Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.) I(+4) + 6s

Q: Find the volume of the solid generated by revolving the region bounded by the given curve and lines…

A: Here, the given curves are y=2x, y=6, x=0 The region bounded by the curve is:

Q: 2. sin x siny dy + cos x cos y dx = x² sin x cos y dx

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Q: Evaluate: O 3 0 S''(√ri+ - i + ln(2) j+ 4 1P ( 1 , 2 + (1+1) 1] (-1) ² e 3 0 2 + + m (2) 1 + (1 - 1)…

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Q: Use the Laplace transform to solve the given initial-value problem. y"" + 2y" y' - 2y = sin(4t),…

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Q: ll is thrown vertically upward from the top of a building (when t-Oseconds). It has a height functi…

A: Topic:- application of derivatives

Q: Can you present the solution in a different format. I do not understand what the solution is…

A: Let's solve given diffrential integration.

Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: Use graphs to evaluate 2π S 2r S 0 sin x dx = cos x dx = 2t S 0 2π sin x dx and cos x dx. 0

A: We will find the required.

Q: If an> 0 and Σ an converges, then Σ(-1)"an converges.

A: We have to check wheather it is true or not

Q: Determine if 4x² + y = -5 is an ellipse. O Not an Ellipse O Ellipse, we can write the equation of…

A: Here given that 4x2 +y =-5  now  4x2 = -(y+5) x2 = -(y+5)/4

Q: 5. Matiu is a talented furniture maker and has decided to build a bike frame out of wood. He likes…

A: Given: the two triangle connected to each other as shown in the question.

Q: Set up a double integral that gives the area of the surface of the graph region R. ƒ (x, y) = xª –…

A: Topic:- application of derivatives and integration

Q: Determine the vector field of F. F(x, y) = 4i - 2j O O Y X X

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Q: Given the function below f(x) = -75x³ + 200 Find the equation of the tangent line to the graph of…

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Q: 5. L Evaluate [F DETAILS F. dr. LARCALC11 15.2.029. F(x, y) = xi + yj C: r(t) = (5t + 8)i + tj, 0…

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Q: Find the value of b for which the differential equation (ye5ay + x) dx + (bxe5y) dy = 0 is exact,…

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Q: Find the solution of the given initial value problem. ty' + 4y = t²t+7, y(1) = 2, t> 0

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Q: Find div F and curl F if F(x, y, z) = 9y¹zºi – 14x³z7j — 5xy³k. div F= curl F=

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Q: function f is given, and the indicated transformations are applied to its graph (in the given…

A: Given the query is to find the equation of the the function after transformation.

Q: Find curl(4z i+ 5x j + 7y k). curl(4z i + 5x j + 7y k) = ( i )i + ( i )j + ( i )k

A: Topic- Curl of a vector

Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

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Q: Use a surface integral to calculate the area of the disk S given by z = 5 − y that lies inside the…

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Q: curl(9z i+ 10x j + 4y k). (9z i+ 10x j+ 4y k) = ( i Textbook and Modia )i + (i )j + (i

A: To find out the curl of the given vector.

Q: Consider the following initial-value problem. y' - y = 2 cos(7t), y(0) = 0 Find L{f(t)} for f(t) = 2…

A: Given the initial-value problem is y' - y = 2 cos7t,  y0 = 0

Q: Use linear approximation, i.e. the tangent line, to approximate 27.1 as follows: Let f(x)=x. The…

A: Our Aim is to find the approximation for 27.13 using linear approximationgiven that f(x)=x3.

Q: Solve: x"-x+ 5 y'=t y" - 4 y-2x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: Find the curvature and the radius of curvature at the stated point ㅠ r(t) = 11 cos(t)i + 10 sin(t)j…

A: The expression for the curvature is: κ=r't×r''tr't3 And The expression for the radius of the…

Q: Use the Integral Test to determine whether the sum converges. ∞     n = 1 4n 1 + n4 Evaluate the…

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Q: Find the average value of on the interval [1,12]. favg Now, find e such that ln(c) = favg. = 2.61 C…

A: Given the query is to find the average value of the function.

Q: Use the formula k(t) k(t) = TEREST {|r' (t) × r"(t)|| ¡|r' (t)||³ r(t) = esti + e-tj to find (t).

A: The given curve rt=e5ti+e-tj

Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Find the volume of the region bounded above by the sphere r = 2a cos0, and below by the cone = a…

A: Given: the sphere r=2a cos theta , cone ϕ=α0<α<π2

Q: Shared with me > 2011- Files Find the Wronskian of two the functions y₁ = cos41_g(t) = e' cos(t).…

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Q: Find the volume of the solid generated by revolving the region enclosed by x = √5y², x = 0, y = -2,…

A: To find the volume of the solid generated by revolving the region enclosed by x=5 y2, x=0, y=-2, and…

Q: Which of the following is the graph of (x+3)² + (y+4)² =257 -10-74444 -10-0744 T a . - → 7 "

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Q: = 2 3 +2 dx² dx -8y = 0

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. 9 3 cos 0+2…

A: Let's convert to Cartesian equation.

Q: dN dt The rate of change of N is proportional to N. (Use k for the propor kN N(t) = Cekt Evaluate…

A: We are asked to find the value of N when t = 3

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-tj² L{f(t)}…

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Q: Consider the function f(x) = 6 - 7x² on the interval [ — 4, 3]. Find the average or mean slope of…

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Q: Find the area of the region inside the inner loop of the limaçon r= 1 + 2 cos 0.

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Q: Give the General Solution of the following Differential Equation 1. (ex-y)(1-e²y)1/2 dx = dy

A: The given differential equation is: ex-y1-e2y12dx=dy To find the general solution to the given…

Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

Q: For an arithmetic sequence, a17 a1 = the sum of the first 65 terms= > Next Question - 47. If the…

A: It is given that, a17=47 and common difference(d)=5 a1=? Sum of the first 65 terms=?

Q: Calculate the indicated Riemann sum Sn​, for the function ​f(x)=x2−9x−4. Partition [1,7] into six…

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Q: Find the general solution to the linear differential equation: y" - y' - 2y = 0 O y = C₁e²x + С₂е¯x…

A: Given that a linear differential equation y''-y'-2y=0. We need to find the solution of this linear…

Q: Problem #1: Which of the following functions is continuous at (0,0)? to yo (i) f(x,y)= = (ii) g(x,…

A: The objective of the question is checking the continuity of the given functions.

Q: V -6 -5 -4 -3 -2 7 Submit Question 8+ gut 7 916104324 -6- -1 -2 -3- 4 --$ 166 46- U 1 2 4 5 Find an…

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Q: Let y 3x². Find the change in y, Ay when x = = 4 and Ax = : 0.2 Comm Find the differential dy when x…

A: We have to solve given Questions.

Q: 6. Find (0) for a solution (x) to the initial value problem (secx)dy = 2√y+Idx; (n) = 3 2 3

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