Find the curvature K of the curve. r(t) = etcos(t) i + etsin(t) j + et k

Q: Hos solv the step? ₁0.9062cos (1-√3x) d x [sin (1-√√3x) -√√3 √³x)] -0.1 -0.1 sin (1-√√3a) - sin…

A: We have to solve the step  sin(1-√3a)= -0.9556+0.9210

Q: T.

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Q: The particular solution (yp) of the equation y" − 3y' + 2y = 5 e* is yp = -5xex False True

A: Explanation of the answer is as follows

Q: Evaluate the following integral: SS², 2*x+yz dadydz

A: Solution given below

Q: The determinant for the following matrix is [511] L4 2 O C 10 2

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Q: Y=(3x+4)² find dy/dx

A: Y=(3x+4)² find dy/dx

Q: 25. f(x): Determine the value of k so that f(x) is continuous. Show work. 2x² - k x < 2 = 2x² - 5x -…

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Q: b. The formula A(t) = 19.6e0.0138 models the population, A(t), of a US state in millions, t years…

A: Given: At=19.6e0.0138twhere At denotes the population in a US state in millions, t years afterthe…

Q: dy Find where y = csc dx Provide your answer below: dy dx = +9). 6x + 9

A: y = csc-(1/(6x+9)) find dy/dx = ?   here we use formula  dcsc-x/dx = -1/xx2-1   using this formula…

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Basic partial derivation is used.

Q: Find the value of y if x=2.5 from the set of points (0,5.5) and (5, 7.5)

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Q: \(\) The geometric representation of the equation -4x² - 4y² = -12 is not a cylinder in R². Select…

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Q: Given f''(x) = - 25 sin(5x) and f'(0) = 2 and f(0) = -6. Find f() =

A: In this question, we want to compute the value of f at the given point.

Q: Choose the angle (in radian) between the following two vectors u = and U = - O 2.059 00 O None of…

A: We know that the angle between two vectors u and v is θ = cos-1 u·vuv

Q: O False

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Q: L sin2t cos3t

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Q: Find the indefinite integral using the substitution x = √x√4 + x² dx + C 2 tan(0)

A: SOLUTION-

Q: For the sequence an = an-1 + an 2 and a₁ = = 1, its first term is 1 its second term is 1 its third…

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Q: b) Determine, showing steps, whether the line [x, y, z] = []+¹] intersects the plane: 3 x + 7y + 8z…

A: We have to find the intersection of plane and line.

Q: x cos 3x dx

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Q: Eliminate the parameter t to find a Cartesian equation in the form z = f(y) for: [z(t) = 3t² y(t) =…

A: We can express x in terms in terms of y as below.

Q: Find the derivative of the function y - 4 sec¯' (x + 2). (Use symbolic notation and fractions where…

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Q: The population of a city is 89​,000. If the population grows continuously by 3.2​% per​ year, in how…

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Q: 5. Solve by using power series: y' = xy. Find the recurrence relation and compute the first 33…

A: To solve using power series.

Q: consider the integral 1² +5) dx 3 x a) Riemann sum using right endpoints and n=4 b) Riemann sum…

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Q: 27. Consider the function h(x) = 2x²e-x² a) In two or three steps, write the properly simplified…

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Q: Consider the function f(x) = 8x³ - 6x² + 3x - 8. An antiderivative of f(x) is F(x) = Axª + Bx³ +…

A: We know that integration power rule is - Integration of xn is xn+1/n+1 +C. Here C is integration…

Q: Using Integrating Factor by Inspection, solve: (y − xy²) dx + (x + x²y²) dy = 0

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Q: 4. Let the universal set U, and the subsets of U are A = {x|x is a letter of your first name}, B =…

A: Disclamier: Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: Find a plane through the points (-7,7,-3), (1,-7,-8), (-2,-1,3)

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Q: Evaluate the following integral using inversion of order: SS²x5 dydx

A: I =∫xn dx= xn+1n+1 Ans = 1/72

Q: 6. If : G H and 8: H K are both homomorphism, so is 0. • : G → K.

A: We can solve as follows

Q: Find the total area of the shaded regions. (-3,36) -6 ₂ Ау 40 32- 24- 16- 8- -8- y=4x (3,36) y=x 5x…

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Q: State the order of the given ordinary differential equation. t7y(5) t4y" + 5y = 0 Determine whether…

A: As both questions are not part of same question so as per policy only first question is answered.…

Q: Evaluate the following integral using inversion of order: of 2³ dydx Remember to show complete…

A: Given integral ∫01∫x3x2 x5  dy dx

Q: so (x − 2)(3x − 4)dx

A: Multiply (x-2) and (3x-4)

Q: Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve…

A: As we know that; The expression for the area of the surface revolution of y=fx about the x-axis on…

Q: Find the area of the surface obtained by rotating the curve about the x-axis. 2) 20 sys 3 Select the…

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Q: 3. Find the solution of the following system of liner inequalities by graphing: (K + 2y > 5x + 3y…

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Q: ODE. Find the general solution of the following. Show complete solution 2. (x - 2y + 3)dx + (x-3)dy…

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Q: The reverse order of 2 2 1 Jo Jy x 1 sinx cos dxdy is sinx cos dydx False True O

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Q: Q3\ Find the Laplace Transform to the following function L sin2t cos3t

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Q: 9. The following data of the velocity of a body is given as a function of time. Time(seconds) 10…

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Q: What is the area bounded by the curves y² = 4x and x² = 4y? A. 5.33 C. 8.22 B. 4.33 D. 9.11

A: There are more than 1 questions, as per the Q&amp;A guidelines i am answering the 1st question. If…

Q: 2π 1. The region R is bounded by the x-axis, x = 0, x = 3 A. Find the area of R. sin(). 2 and y =…

A: Given: Region R is bounded by x-axis, x=0,x=2π3 andy=3sinx2

Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex² False True O

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Q: A) estimate the area of the graph of f(x) = 25 - x² From x=0 to x=5 using approximating rectangles…

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Q: Find the area of the region that is bounded above by the curve f(x) = sqrt(x−7) and the curve g(x) =…

A: The given curves: fx=x-7 and gx=19-x.The area is bounded by the above curves and x axis.

Q: The radius of a circle is increased from 2cm to 2.03cm find approximately increase in area

A: Solving using differentiation

Q: Solve through finite differences with four subintervals: + y = 0, y'(0) + X(0) = 2, dr² x ( + 7) + (…

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