y'+y=e-6 cos St, y(0) = 0

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Q: 1. If L{f(t)} = F(s), then A) L{eat f(t)} = F(s + a) B) L{eat f(t)} = F(s-a) 2. What is the Laplace…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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A: We have to find the laplace transform of given function.

Q: Find the area under the curve y = lines x = 1 and x = 5. 3x² + 4x + 1 bounded by the x-axis and the

A: Area under the curve y=3x2+4x+1 bounded by x-axis and x=1 to x=5.

Q: 45-50. Approximating real numbers Use an appropriate Taylor se- ries to find the first four nonzero…

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Q: Use the model A = Pet or A = P1+ for years. If a couple has $50,000 in a retirement account, how…

A: Please see the below picture for detailed solution.

Q: *A=P(1+²)". Use the model A = Pe' or A= P1+ for 7 years. $8000 is invested at 4.5% interest…

A: In this question we have to find how much it will take to double the amount of invested.

Q: I) Evaluate the following expressions. 17 TT 9 1) sin-1 COS

A: Given, Sin^-¹(cos17π/9) Sin^-¹(sin( π/2 -17/9) π/2-17π/9 18π-34π/18 -16π/18 -8π/9

Q: ). For the sequence, determine if the divergence test applies and either state that lim n→∞ an does…

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Q: (a) Write a function of the form P (1)=Poe to model each population P(1) (in millions) f years after…

A: Consider the table

Q: Consider the function f(x) = 3x³-36x on the interval [-3, 1] Find the absolute extrema for the…

A: We will find the solution

Q: Find the average value of the function f(x) = 2x sin(x²) on the interval [0, √π]. 02 4 — 2 NLE π √T

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Q: Two cars are moving towards an intersection. One car is 160 meters north of the intersection and…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: find dy/dx by implicit differentiation sqrt(xy)=10x+4y^2

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Q: Suppose we have two insects that enjoy feasting on one another. Each of Insect 1 consumes 1.2 of…

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Q: Use the rules of differentiation to find the derivative of the function. f(t) = 7t² - 9t-3 f'(t) =…

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Q: 88-91. Working with area functions Consider the function f and its graph. a. Estimate the zeros of…

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Q: Solve the equation. Write the solution set with the exact values given in terms of common or natural…

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Q: From 1964 to 2014, a certain money stock measure was growing at the rate of approximately 91e0.51x…

A: NOTE: Refresh your page if you can't see any equations. . the rate of change of stock is given by…

Q: n (² f(x) dx Jo Given f(x) dx = 11 and "f'rx (a) f(x) dx. (b) Irox f(x) dx. (c) for f(x) dx. (d) f³…

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Q: Verify the identity. (Simplify at each step.) Let 8 = sin X-2 tan(sin−¹(*²)) = √9+ (x - 2)² X-2 -¹…

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Q: b\ State and prove the theorem of these questions below, for each given functions find the value of…

A: answer is in next step.   as per guideline i can answer only one question .

Q: $9 – 15 = ({¹x) ƒ A ( [9 – 15− − (^ ^x)ƒ ▲O --- ▼f(x,y) -:i-- = (^¨*x)ƒ^ f(x,y) = { 1 O Find Vf(x,…

A:

Q: If sin z 8 , x in quadrant I, then find (without finding x) 9 sin(2x) = cos(2x) = tan (2x) =

A: NOTE: Refresh your page if you can't see any equations. . . use the formula

Q: Find a linear equation whose graph is the straight line with the given properties. --=-5) 6 y(x) =…

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: Find the nth Taylor polynomial for the function, centered at c. P4(x) = f(x) = 1 +2, n = 4, c = 5

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Q: Question 11 For f(x, y) = sin(9xy). evaluate f at the point (2, ○ fx (2. =) = 0 (2²)-18 © ƒ, (2. )…

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Q: If lim (x,y)→>(a,b) True False f(x, y) L and f is defined at (a, b), then f(a, b) = L.

A: The give statement, If limx,y→a,bfx,y=L and f is defined at a,b, then fa,b=L

Q: Find the area bounded by the pair of curves. y = x² + 4x and y = 4x + 1 square units

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Q: A company's marginal cost function is MC(x) (given below), where x is the number of units. Find the…

A:

Q: Find the vertical asymptote(s), if any, of the function below. If there are none, select "none" for…

A: We have to find the vertical asymptote.

Q: The polar coordinates of a point are (12, coordinates of the point. ○(-6√3,6) (6,-6√2) O O (6,-6)…

A: We have to solve above question

Q: Find the derivative of the function by the limit process. g(t) = t³ + 6t g'(t) =

A: We can find the answer as below.

Q: estion 2 Find the directional derivative of the function g(x, y, z) = xye at P(3, 5,0) in the…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Evaluate the limit or explain why it does not exist t t- 2-0 √4+t-√4-t x³+1 lim X-1 X+1 Ix-21 lim…

A: Given that some limit problem and we solve this given problem by using general property of limit.…

Q: Use sigma notation to write the sum. 1 7 (2) + 7 (3) j = 1 1 7(1) + 1 7(10)

A: The given sum 171+172+173+.....+1710

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A:

Q: MTH 32 (13) Define the Inverse Tangent function (or the art and explain the --- MTH 32 (8) For b> 1,…

A: 8. As per Bartleby guidelines for more than one question asked only one is to be answered please…

Q: Find the exact length of the curve. y = 5 + 2x3/2, 0≤x≤1 2.2683 X

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Q: Find the standard form of the equation of the ellipse with the given characteristics. y 10 2 N 4…

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Q: Evaluate the following indefinite integral. $10 dx f10 dx=

A: We can solve this as follows:

Q: Find the volume of the solid generated by revolving the shaded region about the x-axis. 0- 0 3x + 4y…

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Q: Use implicit differentiation to find y² + 8x³ = 3y - 4x² dy dr

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Q: Highway engineers design a parabolic curve for an entrance ramp from a straight street to an…

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Q: The region bounded by f(x) = - 2x² + 8x + 24, x = = 0, and y = the volume of the solid of…

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Q: If 2x² + 2x + xy = 5 and y(5) 11, find y' (5) by implicit differentiation.

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: A spherical snowball is melting at a rate of 9.2- min snowball's volume is 4500 cm³? The radius is…

A: Note that, the volume of the sphere is given by: V=43πr3 So,  dVdt=43π(3r2)drdt⇒dVdt=4πr2drdt...(1)

Q: theres three steps.    A manufacturer of upholstery can sell 33 yards of fabric at a price of $1.63…

A: the demand function D(x)= m(x-x1) + p1 where m= (decrease in price)/(increase in production) p1=…