Find the curvature K of the curve, where s is the arc length parameter. M03 - (1+²)+(1-2) r(s) K =

Q: Find the general solution of the given second-order differential equation. y" - y' - 12y = 0 y(x) =

A: Given differential equationy''-y'-12y=0

Q: Find the curvature K of the plane curve at the given value of the parameter. r(t) = 8 +²³₁ t=2 11…

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Q: The price per share of a stock can be approximated by the function S(t)=t(29-3t) + 28, where t is…

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Q: sketch and find the area of the region enclosed by the graph of the equation r=3 cos Θ....

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Q: You invest $10,000 in Rapid Growth Funds, which appreciate by 3% per year, with yields reinvested…

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Q: Find a transformation 7(u, v)=(x, y) = (g(u, v), h(u, v)) that when applied to region R, its image…

A: R:   equations of boundary lines are    x-4y=0 ,x-4y=-3 , x-y=0,x-y=3   S:   equations of boundary…

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the…

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Q: Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine…

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Q: 2. Find derivative of given function defined as follows 2x y = e = ²

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Q: Sketch the curve represented by the parametric equations Lindices Orientation of the curve), and…

A: Topic :- function

Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

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Q: whether the series is convergent or divergent. 33-50 Determine If it is convergent, find its sum. 1…

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Q: During a prolonged recession, property values on Long Island depreciated by 10% every 6 months. If…

A: Original cost of the property=200,000Value depreciated by =10% per 6 monthst=4 yearsand n=2   (no of…

Q: Find the logistic equation that satisfies the initial condition. dy dt 11y (0, 44) 20 1440 Use the…

A: Given.

Q: Question 4 Find the derivatives of the following: i) iii) f(x)=5 (4x+7)(x-3) (x-2) f(x)=(3x + 1)4(2x…

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Q: f(x)=x²-2x - 15 =( =( ) (smaller x-value) ) (larger x-value) value of x such that f(x) = 0.

A: Topic:- algebra and derivatives

Q: Evaluate ľºm vy I 1-x² x² + y² dydx.

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Q: <press the number as a ratio of integers. 0.28 = = 0.28282828 ...

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Q: Find the area contained between the two curves y = 3x - x² and y = x + x². 71/6 81/5 91/4 62/3 None…

A: This question can be solved using the concept of area between two curves.

Q: Given the scalar function f(x,y)=2xy,calculate the line integral along the ellipse curve from point…

A: Given data:- The given curve is, x29+y24=1 The given scaler function is, f(x,y)=2xy t E 0,π/2

Q: nass function. a give Determine the value of c such that the function is a probability mass…

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(), speed…

A: Given r(t)=etcos(t), etsin(t), et

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A: Given that : r(t) = cos(3t) i + 2sin(3t) j + k and t= π. Find the principal normal unit vector to…

Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6)

A: step 2 complete solution

Q: Find the following for the given equation. r(t) = (e-t, 3t², 2 tan(t)) (a) r(t) = (b) r(t) = (c)…

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Q: F(x)=x4 - 4x³ + 3x², find the following: i) The extrema of the function. ii) The coordinates of the…

A: Given,

Q: In a chemical reaction, a certain compound changes into another compound at a rate proportional to…

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Q: let r be the region enclosed inside y=x2 and y=3x-2 a.sketch the region R. b.Compute the area of the…

A: Given the region R is enclosed inside  y = x2 and y = 3x-2. Interaction between both graphs  x2 =…

Q: 1. If L{f(t)} = F(s) then L{f""(t)} is, A) s²F(s)-sf (0) - f'(0) s²F(s)-sf'(0)-f(0) B) C) D)…

A: Topic = Laplace transform As per guidelines , At a time only one question can be answered out of…

Q: The general solution of the differential equation x dx + y dy = 0 is a family of curves. These…

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

Q: cm min A spherical snowball is melting at a rate of 5.9- snowball's volume is 972 7 cm³? The radius…

A: Take the volume of sphere and derivate it with respect to t and then put values

Q: 7

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Q: x-3 dx x+4 5. The differential equation dy 1. produces a slope field with horizontal tangents at x =…

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Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: Question 1 a) Prove that 1 + cot 0 1 + tan 0 = cot 0. b) The concentration C of a drug in a…

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Q: Find the equation of the tangent line and the normal line at the point corresponding to the given…

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Q: Find a polar equation for the curve represented by the Cartesian equation: x² = 8y. Or= 8 sin cos 0…

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Q: Evaluate √2r - Idr

A: Given,

Q: 4

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Q: II) Solve the following equations. 3) cot ¹(1-2)-tan-¹(x)= TT

A: Given data÷   cot-11-x-tan-1x=π4   Useful formula   cot-1x=π2-tan-1x So, cot-11-x=π2-tan-11-x

Q: Evaluate edrdy.

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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: t = 0, a bacterial culture weighs 4 grams. Three hours later, the culture weighs 5 grams. The…

A: We have to solve the logistic model equation with given data.

Q: Ə(x, y) Find the Jacobian Ə(u, v) 9u x = ₂y = u +4v V O 9u-36v 12 for the following change of…

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Q: etermine whether the given set of functions is linearly dependent or linearly independent on the…

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Q: Evaluate : T SS y sin x dydx

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Q: Find the general solution to the following separable differential equation: 7yy' = 3x. 03x² + 7y² =…

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Q: Integrate 01-In x + C о √(5-2) x – 10 ln |x| X - - - 1 10 In |x| 2 25 Olnx-25x + C ▬▬▬▬▬▬▬▬ X dx. +C…

A: Topic = Integration

Q: Both x and y denote functions of t that are related by the given equation. Use this equation and the…

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Q: Solve the following equation. Express your answer in the form found using Euler's Formula, Iz|" eine…

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