Find the area inside one leaf of the rose: r = 5 sin (30) The area is

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A: The given differential equation is; (D2-2D+2)y=(-8cos3x+24sin3x)e-x

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. +00 xe dx =

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A: "According to the guidelines issued by the company We are supposed to answer only first three…

Q: 6. Let f be a function such that f(1) = 1, ƒ′(1) = 4, ƒ”(1) = −2 and ² ƒ""(t)(2 – t)²dt = 3. Find…

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Q: Divide by g (y) to separate the variables: dy IP fi O dy || gt h = 7/²010 y de 9х = прто

A: ∫xndx=xn+1n+1+cgiven  dydx=x6ypasses through  (1,3)

Q: Amanda invests $7000 in a new savings account which earns 5.0% annual interest, compounded…

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Q: Particle X moves along the positive x-axis so that its position at time t≥ 0 is given by x(t) = 5t³…

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Q: B If angle C measures 3(2x + 2) degrees, and angle A is 30 degrees, what is a? x =

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Q: Determine which of the following is the particular solution for the differential equation…

A: To determine the particular solution of the following differential equation.D2-2D+2y=-8 cos 3x+24…

Q: The Pythagorean Theorem Find the perimeter and area of the right triangle shown below. X Perimeter =…

A: To find the perimeter and area of the right triangle shown below.

Q: (-4√2,-4√2) two sets of polar coordinates for the point 0 ≤0<2m (exact answers). -,0) = -,0) =

A: Given query is to find polar coordinates.

Q: Given f''(x)=−36sin(6x and f'(0)=6 and f(0)=6   Find f(π/5)=

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Q: Integrate each of the following functions using substitution, finding the most general…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) Je sin(6t) dt ecos(6t)…

A: Given integral ∫ecos(6t)sin( 6t ) dt

Q: 1 N 3 2 1 Where: a = 1 2 3 To find the blue shaded area above, we would calculate b [' a f(x) dx…

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Q: Given that = 1/3/₁ x² dx = • √² (7 - 9x²) dx. use this fact and the properties of definite integrals…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) 8x³. -7√x 1. X dx

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Q: Find the arc length of the curve on the given interval. (Round your answer to three decimal places.)…

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Q: A piece of tissue paper is picked up in gusty wind. The table shows the velocity of the paper at 2…

A: The given table for the velocity of the paper is given as                     Time…

Q: Problems In Exercises 5-14, write the vector, parametric and symmet- ric equations of the lines…

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Q: If the national debt of a country (in trillions of dollars) t years from now is given by the…

A: Given   N (t) = 0.5 + 1.1 e 0.01t The relative rate of change RRC = f’ (t)/f (t). (1.1)(0.01)e0.01t…

Q: Find the points at which the following polar curves have horizontal or vertical tangent lines r= 3…

A: We need to find asymptotes.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Given the following vectors, calculate −8u+7v U=(-8,5),V=(8,3)

A: Given query is to find indicated vector.

Q: Evaluate the integral. r1 7x dx

A: To evaluate the given integral

Q: Use a finite approximation to estimate the area under the graph of the given function on f(x) = -1/2…

A: We need to find area under the curve.

Q: Use the divergence theorem to write a triple integral that is equivalent to the flux integral F.ds,…

A: Divergence theorem

Q: Find the equation of the line tangent to the function at the given point. y = (-2x + 6)1/2 at (1,2)

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Q: Find the center, foci, vertices and asymptotes of the hyperbola. (y-3)^2/ 25 - (x+1)^2 =1

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Q: The first 4 terms of the Maclaurin series for e -2x O a) 1 - 2x + x² - 4x³ Ob) 1 - 2x + 2x² – x³ -…

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Q: Given vectors u = (-33, 6) and v = (-19,5), find vector u — v.

A: To find the vector difference

Q: he shape of an ellips following equation:

A: The equation of ellipse is given as   x2a2+y2b2=1where,a = 12*(lenght of major axis)b = 12*(lenght…

Q: What is wrong with the equation? O O -273 Lea-2--10 X dx = X 3 f(x) = x -3 7 288 -3 is continuous on…

A: Solution: Given data,

Q: (a) Find parametric equations for the line through (3, 1, 8) that is perpendicular to the plane x -…

A: For xy-plane, z=0. For yz-plane, x=0. For xz-plane, y=0.

Q: Let f(x) = = 3x + 8 √x+26 I-12 2 if x -1 if x = – 1 Select all statements below that you agree…

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Q: If f(x) = ex- 1,0 ≤ x ≤ 2, find the Riemann sum with n = 4 correct to six decimal places, taking the…

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Q: Given the vectors x = (1, 2) and y = (3, -1) find the linear combination vector z = 2x + 3y

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Q: Use an inverse matrix to find the solution to the system. Find the inverse of the coefficient…

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Q: 120 2 A sides of lengths 6,10 and 7. Find the mesure of it's largest angle to the nearest degree…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Given u = (-2,-3,0) and v= (1, 2, 1), (a) Find 3u + 2v (b) Find 13u + 2v| (c) Find the unit vector…

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Q: D Question 10 Find the derivative. y = Š O 02 √8x+9 dt √√8x+9 (8x +9)3/2 +9 O√√√x+9+√9

A: Given query is to find the derivative.

Q: Find f"(x). 13. f(x) = x² + fr) - r³ 375

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

Q: Find an equation of the plane. The plane through the point (8, 0, 1) and perpendicular to the line x…

A: Please see the below picture for detailed solution.

Q: Inverse laplace 7/(s^2+7s+16)

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Q: Evaluate the integral. [² f(x) dx where f(x) = = {} if -4 ≤ x ≤ 0 2 -x² if 0 < x≤

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Q: Question Consider the region in the first quadrant between the positive y-axis and the functions y =…

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Q: are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by vt)…

A: Given query is is to find the velocity at indicated time

Q: 8) An investment of to 358.24 in 8 year 350 in blue chip stocks grows months. if this growth rate…

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Q: 13. The function ƒ is defined by f(x) = {²_₁ (A) 2 (B) 6 (C) 8 for x < 3 x-1 for x ≥ 3. (D) 10 What…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Find the scalar component of u in the direction of v, scal, u and the orthogonal projection of u…

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