Use cylindrical coordinates to evaluate SG √x²++y² dV, where G is the solid above z = 9 - x² - y² and above z = 1.

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Q: 15-20 Use the method of cylindrical shells to find the volume of the solid obtained by rotating the…

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Q: such f(2x)-f(x) = = b x 1) than f'(x) is alsa a-b 6. f(x) is differentiable On [0,00), lim f'(x) =…

A: Given that, f(x) is differentiable on [0,∞) and limx→∞f'x=b We have the expression, limx→∞f2x-fxx=b…

Q: 4 [5], 9 (a) Write b as a linear combination of a₁ and a2. Let al b a2 = -8 7 and T(a₂) and b = 2…

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Q: To find a particular solution for the differential equation 3y"-24 y' +36 y=e10x with the variation…

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Q: Solve the following initial and boundary value problem by using the appropriate Fourier Transform:…

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Q: √₁² √√¹-x² √1-x²-y² (1 + x² + y²) dzdydx 0

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Q: Question 1 Given the differential equation 3y" - 21y' + 36y=3e-4² a) Classify the given differential…

A: THE GIVEN DIFFERENTIAL EQUATION IS, 3y''-21y'+36y=3e-4x REWRITE IT AS,  y''-7y'+12y=e-4x   (a)  THE…

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Q: Use Lagrange multipliers to solve for the dimensions of a closed right circular cylindrical can with…

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Q: You need to provide a clear and detailed solution for the following Questions: Question Let W be the…

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Q: дz дz = z² əx ду 13. Solve completely the Lagrange PDE: x² +y² √ ² 02²2 =2 non-homogenous PDE (D³ –…

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Q: dw If w= In(4) cos(2yz - 3), x = log(t), y = 4e¹² and 2 = sin (³-1). Find dt -

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Q: Let f: R → R be the function f(x) = x². Fill in the blanks in the following proof. Claim: f is…

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Q: A farmer finds that if she plants 70 trees per acre, each tree will yield 20 bushels of fruit. She…

A: A farmer finds that if she plants 70 trees per acre, each tree will yield 30 bushels of fruit. She…

Q: Q2. Evaluate Sdx using Simpson's rule with N = 4 and hence find the 1+x³ approximate value of In 2

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A: Here we find values of scalar to check whether given matrix is in span of A1, A2, A3.

Q: 17. f(t) = (t 3)u2(t)-(t-2)uz(t) Solution: We can write Differential Equations f(t) = (t2)u₂(t)-…

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Q: Amy, Jim, John, and Kelly are standing on the east bank of a river and wish to cross to the west…

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Q: Find the gradient vector field Vf of f. - y)² Vf(x, y) = f(x, y) = (x 3 Sketch the gradient vector…

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Q: Given A = 03-2 00 1 compute et.

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Q: Suppose the domain of discourse D is all dinosaurs and w F(x): x had feathers; • S(x): x had scales;…

A: This is a question of Predicate logic. One has to translate the natural language to its logical…

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Q: Write a definition for the nth term of Sequence B

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Q: Subject: Math Topic: Linear Programming Instruction:   Use a Table for the Data given, Construct…

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Q: Solve the following DE: [3sin (y) — 5x ]dx + 2x²cot(y) dy=0 Ox²[sin (y) - 2x]³=C'sin³(y) Oy³[sin(y)…

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Q: 9. A biologist has been studying the effects of environmental stressors on a population of frogs.…

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Q: 4. Evaluate the double integral given by [" -dydz

A: Evaluation of double integral

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Q: Use Theorem 7.1.1 to find (f(t)). (Write your answer as a function of s.) f(t) = 4t² - 2 sin(3t)…

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Q: You need to provide a clear and detailed solution for the following Questions: Question Let W be the…

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Q: Solve the area bounded by the parabola y2 = 4x and the line y = 2x - 4 in two ways. Answer: 2 sq.…

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Q: 2. How many gallons of liquid will a container hold if the diameter of the bottom base is 18 inches…

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Q: Evaluate the integral SF ds, where F(x, y, z) = (x, y, 1) and 5 is the upper hemisphere of the unit…

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Q: 15 Given: KR is a median to JO. RP = KM, RM = KM Prove: JMOP is a □. M

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Q: 3. Show that if a ≥ 2 and k € Z+, then k divides y(ak – 1). (Hint: Show that ad # 1 (mod ak – 1) for…

A: Let, if possible, there exists some d such that        1 ≤ d &lt; k and          ad ≡ 1 (mod ak - 1)…

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Q: A 800-lb object is released from rest 500 ft above the ground and allowed to fall under the…

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Q: f(x) = x4 - 8x³ + 8 Answer the following by showing supporting work for each answer. Do not simply…

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Q: 7. Find a fundamental matrix for the system *' (t) = A - *(t) for Го a. A = 0 L8 1 0 -14 01 1 7

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Q: SET-UP the double integral which gives the vol- ume of the solid in the first octant enclosed by the…

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Q: Find the equation y = mx + c

A: To find the line y=mx+c by using least square method.