The velocity function is v(t) = -t² + 3t - 2 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-3,5]. displacement = distance traveled =

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A: Please refer the attached image for complete solution. THANK YOU.

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A: To compute the derivative of rt==7-t, 4t, 8. Solution: Finding the derivative with respect to…

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Q: Find the derivative of the function. 8y9 y= In V+9 6.

A: The solution are next step

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A: Here given y = (t2 + 3t + 1) -5/2

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A: Given function is w=1z1.4+πz. To find the derivative of the functions.Solution: Power rule of…

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A: We will solve the problem

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A: Answer is mentioned below

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A: Explanation and solutions is given below....

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Q: Q3. Find the coordinates of the point(s) of the function y 3x'-5x+2, where the tangent has a…

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Q: The velocity function is v(t)=−t2+3t−2v(t)=−t2+3t−2 for a particle moving along a line. Find the…

A: #  Given  velocity   function   is      Vt=-t2+3t-2

Q: B. Find the indicated derivative. (15 pts) -4 y =;y(3) 2. x2 – 4y2 = 5; y" x2 -

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Q: Find the derivative. 1. y = + VI- 2. y = r (x2 + 1)/3 3. y = In v5x² - 4 V

A: 1. y=1x+x-1x2. y=x3x2+1133. y=ln5x2-4

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A: we have to find derivative of f(t)we will use power rule of deivative

Q: Find the derivative of the function. f(t) = 4t2/3 - 8t/3 + 4 8.

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Q: Find the derivative of the function f(x) = x2 - 5x + 3 at the numbers (a) 2 and (b) a. %3D

A: a. From the definition we have the following, Simplify further,

Q: Iff (x,y)=xcosy+ye*,find the second order derivative ô²f_ ô²f_ôf_ ô²f and дхду ôx² 'ôyôx' ôy²

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Q: Find the derivative of the function Z=3t^(11/3)-2t^(9/4)-t^(1/2)+1

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Q: The velocity function is v(t) = -t + 5t – 6 for a particle moving along a line. Find the…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Gradient problem....

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A: given is 1) y=9-9x    y=9-3xdomain =x∈R : 0≤x≤9range ={y∈R : 0≤y≤3}

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A: We can solve this problem as follows:

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Q: Find the derivative of the function. f(t) = (4t2 − 6t + 7)3⁄2

A: Topic:- derivatives

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Q: B. Find the indicated derivative. -4 1. у: 2. x2 – 4y2 = 5; y" iy(3)

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Q: Find the derivative of the function. 1 y = V7x + 8 2(7x + 8) () y' =

A: y=17x+8y = 7x+9-12

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Q: If s = 3t2 – 16t¯², when will - acceleration be zero? An object moves along a horizontal line…

A: To find  When acceleration will be zero.

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Q: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: We have to solve

Q: The velocity function (in meters per second) for a particle moving along a line is given by v(t) =…

A: For displacement we find out integration of v(t) from -2 to 3

Q: Use derivatives to find two positive numbers a and b such that a^(2)+b^(2)=1 and such that 2a+3b is…

A: Solved below

Q: Find the derivative of the function. Z = 5t11/5 - 2t7/4 - t/2 + 7

A: Solve for the derivative

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, Y)…

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Q: The velocity function is v(t) = -2 + 5t-6 for a particle moving along a line. Find the displacement…

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Q: 3w + w R(w) = 2w2 + 1

A: 1. Use the quotient rule ddxuv=vu'-uv'v2 to differentiate Rw=3w+w42w2+1 with respect to w. Here,…

Q: Find the derivative. dt 12) y = 5t + 6 - 5 1 1 C) 5x + 6 - 5 A) (5x + 6)2 B) 5x + 6 D) (5x + 6)2 36

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: find the first and second derivatives w = 3z-2 - 1/z

A: Consider the following equation: w=3z-2-1z Differentiate w with respect to z:…

Q: A particle is moving in a straight line according to the linear position function s(t)=t^3−9t^2+…

A: To find: The total distance traveled by the particle in first 6 second. Given: The position function…

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

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