Use the Divergence Theorem to evaluate where S is the sphere x² + y² + z² = 1 J[₂ (2x + 2y + z²) ds

Q: Express the answers in simplest form. If a die is rolled one time, find the probability of Part 1 of…

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Q: 13 [ 1.5 11.5 13 Suppose f(x)dx= 4 14.5 (8 f(x) - 7)dx = f(x)dx = 8, 11.5 ["³ f(x)dx = 7, 14.5 13…

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Q: Directions: Solve. 1. A store bought shirts for $5.75 each. If they want to make 65% profit on…

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Q: Resource Allocation Podunk Institute of Technology's Math Department offers two courses: Finite Math…

A: Given:   Podunk Institute of Technology's Math Department offers two courses: Finite Math and…

Q: 12.14 Show that the Fourier series for the function y(x) = |x| in the range - < x < T is T TIR y(x)…

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Q: -2 (a) Consider the functions f(x) = 100 – zª and F(x) = [*¸ ƒ(t) dt. i. Write a simplified form of…

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Q: , solve the following Volterra integral equations by using the Ado- mian decomposition method: 3.…

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

Q: For the curve y = (x-2)² between the points (2, 0) and (4, 1) i. find the Arc Length ii. and find…

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Q: Use the more convenient order to evaluate the integral over the plane region R.

A: To calculate the double integral, ∫∫R6x2dA. Here R is the region bounded by the curves y=0, y=x,…

Q: Suppose a subspace of R² is spanned by the following set of vectors: (4] [2] 18 1. Find a basis for…

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Q: Flying against the wind, a jet travels 3720 miles in 6 hours. Flying with the wind, the same jet…

A: Let x be the rate of the jet in the still air and y be the rate of the wind. Observe that the rate…

Q: Solve the given system of differential equations by systematic elimination. (D+1)x+ (D- 1)y = (x(t),…

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Q: Let V be the subspace of RS with basis B = {V1, V2, V3, V4}, where j = −e₁ + ej+1 for j = 1, ..., 4,…

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Q: Evaluate F. dr where F(x, y) = x²y² + 2xyj and C is the boundary of the square (clockwise) through…

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Q: Using a vertical element, determine the volume of the solid generated by the area bounded by y=1/x,…

A: The curves given is as follows: y=1x, x=1, and the coordinate axes. This curve is rotated about…

Q: You own an a townhome with an assessed value of $184,400. The tax rate is $2.20 per $100 of assessed…

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Q: Determine if the given function is a linear transformation, give the domain and range of T, and if T…

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Q: H„ (x ) = 2″¯ e¨¯ ¶¸ ¤¯¹¹t"+¹ p, ** ¸ **/²*¹ P. (²) di 2"- dt

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Q: 15. y(4) +5y" + 4y = g(t); y(0) = 1, y'(0) = 0, y"(0) = 0, y""(0) = 0

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Q: The function C(t) = Co(1 + r)' models the rise in the cost of a product that has a cost of Co today,…

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Q: 5. [ F · dŘ, where F(R(t)) ·Ï(t) = cos²3t, T is the unit tangent vector to C' : Ē(t), 0 ≤ t ≤ ³, at…

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Q: (d) y" + 2y = 2x+5e-2x (e) y" - 4y = x² - 3+ sin(2x)

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Q: Find the indefnite integral. e2x 36 + e4x dx

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Q: Sketch the graph of y = 3sinx on the interval ( -π , 4π )

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Q: Graph the following quadratic function using its properties. Based on the graph, determine the…

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Q: Determine whether the equation +t + (cos²t)y = t³ is linear or nonlinear. Explain d³y dy dt3 dt why…

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Q: Sketch the graphs of the following:

A: Introduction: The trigonometric ratios can also be seen as functions of the angle measurement as a…

Q: Select the true statements regarding a graph of f and its derivatives. □ If f'(c) · ƒ" (c) = 0, then…

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Q: Problem 8. Give an example of a function f of one variable and a value a such that f'(a) = f'(a) = 0…

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Q: 2. The table below shows the electricity rates charged by the city of Austin. (b) Austin Electricity…

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Q: Evaluate the function. If the value is not a rational number, round your answer to three decimal…

A: Answer a) cosh(0) = ?     cosh(0) = 1

Q: Consider the region bounded by the curve y = x + 4, the line y = 6 and the y-axis. Setup an integral…

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Q: List all families of sequences (give some examples). And Define convergence for sequences and give…

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Q: For what values of p does the series below converge? Select the correct answer below: O p > 2 O p =…

A: Solution :- Take p = 3 : - First option p &gt; 2 ∑n=2∞ lnn26n3Apply the constant multiplication…

Q: Find a power series for the function, centered at c. 4 3x + 2 f(x): = 8 f(x) = Σ n = 0 C = 1 5 Sign…

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Q: -19 -13] Let A = 26 20 Find a matrix P, a diagonal matrix D and P-1 such that A = PDP-¹. P: D || ||…

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Q: We suggest you use technology. Graph the region corresponding to the inequalities. 2.3x2.4y S 2.6…

A: Introduction: In Algebra, an inequality is a mathematical statement that uses the inequality symbol…

Q: 3. Classify the critical points of the function R³ → R f(x, y, z) = x³+xz² − 3x² + 4y² +3z².

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Q: Consider the initial value problem (formulas) b. Solve your equation for Y (s). Y(s) = L{y(t)} = 0…

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Q: (b)2(2y² + 5xy − 2y + 4)dx + x(2x + 2y − 1)dy = 0 Ans. x4(y² + 2xy = y + 2) = c

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Q: Consider the following data x -4,-3,-2,-1,0 P(X=x) 0.3,0.1,0.2,0.1,0.3 Find the variance. Round your…

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Q: (3) For each region shown below, decide whether to use polar coordinates or rectangular J₁² f dA as…

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Q: We say that a space (X,τ) is connected if there exist two open non-empty spaces A,B such that A∩B≠∅…

A: Let X,τ be a connected metric space. We have to show that the only subset of X are both open and…

Q: 16. Find (1) the net area and (ii) the area of the region above the x-axis bounded by y=121-x².…

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Q: - Laplace's Second Finite Integral for P, (x): P₁(x) = -=- √5 - ᏧᎾ 72+1 [***√(x² - 1) cos 0]*¹ Ꮎ NEN

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Q: 5. A tank full of water is in the shape of a box 3m deep, 4m long and 3m wide. What is the…

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Q: Let the random variable X have a discrete uniform distribution on the integers 1 ≤x≤5. Find the…

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Q: T-8 -28 -13 12 Let A = -3 P = من من -421 -18. Find an invertible matrix P and a diagonal matrix D…

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Q: You are given two sequences of non-negative integers below. Decide which sequences below represent…

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