sketch the slope field and answer the following a) is the equation autonomous or non autonomous b) what is an equation if a nulicline c) region of derivative greater than zero dr =t-2r dt

Q: 5. Find the equation of a curve such that y" is always 2 and, at the point (2,6), the slope of the…

A: Solution:-         y''=2         d2ydx2=2      ⤿intrgrating both sides w.r.t  x, we get           ∫…

Q: Area of a regim enilosed is by Curves y= 12 and

A: To find the area enclosed by the given two equations

Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R“, where bị b2 3 3] C1 3 C2 22 a If the…

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Q: Find the equation of the tangent line to the curve of intersection of the surface z = x² - y² with…

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Q: 1. Find the equation of the tangent line to x? + y? = 9, at the point (2, v5). %3D

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Q: Draw a direction field (slope field) of y' = x. Use all 25 grid intersections. 2 1 2 X

A: Note: Slope fields allow us to analyze differential equations graphically. When an explicit solution…

Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

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Q: a) A curve has equation e3x. i) Find dx — e2x e3ye-2y = 3 in terms of x and y. ii) Find the equation…

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

Q: 6 of 9 > Find an equation of the tangent plane to the surface at the given point. 2x² + 2y² + 4z² =…

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Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: Distinguish briefly the Parametric and non-parametric analysis

A: There are two types of analysis in the testing of the hypothesis. they are: 1) Parametric analysis.…

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: 7. Use implicit differentiation to find two equations between x and y such that the tangent line to…

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Q: 1.. Plot the cardioid curve (0)=2+2 sin then compute all angles for which the slope of the tangent…

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Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…