Q3. For the motion vector r(t) = e cost i + e'sint j %3D find: (i) (ii) ат

Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: In what direction from the point (1,-1) is the instantaneous rate of change of f(x.y) = 8x* – 10x?y?…

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Q: A bee with velocity vector r' (t) starts out at (4, –4, –5) at t = 0 and flies around for 7 seconds.…

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Q: Find the tangential and normal components of acceleration for a projectile fired at an angle 0 with…

A: we know that for projectile fired at angle θ with the horizontal tangentialTt and normalNt…

Q: dy Find - for y = du dy du = = [19+ √9 +10t2 dt. 0

A: given y=∫0u9+10t2dtTo find: dydu

Q: (c) t? dy + 2ty = cost , y(T) = 0, t > 0. %3D dt

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Q: I can't find the tangential component of the acceleration

A: The given position vector is,

Q: For f(x, y) 5æ sin(ry) at the point (3, 5), the direction in which the maximum rate of change occurs…

A: The objective is to find the direction in which maximum rate of change occurs.

Q: Two ships A and B are moving northeast with peed VA=22 knots, and west with speed VB= 19 knots,…

A: Given: VA=22 knots in northeast VB= 19 knots in west To find: Relative velocity of A with respect to…

Q: A body of mass m falls from the rest in a medium offering resistance proportional to the square of…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Consider the following equation.  f(x,y) = y^4 / x P(1,3) u = 1/3( 2i + sq root (5)j  ) Find the…

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Q: Express the velocity and the acceleration of a moving point p(r,0)

A: We have given a curve in polar coordinate : r=1+sin(θ) with θ=t2…

Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

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Q: ü=i- where Use directional derivative definition to find Df (2.1) for the unit vector f(x y) = xy +1

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Q: Find a vector equation of the tangent line of f(t) = (cost, sint, t) at the point Po (0, 1,

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Q: dy = V1+y² sin² y; y(0) = 1 У (0) — dx 2

A: In this question, we have a differential equation. dydx=1+y2sin2(y) withy(0)=1/2 here we check the…

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: 4) Find the equation of the tangent plane to the surface r(u, v) = (u²-v²)i − (3uv)j + (4√u+v)k when…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Find the equation of the tangent plane to z=e^x+y+y^2+ 9 at the point (0,4,30)

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Q: At the Find the moments when the two distance, given vectors of velocity and acceleration are…

A: The given vector is R→t=2 i^+5 cost j^+3 sint k^ ,   0≤t≤π ....(1) To find: the moments of the…

Q: 2. Find the rate of change of the function f(x, y) = x² sin y at the point (1,) in the direction of…

A: To find out the rate of change in the direction of the given vector.

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

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Q: A point, p, is moving with acceleration 6t j -k at time t. If at t 1, the coordinates of P are (1,…

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Q: A particle moves in the xy−plane, so that its coordinates at time t≥0 are x(t)=3t3−3t2, y(t)=20t2+2t…

A: Given

Q: A point, p, is moving with acceleration 6t j - k at time t. If at t 1, the coordinates of P are (1,…

A: Answer

Q: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

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Q: cimal places in calculations. ime, s istance, km 100 92 25 75 78 125 0. 32 58 100 Determine the…

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Q: Let f (x, y) = x² + 4xy². Say the directional derivative Du(1,1) with u is the unit vector that…

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Q: c) Find the directional derivative of f(x,y) = 10 – 3x2 + at P(2,–3) in the direction of the vector…

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Q: In what direction from the point (1,-1) is the instantaneous rate of change of f(x.y) = 8x* - 10x°y?…

A: According to question given thatf(x,y)=8x4-10x2y2-11y3

Q: Exercise 1. find the differential dy (la) y = 3z? (1b) Find y = V9 - z2

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Q: Assume that an object moves on a trajectory according to the equations x(t)=t+cost, y(t)=t−sint.…

A: An object moves on a trajectory according to the equations  Differentiating  with respect to t, we…

Q: For f(z, y) is: = 5a sin(xy) at the point (2, 4), the direction in which the maximum rate of change…

A:

Q: For time t > 0, the position of a particle moving in the xy-plane is given by the vector (, et).…

A: Position of particle = (1/t, e3t) Velocity = derivative of position of particle = (-1/t2 , 3e3t)

Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

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Q: For time >0, the position of a particle moving in the xy-plane is given by the parametric equations…

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Q: A bee with velocity vector r' (t) starts out at (2, 5, -2) at t = 0 and flies around for 1 seconds.…

A: We can answer first question as per the honor policy. Please resubmit other parts as well to know…

Q: dy If y = (t + 5t + 6) (2t² + 4), find dt dy %3D dt Submit Question

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Q: A curve is given by the parametrization r(t)= [²,-t, ť ]. If the tangent vector to this curve at a…

A: The given curve is,  ,

Q: Find the vector equation of the tangent line to 7(t) = 2 (e1 %3D

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: The given function isfx, y=5x.sin(xy)to find the direction in which the maximum rate of change…

Q: are two linearly independer d'y 3dy equation dx? dx

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Q: The directional derivative of xy f(x, y) = V2 (x + y) at (1, 1) in the direction of the unit vector…

A: We have ,  f(x , y) = xy2x + y   We know that , directional derivative at any point x , y is defined…

Q: For the position vector R(1) = e'i+e²ª j, the velocity at t=ln3 is:

A: Consider the given position vector: R→t=eti+29e2tj Find Velocity vector: Differentiate w.r.t "t",…

Q: Find the equation of the tangent plane to z = e² + y+ y*+3 at the point (0, 5, 634).

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Q: Q, Solve he differnktial equntion by Laplace troms form. ý-y =t, yW=1, ý(0) =1

A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post…

Exponential Growth Model

The relation that represents an exponential function is: