d²y Find- when t = 1 if given the parametric functions as below, dx2 x = 3e5t y = te-5t

Q: For timé t> 0, the position of an object moving in the ryplane is given by the parametric equationsz…

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Q: From the two parametric equations below, find dy dx x = (2 − 3t)/ (1 + t) , y =(3 + 2t)/(1 + t)

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Q: Given the the parametric curve Į æ(t) = ecost y(t) = t³ – 243t

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Q: Find ď²y dx² x = 3 sin t in the parametric equation y = 3 cost 0≤t≤ 2π.

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Q: c) A curve has a parametric equation x = 2t - 1 and y = t* -t'. dy Evaluate dx? 1 at t = 2

A: Given, The parametric equations x=2t3-1, y =t4-t3.

Q: Find dy/dx of the following set of parametric equations 1. x = 3(t-2)2 ,  y = 9t2 + 4 2. x =…

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Q: 2. For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). x = 3t? –…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Parametric Equations Parameter - V, y = V1

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Q: The parametric equations of a curve are x = and y = t³ + 4 – . Given = -;(t* + 1). Find the value of…

A: The parametric equations of curves are x=6t, y=t3+4-3t   Given dydx=-12t4+1 We have to find that…

Q: de termine d3y f the parametric equatio ns. of dx2 x (t) = tlht and ylt) = (t-1)-

A: This question is based on diffrentiation of parametric curves.

Q: Let x = 9t?, y = 7t° – 8t?. d²y as a function of t, then find the concavity to the parametric curve…

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Q: A curve C has parametric equations 1 y = 1-1 t t+±1. 1-t dy (i) Find in terms of t. dx

A: From the given information. Write the expressions for x and y.

Q: A curve C is defined by the parametric equations x(t) = -8t2 +7 and y(t) = 2t3 – 8t. Write the…

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Q: The function y=f(x) is given in parametric form by the equationsx=t3,y=t2+1,where t>0. Find…

A: Given:

Q: 2. For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). X = 3t? –…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first question. Please…

Q: d/dx(y(x)) if x and y are related by the parametric equations x = t+sint, y = t^t.

A: As we know that; The Power Law: ddxxn=nxn-1 The Product Rule: f·g'=f'·g+f·g' The Chain Rule:…

Q: Sketch the curve x = 3sin?t, y = 4cos?t (0<t <÷) by eliminating the parameter, %3D and indicate the…

A: Introduction: When a function y=fx can be expressed as x≡xt,y≡yt by introducing a new variable t,…

Q: x = 4e° dy Find for the set of parametric equations dx y = e

A: There are multiple question. As per company policy ask other question separately. 1.

Q: A curve is defined by the parametric equations x (t) = at² and d² y y (t) = bt where a and b are…

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Q: Find dx for the parametric curve c(t) (31°, 312 – 7) at the point t = 4. %3D (Use symbolic notation…

A: Given: Parametric curve ct=3t3,3t2-7 Parametric curve c(t) is represented as c(t)=(y(t),x(t)) So,…

Q: 7. The curve at right is given by the parametric equations t2 z = v2t. x = In t, y = Find its length…

A: Given that, x=lnt,y=t22 and z=2t. That is, r→t=lnt,t22 ,2t. It is known that, the length of the…

Q: Find for the parametric curve c(t) = (41°, 2r² – 8) at the point t = 2. (Use symbolic notation and…

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Q: Consider the parametric equations defined by x(t) = 3t² – 3 and y(t)= 2t +1, for t> 0. d'y at t= 1.…

A: Option A is correct option.

Q: equation

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Q: Consider the parametric equations: x = 2t2, y =t³. Find at the point t = dx? 8 without eliminating…

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Q: d y Find dx? for the parametric equation: x = et;y3Dt³ +t+1

A: Find your answer below

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

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Q: tind the area of the parametric curve X = t ,4=9t-73

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Q: dy (ii) Find dx? for the parametric equations x = t+ sin t, y= 1+cost

A: • This problem can be solved by using Chain rule as explained in step 2.

Q: Find the length of the parametric curve: x = 2t + 1; y = t? – 3,0 <t < 5

A: Given that: x=2t+1,  y=t2-3,0≤t≤5To  calculate   dxdt  and   dydt,dxdt=ddt2t+1=2dydt=ddtt2-3=2t

Q: (ii) Find for the parametric equations dx2 dy x =t – sint, y = 1 – cost

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Q: Find for the parametric curve c(t) (t-1 – 5t, 41) at the point t = -2. dx (Use symbolic notation and…

A: Given problem:- Find dy/dt for the parametric curve c(t) = (t-1 - 5t, 4t3) at the point t = −2.

Q: dy at t = of the parametric curve: x = csct, y cot. dx 7C Find Select one: V3 21 -V3 none 2.

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Q: Find the dx² for the plane curve with the parametric equations X = t³ – 4 and y = t2. -2 9t4 2

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Q: [x(t) = 3t² – 3 v(t) = 2t +1 Find the slope of the tangent to the parametric equations at t=1.

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Q: dy in terms of t: Differentiate parametrically to find dx x = 4t2,y = 2t3 None of the other answers

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Q: Find the equation for the line tangent to the parametric curve: at the points where t = 5 and t =…

A: Solution is given below:

Q: Find dy/dx at t=1 by the given parametric equations. *=t² and y=t°. dy/dx is Blank 1. The answer…

A: Given,           The parametric equations are x=t2 and y=t3.To find : dydx at t=1

Q: dy dy Find dx 1 and for the parametric curve x = y = dr? NOTE: Enter the exact answers. dy dx It=2…

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Q: dy 1. Evaluate the dx for parametric equations x = 2t? – 4t and y = t2 – 2 with respect ot the…

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Q: = t4 + 1, 2t. y = d²y dx? For the parametric curve defined by x = O 3t2 None of these 6t? 12t? O 2t2…

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Q: 1 = sec.tAt the point (- dy 2 consider the parametric curve x (t) = tant and y (t) V3' V3' dx Vhat…

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Q: dy Find and dx d²y given the parametric equations: x = 2 – t and y = -1+5t2. dæ?

A: y=-1+5t2 dydt=ddt-1+5t2 dydt=-ddt1+ddt5t2 dydt=-0+10t dydt=10t take the second derivative…

Q: The curve C have the parametric equation: x(t) = t² + 1 and y(t) = t³ – 1 a) Make a sketch of curve…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

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

A: Givenx=t+1y=t2+3tt=−2

Q: Determine dæ dy and of the parametric equations dy dæ? 1. x (t) = t2 – 4t and y (t) = 2t³ – 6t - -

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Q: What is the length of the parametric curve x = t² – 1, y=– t on the interval 1s ts 3? Оa. 34 3 О. 32…

A: Given, x=t2-1, y=t33-t1≤t≤3

Q: For the parametric equation: x = 4t - 3 & y = t? +4, find dy/dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find 2 for the parametric curve c(t) = (3r³, 3r² – 3) at the point t = 4. (Use symbolic notation and…

A: Consider the parametric curve  ct=3t3,3t2−3 To find : dydxt=4

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.