← Find a general solution to the differential equation using the method of variation of parameters. y" + 2y'+y=2e-t The general solution is y(t) = ***

Q: Solve the initial value problem. y''+4y'+4y=6 , y'(0)=0 , y(0)=1

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Q: O Write an equation for an expone function with no horizontal or vertical shift that goes through…

A: The exponential function is of the form y=abx

Q: The following table shows the results of a survey of 500 authors by a publishing company.…

A: From the given table

Q: If B is added to C = 7.11 +4.7, the result is a vector in the positive direction of the y axis, with…

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Q: Use finite approximation to estimate the area under the graph of f(x) = 6x² and above the graph of…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Q2 Given marginal cost is C'(x) = 2x + 5. Find the cost of the 3rd unit.

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Q: Find the area of the region that lies inside both r = sin and r = cos 0.

A: We need to find the area of the region that lies inside both r=sin(theta) and r=cos(theta).

Q: - Find the length of the polar curve r = €²0,0 ≤0 ≤ 2π.

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Q: A rectangular box with an open top is to be made from a 10-inch by 16-inch piece of cardboard by…

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Q: 1) Find the fourth degree Taylor Polynomial for the f(x): f(x)=e* In(1-x) f(x) = (1+x)1/4 f(x) =…

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Q: A can in the shape of a right circular cylinder is required to have a volume of 500 cubic…

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Q: A producer and distributor of gift cards produces a boxes of cards per day at an average cost C (x)…

A: given  C¯(x)=16x+100004x+200(a)  for produce 200 boxes put x=200

Q: 16. Find the area under y Step one: Integral. Step two: Evaluate Bonus. = xcsc (tan (x²))sec² x²…

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Q: Change the order of integration for the double integral You do not need to compute the integral. 2…

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Q: at width rate The length rate of of the rectangle of 6 the length 20 inches anca 13 rectangle is…

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Q: When a drug is intravenously administered to a patient on a continuous basis, the amount A (in…

A: The equation for finding the amount of drug in the patient's bloodstream after t minutes is,…

Q: x²y + y = 1 find by implicit differention b. find the tangent line at (-1,1)

A: We need to calculate the derivative by implicit differentiation and then calculate the tangent line.…

Q: Using Cramer's rule to solve the following system of equations, what are ? 4x + 3y + 12z = -4…

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Q: Give an equation for the line which passes through the points (−1, 2) and (3, 4).

A: The points are given by x1, y1 = -1, 2x2, y2 = 3, 4 To determine: The equation of line passing…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 300…

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Q: Once an airplane has reached its cruising altitude, its computer shows the destination to be 2,400…

A: The linear function we used to model the distance of the plane from its destination is an example of…

Q: Let f(x) = x for f B 2 3x² + 4 interval(s) of increase: interval(s) of decrease intervalls) of…

A: For a function f( x ) critical points can be find as f'( x ) = 0  For increasing function f'( x )…

Q: 3 1 13. Jisc(2)csc (2x)cot (2x)dx cresc 8 Type. U = U' =

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Q: Rotate area between y =6-X and y= x^2-6x about X-axis. Compute the volume (Washer Method)

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Q: use the given information to determine the equation of the parabola. Vertex: (0,0), focus: (0, - 2)

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Q: Find a function f(x) such that f'(x) = 4x² + 5 and f(0) f(x) = = 3

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Q: The area of the region that lies to the right of the y-axis and to the left of the parabola x = 8y -…

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Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 1 and roots of multiplicity 1…

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Q: 1. For all n > 2,¹ 1, e, 4. For all n > e, arctan(n) n³ In(n) n In(n) >, and the series n >, and…

A: we are not allow to solve more than 3 subpart in each question.  Thank you

Q: Consider the function h(t) = 6 ² + restricted to the interval absoluto max explain why. or min on…

A: The given function is: ht=6t3-2t This is restricted to the interval 0,8.

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: SITUATION 1: A plane region is bounded by the following curves: y = x² and y = -x + 2. a. Graph the…

A: since you have posted multipart question i can do first three question as per our company…

Q: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 5 and a root of multiplicity 1…

A: We have to find the formula for P(x). We know that a polynomial of degree n can be written in…

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: Find an angle with 0° < 0 < 360° that has the same: Sine function value as 210° 0 = Cosine function…

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Q: Let us model the number of automobile sales in a developing country as 151,000 N (t) = where N is…

A: (a) To find the number of cars sold in 2010, we substitute t= 2010 into the equation:…

Q: An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to…

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Q: Find the area between the curves. x = -5₁ x = 3, y = 2x² + 5, y = 0

A: The equation of curves are: x=-5, x=3, y=2x2+5 and y=0 To determine: The area between the curves.

Q: Use partial fractions to find the integral f 17a-149 2-17+70 dr. O 10x + 70 ln 7-z|+7+70 In 10-x|+C…

A: I=∫17x-149x2-17x+70dx

Q: 10. f(x) = In (csc (e-3x)) Туре.

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Q: My topic is about Higher Order Derivatives and Optimization for reference. A cardboard box…

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Q: x = 2y² find the vertex, focus, and directrix of the parabola.

A: x=2y2

Q: (a) Find symmetric equations for the line that passes through the point (2, -2, 7) and is parallel…

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: Evaluate the following integral in spherical coordinates. This integral calculates the volume of the…

A: The integral is given by ∫02π∫0π4∫04 secφρ2sinφ dρ dφ dθ To determine: The value of the integral.

Q: K Graph the system of inequalities from the given problem, and list the corner points of the…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) fo Find the general…

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Q: 39. Evaluate sin4x if sinx 2. A 142 B. 33 C. 73 (0.-156√3

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Q: (c) semicircles 125 -π 6 X

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: A chemist, running tests on an unknown sample from an illegal waste dump, isolates 61 grams of what…

A: Given: Initial amount=61g Final amount=12g  Time=66days