Suppose the position (in s(t) = -2t2 + 12t for 0 s %3D a). Find the velocity fu stationary, moving to th. b). Find the acceleratio- increasing? c). Graph s(t), v(t), a(t

Q: Find the x value of the stationary point of the function: Y = ax² + bx² + cx + dx + e where a = 8, b…

A: The given function is quadratic and substituting with the provided values , we get…

Q: If y = Vx(3 – x)², show that- dy (3-х) (3-4x) Find the x coordinates of %3D dx all points on y =…

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Q: Find the slope at the point (1, 1)  for the curve defined implicitly by ln y = x2 – y2.    a m = 2…

A: Given query is to find the slope of the function.

Q: Let x(t) = 3t, y(t) = 8t*. Then the slope of the tangent at t = 9 is O 12

A: The curve is defined by the following parametric equations xt = 3t ,  yt = 8t32 To evaluate : The…

Q: Find the equation of the line that is tangent to the curve r = r In y, I> 0, at the point (1.e).

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Q: (c) (15) Let y3 + 2xy + x = 0. Find . Then find an equation for the line L tangent to the graph of…

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Q: Find y as a function of t if 36y′′+72y′+48y=0, y(0)=3,y′(0)=6.   Help me fast.I will give good…

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Q: Consider the curve given by y² = 2 + xy. dy dx (a) Show that = 2y-x (b) Find all points (x, y) on…

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Q: D. (a)S sec? 3x dx (b)S 2cosec2 4t dt 2cosec24t dt

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Q: (3) Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy dx -2. What is f(x)?

A: The function y=fx that satisfies f0=3, and dydx=-2. We have to find fx and sketch its graph.

Q: Find f(x) dx for each graph of y = f(x). (b) у (a) y 1

A: Integral of the function between the limits represent the area under the function. Since both, the…

Q: d'y as a function of t if x t+ (a + B) (a+ B) (a) Find , y=t- t (6) t

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Q: 5. Consider the function y(t) = rect (a) Sketch y(t). (b) Sketch (d+1)y(t). d-5 (c) Sketch y(t-(a +…

A: We have been given: yt=recttd+5 We have to sketch: a ytb yt-a+1c d+1ytd y2t-a+1

Q: Find the equation of the curve that passes through the point (8, 6) if its slope is given by dy = 5x…

A: Given that, the curve passes through the point 8,6 and the slope is given by dydx=5x-7

Q: Find the point at which the line y = 8x – 31 is tangent to the graph of y = eXf-16). %3D The point…

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Q: The population be represented of rabbits in a forest over a 12-month span ca by : () r(t) =…

A: The given relation is r(t)=1000-500sinπ6t. To Explain: (a) Why it represents the population of…

Q: Find y as a function of t if y(0) = 5, y(0) = 3. y(t) = 36y" - 84y +58y = 0₂

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Q: Use the chain rule to find the following derivatives: d 2. - (0²³² - 4x + 3) = [ a. @+³ 5 dx d b. -…

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Q: Find the slope of the line tangent to curve y = x³ - 2x +1 at x = 1 A. B. C. D. 1 1/2 1/3 1/4 Give…

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Q: Graph z(t) = 4eit

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Q: consider the following function: f(x)=cos(2-2x)

A: The given function .The aim is to find the period of the function.

Q: Let c(t) = (9r2 – 6, 5t² – 10t) . Find the equation of the tangent line at t = 1. (Express numbers…

A: According to the given information, it is required to find the equation of tangent line at t = 1.…

Q: Solve and sketch the graph of the IVP. dy dt = 81 (1)-82(1) +83 (1)-84(1)+.... y(0) = 0

A: As per the question we are given the following IVP : differential equation(DE) : dy/dt = δ1(t) -…