your answer(s). Eliminate the parameter t. x = 4 sint - 4, y = 4 cost – 3

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A: We use a graphing utility to graph the given function.

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A: we need to integrate ∫0πe-tcose-t dt   we can do this integration by substitution.

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Q: 10. Answer the questions by comparing the equation, f(z) = 7 cos s(+9)) +1, to the general equation,…

A: To answer the question by comparing the equation, fx=7 cos2π7x+9+1,  to the general equation, fx=a…

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Q: Find T(t) and N(t) at the given point. T(0) N(0) x = e cost, y = et sint, z=et; t = 0

A:

Q: S(t)=t°-3tー+5 find accelercstuon of the purticle at t=1.

A: Here s(t)=t6-3t2+5 We have to find the acceleration at t=1.

Q: Example 3 Find k (t) for the circular helix K x = a cost, y = a sint, z = ct where a > 0.

A: Curvature k(t) of the vector

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Q: X= cos t, y= sin t; t= 6

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Q: Find T, Ñ and B for the curve 7 (t) = (5 cos(4t), 5 sin(4t), 2t) at the point t = 0 Give your…

A: the given curve is  r→(t)=5cos(4t),5sin(4t),2twe have to find a) T→(t)=unit tangent vector at t=0b)…

Q: 1.) y=sin(x) with an inflection point at t=pi 2.) y=cos(t) with an inflection point at t=pi/2 3.)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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A: both of the equation can be solved using the method of variable separable.

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Q: Solve the initial value problem for y as a function of x. dy x² + 121) 3 23, у(11)%3D0 dx The…

A: Topic:- integration

Q: (c) f(t) = e e-2t cost MUCS Yp(t) (d) f(t) = (3t² +t) cos t MUCS Yp(t) :

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Q: 9. Find a suitable initial interval for finding a positive root of the following equation which…

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Q: 1. Where does the graph of y = x“ + 4x – 1 have horizontal tangent? %3D - 2. Use the chain ule…

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: Find the length of the curve x=t/(1+t),  y=ln(1+t) ,0≤t≤2

A: Given curve x=t/(1+t), y=ln(1+t) ,0≤t≤2. Now we have to find length of curve as shown below

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A: solution:-v(t)=-2ln(t2+8), -10e-8tcos5tat t=5v(0)=-2ln(52+8), -10e-85cos55       =-2ln33,…

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Q: II ACTIVITY # 8: esinx dx use N=5 SOLVE USING TRAPEZOIDAL AND SIMPSON'S RULE

A: For trapezoidal rule  h = b-anh = π-05h = π5 x 0 π5 2π5 3π5 4π5 π esin x esin 0 = 1 esinπ5 ≅…

Q: 17. The displacement of a structure is defined by the following equation for a damped oscillation: y…

A: here the calculations are done taking t as x so just the variable change nothing different. Here…

Q: 2nt ), where S is the size in 24 The size of a fungus is given by the function S(1) = 3.61 +1.2…

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Q: Find T, Ñ and B for the curve 7(t) = (2 cos(4t), 2 sin(4t), 5t) at the point t = 0 Give your answers…

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Q: 6) Let x = t2 + 4t , y = 2 - t, for -4 <t < 1. (a) Eliminate the parameter and write the equation in…

A: 6 )  given :  x = t 2 + 4t , y = 2 - t  for - 4 ≤ t ≤ 1  Formula of equation of tangent line is , y…

Q: 10 has minimum value of 3 Зл The function y=2a sin| b(x+ 5)+a, 0<x< 2b2 and a y-intercept at the…

A: Solve the following question carefully as shown in the steps below.

Q: Find T, Ñ and B for the curve 7 (t) = (3 cos(3t), 3 sin(3t), 5t) at the point t = 0 Give your…

A: Space Curves and T, N, B vectors The unit tangent vector T, the unit normal vector N and the unit…

Q: 2. A curve C with equation y = sin2x 0 < x <5, has a stationary point, P. e3x dy (a) Find an…

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Q: 10. Circles tangent to the X-axis. Amm. [1 + (y)*]° =[yy +1+(]".

A: Every function can be described through a differential equation. The differential equation defines…

Q: for the functions below: a) if y-sinu, u-3x+n find dy/dx at point(0,1) b) Find for the function y =+…

A: we are given: y=sin u and u=3x+π ⇒y=sin (π+3x)=- sin 3x ⇒dydx=-3 cos 3xdydx(0,1)=-3 cos 3(0) =-3…

Q: Which of the following methods can be applied to find a particular solution yp of y"+y=cos(e-x)? A)…

A: Solution :-

Q: the eメロレt Solution of the folMoning equation

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: dy sin(y) - 4t with initial condition y(0) = 2 dt |3D Apply the forward Euler method with a step…

A: Since the given differential equation dydt=sin(y)-4t, y(0)=2 is in appropriate form for Euler's…

Q: Q1. Consider a spring mass system given in Fig 1 with mass of 1kg attached to a spring with K=10.…

A: The diagram showing the net forces on the mass is shown below. From the diagram,…

Q: 5. (4.9) A particle is moving with the given data. Find the position function of the particle:…

A: Acceleration function is given as a(t) = sin(t) + 3cos(t).Integrate the acceleration function to get…

Q: g. L[cos(3t – 4)] h. L[t³sin(2t)cos(2t)] i. [[te-atsin(at)]

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…

Q: 7. (a) Consider the cyloid given by x(t) = t - sin t and y(t) = 1- cost for 0 < t < 27. Find any and…

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Q: Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

A: The given function is y=t+sin t    for  0≤t≤2π. Sketch the graph of the above function as shown…