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Q: Find the inverse Laplace transform following: 0.2s+1.8 1. s+3.24

A: The problem looks difficult with decimal point but it isn't. Note that 3.24 = (1.8)^2 and so the…

Q: of 1 Volume: V= s Surface Area: S = 6s? Surface Area Volume Ratio (Now/Original) Scale Surface Ratio…

A: Mensuration deals with the measurement of areas and volumes of plane and solid figures. Solids are…

Q: Find the Volumes for the fa Ilowing solids whose ZCX,y) and bases are the regions theights are…

A: Volume bounded by the xy-plane

Q: 10 -7 Let u = and v = Compute u • v, v · v, ||u|| and find the dis- 13 16 tance between u and v.

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Q: Use polar coordinates to evaluate the integral + dA R where R is the region that lies in the second…

A: We want to find given area.

Q: Evaluate the upper and lower sums for f(x) = 2 + sin(x), OSXSA, With n = 2, 4, and 8. Illustrate…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: What is the correct answer in questions 1 and 2? 1. Calculate the principal sum which, if deposited…

A: Let us considre P be the principal amount, r be the rate of interest and t be the time period . Let…

Q: Consider the initial value problem (x + 1)y" – y" – (x + 1)y' + y = 0 y(0) = 2, y(0)' = 1, y(0)" = 1…

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Q: Find the characteristic polynomial of the matrix [7 a- 7 -3 p(x) =

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Q: Calculate the line integral f (VS) ·d7 for f(r, y) = -cos(2r-y)+ yr + y? and the curve C given…

A: Solution

Q: Let D be a noetherian integral domain. Show that D is a unique factor ization domain if and only if…

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Q: Find the total arclength of the following 3-leaf rose.

A: To find the arc length of the 3-leaf rose depicted below:

Q: Question 1 . between x2 + y? lies within the second and the third quadrant. Let D be the region…

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Q: What proof techniques are used to show that the cardinality of the power set of a finite set S is 27…

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Q: Corollary 11.3.3. Suppose Do anc" diverges for some real number c. Then Eo anx" diverges for all æ…

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Q: Suppose there are n lines in the plane, no two are parallel and no three are intersecting at one…

A: suppose there are n lines in the plane ,  no two are parallel  implies, each line intersect every…

Q: Which of the following functions represent power functions? Which power functions represent direct…

A: a. It is not a power function.

Q: Example :- Solve the following differential equation where d²y + y = 0 dx2 Subject to boundary…

A: As per the question we are given a second order linear homogeneous differential equation with…

Q: 27 1. Let f(x) = (1 – 2)?* (a) Express f(z) as a power series. (b) Using the result in la, find the…

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Q: Evaluate (1 + i)(1- ».

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Q: What proof techniques may be used to prove a result for the number of objects of S that have none of…

A: To determine: The proof techniques that may be used to prove a result for the number of objects of S…

Q: A cylindrical tank of radius R 1.5 m and height H = 3 m initially filled with water. At the bottom…

A: Solution

Q: z = 1- e"

A: This is a problem of 3D tracing and calculus.

Q: H3 R + G2 G3 G4 G1

A: Block Diagram Reduction Rules : 1)Rule 1 − Check for the blocks connected in series and simplify.…

Q: Name and sketch the graph of y² = z in R³.

A: To Sketch: y2=z  in ℝ3.

Q: Compute the Laplace transform: (t) + u4(t)t*e

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Q: Q: A loxodrome is a curve C C R^2 that intersects each meridian in the same angle. Let A C R^2 be a…

A: Given below clear explanation

Q: Calculate the Laplace inverse of .2 4s +8 11. F(s) = (s² – 4)(s² – 6s+13)2

A: Using partial fraction and convolution of laplace transform

Q: Let r > 0. Consider the cone f(x, y) = r vx² + y². Show that the steepest ascent is the same at any…

A: Solution

Q: Which of the following is equivalent to -p → (q → r} O q→ (q ^ r) O (p V q) → r O q→ (p V r) O (p^q)…

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Q: Convert the first three terms of the Tay lor series expansions For coshx) in to chebyshev…

A: Follow the steps.

Q: (t - 5)'y"-2(t-5)y' + 2y = 0, t>5, V = (1- 5)

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Q: Identify and sketch the graph of the following equations in R³. z = 1 – In y 22 = 1. Show the traces…

A: Graphing z=1-ln(y):

Q: What is the correct answer to questions 1, 2 and 3? 1. What will be the value three years from now…

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Q: ) Consider the Cardioid r = 2 - 2 sin 0. (a) Find its total arc length. (b) Determine the area of…

A: Solution

Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx + x²dy by the curve y y = x2.

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Q: Prove that the function f(x1,x2) = In (e*i+= + eV=i+1) is convex over R².

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Q: 6s – 5 Find the Inverse Laplace Transform of F (s) s2+7 5 f (t) = 6cos(/7t). -sin(/77) _cos(/7 ) 5 B…

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Q: 5. u is defined on {(x, y)|x² +ỷ < 1} and u +u =0 where u=2(x+y)% on {(x, y)|r² + ỷ = 1}. Find u as…

A: Solution

Q: Consider A = (0, 4, 2), B = (6, -1, 0) and C = (3, 0, 1). (i) Find the unit vector having the same…

A: We have to find the unit vector having the same direction as B-2A+12C Then, we can proceed further.

Q: The problem constraint arising from labor contracts has the form ax + by Oc, for some values a, b,…

A: A drive-through restaurant requires 7 employees, so if there are x number of drive-through…

Q: Answer item 2 only!

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Q: 3x2 + 7x + 28 dx x2 + x3 + 7x Using partial fraction, evaluate 7/27 2x+1 A In + 27 arctan V27 + C +…

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Q: uadrilateral are in the ratio 2 :

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Q: 9. Solve the following Neumann problem: Uzz + Uyy = 0, 0<x< 2, 0 < y < 1, Uy(r, 0) = u„(x, 1) = 0,…

A: Solution

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: The solution is given as

Q: 1. Evaluate the following integral: (6 + 3 cos x) dx a. Analytically b. single application of the…

A: "Since you have posted a question with multisubparts and asked first three subparts to be solved, we…

Q: Vaæ (L(a) F(æ)) 3a (L(a) AC(æ)) . Ba (F(a) A¬C(x)) Statement Reason ...... ........

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Q: 8. Use the formula eAt = L-1 {(sI – A)-!}, to compute the matrix exponential for the matrix A =

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Q: The graph of /(t) is given below: (Click on graph to enlarge) a. Represent f(t) using a combination…

A: Solution