Find the general solution of the differential equation. y (4) - y = 8t+cost. NOTE: Use C₁, C2, C3, and c4 as arbitrary constants. y(t): 3

Q: Consider the following autonomous first-order differential equation. =y² - 2y dx Find the critical…

A: Given differential equation:- dy/dx =y2 -2y

Q: 3Q Express each vector as a product of its length and directions i. 2i+j-2k ii. 3/51+4/5k iii.…

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Q: Find the indicial equation and the exponents for the specified singularity of the given differential…

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Q: 1. Find the solution of the differential equation. y’’-6y’+9y=0 theme: repeated roots; order…

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Q: Find the critical points c that correspond to local minima. (Use symbolic notation and fractions…

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Q: Find the solution of the differential equation. 4y’’+12y’+9y=0

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Q: Express the number 3√3 - 6i in the form R(cos(0) + i sin(0)) = Re¹0, where R> 0 and -T≤ 0 ≤ T. NOTE:…

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Q: A plane begins its takeoff at 2:00 p.m. on a 2170-mile flight. After 5.1 hours, the plane arrives at…

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Q: Find the critical points of f(x) = -6x² + 2x² - 9 and apply the Second Derivative Test (if possible)…

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Q: The Laplace transform of a continuous function over the interval [0, ∞o) is defined by F(s) = [ e…

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Q: Transform the given polar equation r = sectan to rectangular coordinate.

A: This question is related to coordinate systems, we will solve it using given information.

Q: Find the solution of the differential equation. 9y’’+6y’+y=0 theme: repeated roots; order…

A: topic:- differential  equations solution

Q: Determine whether the series n=1 √n 2-√√n converges or diverges using the integral test.

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Q: Sin (Imx) = h+, hx +,hax

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Q: In some manufacture company, which sales certain product, the price function p and the cost function…

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Q: 15) dy dx 1-x Find given that y = x²

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Q: (a) Find the derivative of f (x) = (x² + 2) (4x − 3) by first expanding the polynomials. Enter the…

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Q: Use the method of partial fraction decomposition to perform the required integration. 6x² +22x-23…

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

Q: Explain why S is not a basis for P₂. S = {1, 6x, -2 + x²,4x} O S is linearly dependent. OS does not…

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Q: Determine the length of the parametric curve given by ㅠ = cost, 0≤t t≤ 2. X = sin³ t, y

A: To determine the length of the parametric curve given by x=sin3 t, y=cos3 t, 0≤t≤π2.

Q: A biologist has two brine solutions, one containing 4% salt and another containing 20% salt. How…

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Q: Use a graphing utility to find the points of intersection of the graphs of the equations. Check your…

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Q: f(x) = 1 f(x) = x f(x) = cos(2x) f(x) = ax

A: Solution is given below:

Q: Determine whether S is a basis for the indicated vector space. S = {(1, 0, 0, 2), (0, -1, 0, 2), (3,…

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Q: a. Which of the following are functions? Justify your answer. f(x) 5+ 4- 3- -4-3-2-1 O -2- -3+ -4-…

A: Let's find function or not.

Q: 3. Evaluate S dA where R is the region between y = 2x and y² = x³ lying to the R left of x = 1.

A: Let's evaluate double integral.

Q: 1. 8. (v³ - 3y + 2)√√9+x²dx + x²dy = 0 (x² - 1)y" + 2y' — (x − 1)(x + 1)² = 0

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Q: Q1 (a) Show that y= Ae²* + Be ³*, where A and B are constants, is the general solution of the…

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Q: Find the solution of the differential equation. 2y’’+2y’+y=0 theme: repeated roots; order…

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Q: The area of the sector of a circle with radius 8 inches formed by a central angle of 100° is inches.…

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Q: Let f (x) and g(x) be defined by f(x) = 2 - x      g(x) = (x2 + 2x+ 2    x < -1…

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Q: Using rectangles each of whose height is given by the value of the function at the midpoint of the…

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Q: Sketch the region enclosed by the given curves, y = 3x² and y = x² + 4. Find the area of the region.

A: Given curves are y=3x2 and y=x2+4.

Q: A baseball is hit at an angle of with the horizontal and with an initial velocity of vo = 119 feet…

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Q: if x - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. f(x) = Let f(x)…

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Q: 4. [ x sinh x dx

A: ∫x sin(hx) dx

Q: Consider the following linear differential equation x dy/dx + 2y = sin(x). a) Calculate the…

A: The objective of the question is determine the I.F. and solution of the differential equation.

Q: For the function given below, find a formula for the Riemann sum obtained by dividing the interval…

A: Solve the following

Q: Solve the initial value differential equation: (x² + 1) + 3xy = 3x where y(0) = 2

A: Given Differential equation,x2 + 1dydx + 3xy = 3xandy0 = 2

Q: Your broker has suggested that you diversify your investments by splitting your portfolio among…

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Q: Determine the remaining sides and angles of the triangle ABC. A 140° 40', C = 20° 20', AB = 3

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Q: The monthly sales S (in hundreds of units) of skiing equipment at a sports store are approximated by…

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Q: Question 2 Choose the correct answer. The average rate of change of the function f(x) = x² + 1 from…

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Q: 9. Prove: csc(x)-csc(x)cos² (x) = sin(x)

A: To prove: csc(x)-csc(x)cos2(x)=sin(x) Note that, sin2(x)+cos2(x)=1

Q: 7. Find the solution of the differential equation. 4y’’+17y’+4y=0 theme: repeated roots; order…

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Q: Σ k=1 3k! k Choose the correct answer below. A. The series converges absolutely. B. The series…

A: The given series is: ∑k=1∞3kk!kk Now, it is a positive term series. So, it is either absolutely…

Q: Let f(x) = ²15 Find the critical points c that correspond to local minima. (Use symbolic notation…

A: Given :fx=xx2+15

Q: Using Midpoint Rule, with n = 10, approximate the integral below. Give the error of approximation π…

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Q: Let f(x) = 3x² + 2x − 10; a = 1. 1. Use the definition to find the derivative function f' 2. Find an…

A: The given function is: f(x)=3x2+2x-10

Q: A 25-ft ladder leans against a building so that the angle between the ground and the ladder is 84°.…

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