(a) Find a function that gives the position of a particle that moves with constant velocity, with speed equal to 5, that is at (1, 4) at time 3, and that eventually intersects (6, 2). (b) Find a function that gives the position of a particle that moves with constant velocity, with speed equal to 3, that is at (2, 1, 5) at time 1, and that eventually intersects (7, 2, 0).

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives and fz = 44,…

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Q: Find the perticular number or orthogonal trajectories of x2+cy2=1 passing through the point (2,1)

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A: fx=x+3

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Q: (a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of…

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Q: 4) Find the orthogonal trajectories of the family of curves

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Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ + 10

A: Here we have to find the orthogonal trajectories

Q: In Problems 23–38, for the given functions f and g, find:(a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘…

A: In Problems 23–38, for the given functions f and g, find: (a) f ∘ g (b) g ∘ f (c) f ∘ f (d) g ∘ g…

Q: # 22 A right circular cone of radius 6m and height 10m is initially filled with water. An empty…

A: We know volume of water in cylinder = volume of cone - volume of water remaining in cone

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A: Here, f1(x)=ex+3 and f2(x)=ex-4

Q: 3) f(x) = x--x- 1; [3] [1, -1: 01.4 5) f(x) = 2x² - 2x -1; 4) f(x) = −x- - x + 1; [2, 1 x-1 6)…

A: Average rate of fx change over interval a,b=fb-fab-a

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A: Given that: Total area =1500000 sq. ft.The field is to be rectangular.and then divide the field with…

Q: 4. Find the orthogonal trajectories of the family of curves y = Ce* +10

A: Given that : y = Ce2x + 10

Q: Find the orthogonal trajectories of the family of circles passing through the points (1, −2) and (1,…

A: Given that

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Q: A function f has derivative f′(x)=x^3(x−1)^2(x+1)(x−2). At what numbers x, if any, does f have a…

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Q: Suppose (0, 2) is a critical point of a function with continuous second derivatives. In each case,…

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A: Solution-

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Q: 1. f(x) = x² – 4x + 1 at point (0,1) 2. f(x) = x³ + 2 at point (1,3) 3. f(x) = 2x* + 3x³ – 2x + 7 at…

A: Given : The functions and the points.

Q: | 1) Find a function y whose graph passes through the point (1, ) and satisfies x²y' = y.

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Q: Determine all critical points for the function. 3 12x 2 Ox= -2 Ox=-2, x = 0. and x = 2 Ox= 2 Ox= -2…

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Q: [1] Determine the orthogonal trajectories of y(1+2x²)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1) Determine the orthogonal…

Q: f(x) = lim (6x + 2 4x + 3) = 6x + 3 Ax-->0 f (x) = lim (6x + 2 4x + 2) = 6x + 2 %3D 4r-->0 f (x) =…

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Q: Find the DOMAIN of 8z-24r-320x f (x) = 7z+28z2-315z Section 3.4 O + -5, 9 O+0,-5, 8 Ox+0,-5, 9 O…

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Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ +10

A: Given that, Family of curves is following, y = Ce2x + 10…

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives. In each case,…

A:

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A: Given  fx=5x6-14x4 f'x=30x5-56x3 Let f'x=0      30x5-56x3=02x315x2-28=02x3=0    or     15x2-28=0   x…

Q: A tank contains 100 gal of brine in which 50 lb of salt is dissolved. Brine containing 2 lb/gal of…

A: 1 st we will make differential equation for amount of salt and then solve it to get amount of salt

Q: 9. Find the family of the curve whose slope at any point is √x + √√x and also the member which…

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Q: 5. Find the orthogonal trajectories for a family of circles tangent to the y - axis and centers at x…

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Q: 2. Find all critical numbers for the function: g(x) = x/2x +1 B. 0. ÷.글 1 1 А. - - | 2 3 2 c. - D.…

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Q: On the interval x∈(1,2), the curve y=x^3−6x^2+9x+1 is. decreasing and concave down horizontal…

A: Option A is correct..

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Q: 5  please answer, type the solution if you can please. or write clearly

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Q: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) x2 + 2y2…

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Q: The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: 8. A motorbike company finds that it costs $250 to produce each motorbike, with fixed costs of $1400…

A: Here we solve the given problem of application of derivatives.

Q: So x, = c,e +c,e", and x, = 3c,e" +c,e" Sketch the trajectories in phase plane 2 -2 -2 Comment

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Q: 1. Find the orthogonal trajectories of the family of curves y³ = 3(x – c). Draw a few representative…

A: The orthogonal trajectories are the curves that are perpendicular to the family everywhere.

Q: 12. Differentiate the function (use chain rule): y = 2x2 Vx+1'

A: To differentiate the given function

Q: Find the critical numbers of the function f(x) = 2x -15x2 +36x- 24. O a. -2 and -3 O b. 2 and-3 O c.…

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Q: c) A function with an absolute minimum at (4, -3) and a local maximum at (-2,6) 6- 4- 2- -4 d) A…

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Q: 1) Find a function y whose graph passes through the point (1, 2) and satisfies x?y' = y.

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…