you have posted multiple questions according to guidelines I will answer first question for…

Q: Q3/ Express in Polar form for the following 2) z = (3-1²) ²

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Q: a. A", n21 b. kA, k any scalar. c. p(A), p(x) any polynomial (Theorem 3.3.1) b. Show that 2³-22+3 is…

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Q: Approximate the integral with an error less than 0.0001 using power 0.5 series 5x³ tan-¹(2x) dx. You…

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Q: Use (1) in Section 6.4. x²y" + xy + (x² - v²y = 0 (1) Find the general solution of the given…

A: The differential equation is as follows:..To Find:Using the equation  determine the general solution…

Q: Use Stokes's Theorem to evaluate F. dr. Use a computer algebra system to verify your results. In…

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Q: Evaluate [(x (x + y)ds, C: x = 3t, y = -3t+2, for -2 ≤ t ≤0. Check Answer

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Q: For the system of differential equations x' (t) = − ²x + y + 2xy y(t) = -x +2y-xy the critical point…

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Q: Solve the following polynomial equation by grouping and factoring. Enter the exact answers. 25y3 -…

A: We solve the given polynomial equation by factor method.

Q: A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1),…

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Q: Approximate the integral with an error less than 0.0001 using power series x³ tan-¹(2x) dx. You have…

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Q: Write a stochastic matrix corresponding to the transition diagram. The stochastic matrix is (Type an…

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Q: The following initial value problem is shown below: mx"+cx'+kx=F(t), x(0)=0, x'(0)=0 It represents…

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Q: Theorem 5.3 Any linear operator T: V→ V leaves invariant a maximal flag.

A: A linear operator T is a map from a vector space V to itself such that it respects both vector…

Q: The Spacecraft Password Entering the room, you see the spacecraft. Finally, you will be able to…

A: Derivative of a function is 7cos(x)7cos(x)

Q: A Verizon IPhone 5SE sold for $120 after a 40% discount was applied. Find the original price of the…

A: A Verizon IPhone sold for after a  discount.The aim is to find the original amount of the IPhone.

Q: 16. Which of the following lies between 0.83 and 0.834 a. 0.834343... b. 0.8345 C. 0.8333 d. Both a…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify an Since lim…

A: We have to evaluate the limit .

Q: Give the general solution to the 3rd-order ODE y" - y" ex 2-1

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Q: Use (20) in Section 6.4. +1-20 y² + (6²c²x²c-24 0²-p²c²y = 0, )y pzo (20) X Find the general…

A: GivenThe expression .To Find:The general solution of  on .

Q: Calculate how many miles there are in 90 km (Given 1 Km = 0.6214 miles) 145 miles 56 miles 52 miles…

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Q: Evaluate I = √ (sin(x) + 4y) dx + (8x + 2y) dy for the nonclosed path ABCD in the figure. D = (0,6)…

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Q: kh= •a+h [ath 2xƒ(1) √ √ 1 + (ƒ' (1))² dt 2лf(t).

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Q: Question 2: Calculate the Laplace transform of the following functions: (2.1) tsin 2t. (2.2)…

A: (.)  Given ,(2.1)   (2.2)   (2.3)   (.) Some Laplace transformations:

Q: Solve the following IVP with the Laplace transform. y"-6y + 13y = 16te³t y(0) = 4 y'(0) = 8

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Q: Find a basis of the subspace of R4 defined by the equation 6x₁ + 9x2 + 6x3 + 9x4 = 0.

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Q: Calculate f (3xy + 4e²) d.S, where S is the triangle with vertices (0, 0, 3), (1, 0, 2), and (0, 4,…

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Q: Using the Newton's method, find the general formula to compute A where A is any real number. Show…

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Q: For the parametric curve given by x = t + sin 2t, y = cos 2t, dy d²y (i) calculate the derivatives…

A: Given parametric equations: Objective: To calculate the derivative of and .To find the equation of…

Q: 10 3 1 Give a basis for the nullspace of 0 0 -3 2 01 10

A: We have to find the basis of  null space of the matrix

Q: Write an equation for the line graphed below 5 4 3- 2 14 -6 -5 -4 -3 -2 -1 -1 -2- -3- -4 -5- 6 y 12…

A: If there is a straight line in a given graph, then the equation of the graph is of the form y =…

Q: how the element 2+√3 has a multiplicative inverse in Q(√3). Show that Q(√3) is a subfield of C

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Q: 2. The graphs of sin² 0 1+cos 0 and your answer to question 1 indicate about the equation " in red,…

A: Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Find the gradient vector field Vf of f. f(x, y) = x²-8y Vf(x, y) =

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Q: Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. √7t +…

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Q: Simplify. State ALL restrictions. x² + 2x - 15 x²2x-8 2x²15x8 x² - 25 + -x² + 13x - 40 x²-x-6 1

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Q: Evaluate (a+y-32) dV where E = {(x, y, z) | -7 ≤ y ≤ 0,0 ≤ x ≤ y,0 < z < x + y²} . Round your answer…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify an Since lim…

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Q: A uniform limit of continuous functions is continuous.

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Q: Answer the given question with a proper explanation and step-by-step solution. Please provide the…

A: From the given data,Cost function:Now differentiate w.r.t xFor critical value of "x" Solve and get,