Use Laplace transforms to solve the following initial value problem. x' + 2y' + x =0, x' - y' + y = 0, x(0) = 0, y(0) = 361 The particular solution is x(t) = and y(t)=

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A: Acceleration of the object:a(t) = -9.8 m/sec2The maximum of the height function is 800 meters.

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A: An object is thrown upward on Saturn with an initial velocity of 17 m/s. Its height in meters after…

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A: ;

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A: The given integral

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Q: Solve the given initial value problem. O x²y² + xy³ = -18 Ox³y² +xy³ = 18 O x³y²+y³ = 45 Ox³y² - xy³…

A: The given differential equation is; dy/dx = - (3x2y+y2)/(2x3+3xy), y(2)=-3.

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A: Now to find the undefined points, take the denominator equal to zero.

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Q: Identify any horizontal or vertical asymptotes in the graph. State the domain of f. ... OA. The…

A: We are asked to find the asympotote of the given  graph

Q: Find and simplify the derivative of the following function. h(x) = (3x5 + 3x) (4x³ + 2x² + 2) h'(x)=…

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Q: 3. We study the function f defined below: { f(x) = (1) (2) if x is rational if x is irrational Prove…

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Q: Let C be the curve of intersection of the cylinder 25x² + y² = 25 and the plane x + y + z = 4. (a)…

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Q: Let f(x) = g(x) h(x) and consider the following table of values: The value of f' (-9) is Number…

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Q: Determine the following limits: (a) 42³-19z²+12z lim x 0 7x³-23x2-20x Number (b) 423-192²+12x lim x…

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A: Let the horizontal distance of foot of ladder from the wall be x and vertical distance from top of…

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Q: If f(x) = Σ22" and g(x)= n=0 n=0 n=0 na", find the power series of f(x)g(x).

A: Givne series

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Q: Evaluate the derivative of the function at the given point. Use a graphing utility to verify your…

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Q: 7. f(x) = ex (1) lim f(x)= (2) lim f(x)= of $ 8 2- (1) lin (2) (a (3) (

A: As per our guidelines we are allowed to answer only one question. Kindly repost the other question…

Q: Differentiate the function.

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A: For the right-angle triangle use the Pythagorean theorem.

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y=x√√4-x² Step 1 Recall that if y…

A: The differential formula for a product rule is given by,Where

Q: 12. Graph the following function by starting with a function from the library of functions and then…

A: By using the transformation, we will draw the graph.

Q: (1) Evaluate solution= Hint: Express cos a in terms of sin a. Then use the substitution usinx. Back…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Body temperature is usually maintained between 36.4°C and 37.4°C, inclusive. Determine the…

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Q: The function P(x) = − 2.25x² + 1775x – 9500 gives the profit when a units of a certain product are…

A: a=According to Bartleby's guide line we only do first three parts of multiple part questions.Given,

Q: For the piecewise function, find the values h(-9), h(3), h(4), and h(5). -5x-11, for x < -7 h(x) =…

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Q: The function y(t) = 4e³t - 2e5t is a solution (but not the general solution) to y" + py' + qy = 0.…

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Q: 5 Find the plane that contains the point (2,0, 3) and the line x = -1+t, y=t, z = -4+ 2t. (Hint:…

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Q: Solve the following system of equations by using the inverse of the coefficient matrix if it exists…

A: The system Ax=b is,The matrix A is

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Q: How can I find the approximate volume of the solid generated by revolving the region bounded by the…

A: We have given,   y = sqrt(1 + sqrt(x)), x = 0, x = 2, x-axis

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Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 12. y' = x - 2y cot…

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Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: In this question, we will find the value of 'c'.