Solving Differential Equation by Laplace Transform Solve the following initial value problems using Laplace transform and plase your solution using the indicated format: 1. (D³+2D² + D + 2)y=5+4sin(t): y(0) = 3, y (0) = 1, y" (0) = 2

Q: Determine whether or not the vector field is conservative F(x,y) = 18x²y²i + 12x³yj conservative O…

A: NOTE: Refresh your page if you can't see any equations. . compare this vector field with  so here…

Q: dx Assume that x = x(t) and y = y(t). Let y = x² +5 and dt dy Find when x = 1. dt (Simplify your…

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Q: At what point in the first quadrant does the line with equation   y = 0.5 x + 4   intersect the…

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Q: Consider the following planes. 3x + 6y-z = 126 x - 12y + 2z = 0 (a) Find the angle between the two…

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Q: The series 8 Select one: O True O False n=1 2 5" is a geometric series with r = }/1. -iin

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Q: 9. Find a formula for the general term an of the sequence: {1,0,1,0,1,0,1,0,...}

A: Given sequence is  { 1,0,-1,0,1,0,-1,0,....} Now we give formula of this sequence

Q: Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are…

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Q: please solve d-f now. thanks.

A: We have to find the composition of functions.

Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

A: topic- application of derivatives

Q: Find the average value over the given interval. 32) y = 5x2; [-1,2]

A: We can find the average value as below.

Q: (e) Determine whether the following series converges or diverges by using the comparison test: Σ 1=0

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Q: Give an example of a derivable function f (x) with f ′ (- 4) = - 1

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Q: Find the domain of the vector-value function r(t) = www Domain: {tt # MORA 4t4, t², 1 (t - 2)5

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Q: Current Attempt in Progress Evaluate the integral by applying the following theorems and the power…

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Q: (d) Determine whether the alternating series converges or diverges by using the alternating series…

A: Two tests are done.

Q: Let R be the region bounded by y = 2x, y = R and evaluate the double integral R and x = 0. Sketch…

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Q: n=1 5 4(--)"-2. 3

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Q: A farmer has 2,400 feet of fencing and wants to fence off a rectangular field that borders a…

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Q: 27. A function on [0,2] defined by f(x) = -x² |5x – 4 4x³ - 3x (3x + 4 if x ≤ 0 if 0 < x≤ 1 1<x<2 if…

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Q: Find the radius of convergence for n! n=1 -xn nn

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Q: Find an equation for the line perpendicular to 3x + 27y= 135 and goes through Write your answer in…

A: Topic:- coordinate geometry    Hint:-  if slope of line is m than Slope of perpendicular line  to it…

Q: 2. If y is the solution of the initial value problem = 3(y - 1)(y-2) with y(1) = 3, what is lim…

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Q: (9x - 8) dx || +C

A: Solution of given question is written in below steps.

Q: 1a) Convert the Cartesian equation (x^2 +y^2-1)^2 +4y^2-1 = 0 to polar coordinates. 1b) Use a…

A: By using the following substitution we can convert the Cartesian equation to polar form. x²+y²=r²…

Q: II. Solve each of the given LDE of order n.

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Q: Without using a calculator, for the following, determine the slope of the tangent line, then find…

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Q: Find y' and the slope of the tangent line to the graph of (3x - 5y)5 = 2y2-9 at the point (3,2).…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the given…

Q: Find the lim inf (xn) and lim sup (x₂) of Xn = COS nπ

A: I have calculated the limits

Q: 3. An amusement park charges $8 admission price (P) and averages 2000 tickets (T) sold per day. A…

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Q: Find the area under the graph of the function over the interval given. 1 √x [1,4] 25) y =

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Q: (2x - y)dx(x + 4y)dy = 0

A: As per the rules, we can answer only the first question and other can be reposted.

Q: Use the Integral Test to determine if the series shown below converges or diverges. Be sure to check…

A: Suppose that f(x) (here f(n)=an) is a continuous ,  positive and decreasing function on the interval…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. x³ (3x4 + 2)³…

A: We need to integrate ∫x33x4+23dxSubstitute 3x4+2=tDifferentiate w.r.t t12x3dx=dtNow∫112t3dt ---{1}

Q: Ιπ 10. State the exact value of tan- 6

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Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose…

A: The given integral is;  12/y3/4 - 3sqrt(y) +5/sqrt(y).

Q: The gradient vector of the function f(x, y, z) = ln(yz) - x² is: Select one: ○ (−2x,, 1) O None of…

A: To find the gradient vector of the functionf(x, y, z) = ln(yx)-x2

Q: divergent: Select one: O True False ts) The following series is 8 Σ6- n=1 3 n-2

A: Given: ∑n=1∞6-35n-2

Q: = 0, y = x, and x = 5. n, the region D expressed as type I is: = {(x, y)|0 ≤ y ≤ x,0 ≤ x ≤ 5} ect…

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Q: b) [. Determine whether the series Σnº n=1 поент is convergent or divergent.

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Q: Timothy purchased a $9,000 bond that was paying a 4.25% compounded semi-annual coupon rate and had 6…

A: This is a Compound Interest problem

Q: ne estimated value of x²dx, using the trapezoidal rule with 4 trapezoids is 2.75

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Q: Evaluate and show all necessary solutions. 1.S cosxsin²x V1+sinx √25-4x² 2. S 3. S 4. fxcosxsinxdx…

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Q: Page 1 Page 2 Example 2.1.6 Consider the integral = [(a log₂ (x)) da

A: Given     ∫ (x ln x) dx

Q: a. b. .) Solve the following integration problems. ‘s) [ e2* .xdx 1 (2x sin(√x) √x dx

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Q: True or False If determinant of matrix A is equal to 1, then the transposed matrix of cofactors of…

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Q: Find the absolute extrema of the function on the closed interval. f(x) = 7x² + 2, [-1, 2] -(0,2…

A: The answer is given below:

Q: A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An…

A: Solution: Let the radius of hemisphere and cylinder is 'r' and the height of cylinder is 'h' Then,…

Q: The value of the integral is equal to: Select one: O 4 O с صرا من م من ته 3 x ²² (4x - 4y) dy dx

A: The given integral is: I=∫01∫0x4x-4ydydx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: ( 3x³ - xy² 2 3xy+y dy 3 dx = 1 |

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Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…