The parametric equations of a curve are x cos 20, y = 1 + sin 20. Find dy and dx d²y at 6 1/6. Find also the equation of the curve as dx? a relationship between x and y. Exercise 167 Further problems on

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Given  equation r=2+3sinθwe have…

Q: The parametric equations x= 3 - 8 sin 3t and y = 9 + 8 cos 3 t for 0 sts x/4 represent a curve C.…

A: Given data: x(t)=3-8sin(3t) y(t)=9+8cos(3t) for 0≤t≤π4 Solution: Length of parametric curve is given…

Q: The parametric equations of a curve is * = cos(t), y = sin(t – t) (a) find the equation of the…

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Q: Consider the following. X = sin y = os(플e), -π sθ<π (a) Eliminate the parameter to find a Cartesian…

A: As we know that the trigonometric identities:- cos2(θ)+sin2θ=1

Q: Find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the…

A: x=4cosθ and y=4sinθ We have to find: (1) dydx (2) d2ydx2 (3) Slope at point θ=π4 (4) Concavity at…

Q: 1. The parametric equations: x = a cos 0,y = a sin? 0;0 ses 2n, define a curve called an asteroid

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Q: Given the parametric equations x = 2(8 – sin®) and y= 2(1 - cose). The slope of the tangent line to…

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Q: d?y and dx2 and find the slope and concavity (if possible) at the given value of the parameter. (If…

A: On differentiating, we get Now

Q: Consider the parametric equations x= cos t, y = sin t, 0sts 2n. a. What curve do the points of these…

A: Convert the parametric equations to the Cartesian equation, to find the equation of the curve . The…

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

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Q: Given this pair of parametric equations and value of t, x = Vt, y = at t = 4 a) Find the point…

A: To solve this put t=u and then solve it Here we are going to use formula of differention of tn…

Q: 1 cos(t) Find the slope of the tangent line to the parametric curve at the point y = 2 sin(t)

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Q: a) A curve has the parametric equation given as x = 4+3 cos 0 y = 3 sin 0 – 2. i) Convert the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 1 cos(t) - 2 sin(t) Find the slope of the tangent line to the parametric curve at the point

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Q: I = 4 cos(t) Find the exact slope of the tangent line to the parametric curve y = 3 sin(t) at the…

A: Here we use the chain rule of differentiation.

Q: A ball is thrown at an initial height of 100 feet at an initial velocity of 80 feet/second at an…

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Q: The parametric equations x= 8 − 6 sin 3t and y = 8 + 6 cos 3 t for 0 ≤ t ≤ π/4 represent a curve…

A: Given: Parametric equations Formula used

Q: The following are the parametric equations for the motion of a charged particle: x = a(θ − sin θ),…

A: Given the equation of curvesx=a(θ−sinθ)y=a(1−cosθ)

Q: ´x = 3 cos(t) 5 sin(t) Find the exact slope of the tangent line to the parametric curve at the point…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: what points does the curve described by the parametric equations x = 2a cos t – a cos 2t d y = 2a…

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Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Find the attached handwritten solution.

Q: The equation of the tangent line to the parametric equations, x = sine, y =20+ cose at e = 0 is y =

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Q: Consider the parametric equations x= cos 1, y = sin t, 0sts 2n. a. What curve do the points of these…

A: slope = dy/dx = dy/dt /dx/dt

Q: An arrow is shot upward, with an initial velocity of 85 meters per second, at an angle of 31° with…

A: When an object is thrown in air against the gravitational pull, then the motion of object is called…

Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0S <2M. 3.1. Find an equation…

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Q: x = 6 cos(t) Find the exact slope of the tangent line to the parametric curve at the point where |y…

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Q: Consider the following parametric equation. x = 7(cos 0 + 0 sin 0) y = 7(sin 0 – 0 cos 0) 11 What is…

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Q: Find dy/dx and d2y/dx2 , and find the slope and concavity (if possible) at the given value of the…

A: Given: x=10cosθ                                           ..1y=10sinθ…

Q: dy for parametric equation below in term of t: Find dx y = 4 and x= sin 61

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Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: Given   x = 8 cos θ∴ dxdθ= ddθ(8cosθ)dxdθ=8(-sin θ) = -8sin θy = 8 sin θ∴ dydθ= ddθ(8sin θ)dydθ= 8…

Q: Given the parametric equations x = 2(8 – sine) and y= 2(1 – cose). The second derivative of y with…

A: Let's find.

Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=&lt;t+1,t,1t&gt;=&lt;x, y,…

Q: The parametric equations x= 4 − 6 sin 4t and y = 6 + 6 cos 4 t for 0 ≤ t ≤ π/3 represent a curve…

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Q: What curve is represented by the following parametric equations ? x = sin(t) ; y = cos(2t) ; 0 ≤ t ≤…

A: x = sin(t) ; y = cos(2t) We need to represent the curve determined by the given parametric…

Q: 1.Given x=3( θ-sin θ) and   y=3( 1-cos θ) a. Trace the parametric curve b. Find dy/dx c. Find…

A: Givenx=3(θ-sinθ)y=3(1-cosθ)To find1)Trace of parametric curve2) dydx

Q: Given the parametric equation: x=cos(3t), y=sin(3t), 0 less than or equal to t less than or equal to…

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Q: Eliminate the parameter from the parametric equations: æ = 3 sin t y = 2+ cos t The resulting…

A: Given: x=3sint                                                                   ..1y=2+cost…

Q: S* = 6 cos(t) |y = 5 sin(t) Find the exact slope of the tangent line to the parametric curve at the…

A: We have to find exact slope of the tangent line to the parametric curve: x=6costy=5sint at t=π6 For…

Q: x= et cos t y=et sin t given the parametric equation, solve its dy/dx and d2y/dx2

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Q: Find the slope of the line tangent to the polar curve at the given point. 5 7x r= 5 sin 0; 2 6 dy…

A: Slope of line tangent to the polar curve is given by- dydx=drdθsinθ+rcosθdrdθcosθ-rsinθ

Q: Eliminate the parameter to find a Cartesian equation for the curve. Then describe the motion of the…

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Q: Consider the following parametric equation. x = 3(cos 0+ 0 sin Ø) y = 3(sin 0 -0 cos 0) What is the…

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Q: (* = 8 cos(t) y = 7 sin(t) Find the exact slope of the tangent line to the parametric curve at the…

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Q: The parametric equations: x = a a cos 8,y = a sin 0;0 <e< 2n, define a curve called an asteroid

A: Given: The parametric equation is where 0≤θ≤2π   To determine: The slope of the tangent wrt θ i.e…

Q: The parametric equations x= 6 − 9 sin 2t and y = 5 + 9 cos 2 t for 0 ≤ t ≤ ?/4 represent a curve C.…

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Q: The parametric equations for the paths of two projectiles are given. At what rate is the distance…

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Q: 4 cos(t) { Find the slope of the tangent line to the parametric curve at the point 1 sin(t) 6 Y =

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Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: slope is defined at dy/dxand concavity is defined at d2ydx2

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.