Find the set on which the curve 8 dt t2 + 8t + 22 y = e downward. n interval notation):

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A: The minimum distance from the point P(1,2,1) to the line r is the perpendicular distance between P…

Q: Compute the length of the curve r(t)= 8t i+ 4t j+ (t² – 8) k over the interval 0 <t < 3. HINT: use…

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Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

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Q: Find the set on which the curve is concave upward. Answer (in interval notation): | 2 y = ₁² 1²+ 3²…

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Q: a bounded by the curve y = 3VI and the lines z = 6 and z= 8 above the z – azis is Võ+ 12v6 O 10

A: We have to choose the correct answer

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Q: At what interval is y=x^3-3/2x^2 concave upward?

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Q: Find the length of the curve y = V4t2 – 1 dt, 1<x<2 O 3 O 8 O 104 3. O 15

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Q: Find the length of the space curve parameterized by r(t)= (3t,3t2,2t3), where 0≤t≤1.

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Q: Find the linear approximation of the tunction fox) = NT-x at a-0 %3D and use it to approximate the…

A: We find f'(x) using the power rule.   then we find f(0) and f'(0)

Q: Find the family of oblique trajectories that intersect the family of the paraboles y = Cx at angle e…

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Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: 7. Find the length of the curve y = (* Vt3 -1 dt 1<t<4. 12.4

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Q: Determine the interval I for which the following DEQS have a unique solutio whose graph passes…

A: We will solve this by existence theorem of ode

Q: of the valve matix is consistant e an linear

A: Given augmented matrix is: -412h2-6-3 Let the variables be x, y. The above augmented matrix will…

Q: Find the set on which the curve 7 dt t2 + 6t + 15 y = is concave downward. Answer (in interval…

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Q: 1 dt 7+t+3t2 Y =

A: Explained below

Q: ди ди + x - Əx %| ду 0 =

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Q: The first car A moves in the northern direction at a speed u(mph), and the second car B moves to the…

A: The first car A moves in northern direction i.e. towards positive y-axis and the second car B moves…

Q: Consider the inmplicitly defined curve xy +3x2 4. %3D O Verify that the point (1, 1) is on the…

A: Consider, the implicitely defined curve                          xy2+3x2=4 We have to verify the…

Q: at what interval is  y=3x^5-5x^3 concave upward?

A: Given y=3x5-5x3

Q: Compute the length of the curve over the given interval. r(t) =〈3t, 4t − 3, 6t + 1〉, 0 ≤ t ≤ 3

A: Given rt=3t,4t−3,6t+1,  0≤t≤3Formula→Arc length=∫abr't dtr't=f't2+g't2+h't2    rt=xt,yt,zt

Q: Compute the length of the curve r(t)= (-3t, 3t + 7,–7t + 1) over the interval 0 <t <7

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Q: compute the length of the curve over the given interval.  r(t) = (2t2 + 1, 2t2 − 1, t3), 0 ≤ t ≤ 2

A: Length of a curve is also like computing distance between two points but with the restriction that…

Q: By using Green's theorem evaluate (4.ry – y') dr + (x + 3ry) dy where C is a closed curve starting…

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Q: compute the length of the curve over the given interval. r(t) = 2ti − 3tk, 11 ≤ t ≤ 15

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Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: Find the Felative Maximum vasve of Fx,x) = x*- y, Subuicct to the Construint X-Y=24.

A: The given function is as follows. fx,y=x2-7y2 the given constraint is as follows. x-y=24y=x-24 The…

Q: Compute the length of the curve r(t)= (-5t, 4t – 3, – 5t + 5) over the interval 0 <t< 7

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Determine whether the work done along the path C is positive, negative, or zero. y

A: The work done along the path C is

Q: Find the length of the curve y = S Vcos t dt, 0 <x<n.

A: Given; The curve y=∫0xcost dt,      0≤x≤π .

Q: The length of the curve y = (2+ 2x )3/2 between x=0 and x=2 is O 41/3 O 45/2 O 43/2 O 47/3 49/6 ООО…

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Q: Compute the length of the curve r(t) = 8t i+ 8t j + (t² + 7) k over the interval 0 <t < 3. HINT: use…

A: We will find out the required length.

Q: Find the length of the the interval -2sxs-1. y = L, V3t² – 1 dt curve in

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Q: Use Green's Theorem to evaluate / F · dĩ, where F = (VE + 3y, 2x + vũ) C consists of the arc of the…

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Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: Compute the length of the curve r(t) = 3t i+ 2tj+ (t² – 2) k over the interval 0 <t < 5. HINT: use…

A: Given problem is :

Q: Determine the length of the curve y = x +x in the interval 1 <a <2. %3D 59 24 O 2.86 O 3.01 127 50

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Q: Compute the length of the curve r(t) = (2t, In(t), t² ) over the interval1<t < 4. (Use symbolic…

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Q: Which of the following two families of curves are orthogonal trajectories of each other? 1, .y = e,…

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Q: Compute the length of the curve r r(t) = (2t, In t, t²) over the interval 1 < t < 3 L =

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the interval on which the curve (x) = J di is concave downward. 6+ 8t

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle 0…

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Q: Use Green's theorem to find the k number that satisfies (k + 3) ∫C((k/2)*(x^k)*(y^2))dx + ((yx^(k +…

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Q: Find the family of oblique trajectories that intersect the family of the paraboles y =cx at angle e…

A: The answer is given below:

Q: oves from origin at the curved Path -³x) m

A: Concept used: Velocity is the derivative of position with respect to time. Acceleration is…

Q: y = In(1 – a²) ; 0 < æs

A: Solution:-