Given the parametric equations x = 20 + sin 20, y =1- cos 20, dy whereð is the parameter, dx

Q: Consider the parametric equations x = 4 cos(0) and y = 2 sin(0). (a) Create a table of x- and…

A: We know that   cos(-θ)=cosθ  and   sin(-θ)=-sinθ

Q: Find the Cartesian equation of the curve: [2r/r2 = 1+ cos a]

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

Q: Consider the following parametric equation. x = 5(cos 0 + 0 sin 0) y = 5(sin 0 – 0 cos 0) What is…

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Q: A set of parametric equations is given as x = t+2 cos t and y =t+sin t. Find dy in terms of t. i. dx…

A: Given parametric equations arex=t+2cost and y=t+sintfindi) dydx interms of t.ii) d2ydx2 when t=π3

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: Graph the parametric equations x(t) = cott ly(t) = sin² t

A: Consider the parametric equations x(t)=cot ty(t)=sin2t

Q: By eliminating the parameter, determine the rectangular equation equivalent to the parametric…

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Q: Match the parametric equations with the correct graph. x = t cos(t), y = t, z = t sin(t), t2 0

A: First we add x2 and z2

Q: Given the parametric equation x = t+ lnt and y = t - Int %3D dy d²y Find and dx da? Find the point C…

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Q: Given the parametric equations below, eliminate the parameter t to obtain a Cartesian equation 0 <t…

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Q: A ball is kicked upward from the ground, with an initial velocity of 44 meters per second, at an…

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Q: (b) Given that cos (t) Vos(21) sin' (t) Jos(2)" |cos(2t) dy Find for the parametric equation given…

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Q: 1.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

Q: Determine the number of cusps for the hypocycloid described by the parametric equations x(t) =…

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Q: Given the parametric equation of a curve: x(θ) = sin θ − 1 and y(θ) = θ + cosθ a. Find dy/dx b. Find…

A: Given that  x(θ) = sin θ − 1 and y(θ) = θ + cosθ To determine the  Find dy/dx b. Find d2y/dx2   c.…

Q: Show that cos(18θ)=cos^3(6θ)−3cos(6θ)sin^2(6θ) and use this identity to find an equation in…

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Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: Find Dx 2 y of the following parametric equations: x= cos t y= sin t

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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: Match the parametric equations with the correct graph. e0.9t t 0 cos(9t), y sin(9t), z e = ZA Z A 2…

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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: What Cartesian equation is equivalent to the given parametric equations? x (t) = 4 sint ly (t) = 4…

A: Squarring then add

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: 20. Find y" in the parametric equations x = cos 0, y = 2 sin“ 0. A) sec' Otan 0 B) sec 0 C) sin…

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Q: Write the parametric equations x = 2 sin? 0, y = 9 cos? 0 in the given Cartesian form. y = with 0 <…

A: Simplification of the functions helps to find the parametric equation. Trigonometric identity…

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: Given: R(t) = (cos t + t sin t) î + (sin t – t cos t) ĵ + t?k ,t>0 Find parametric equations for the…

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Q: Find in terms of t for each of the following parametric equations. and dx dx a x=r - 3, y =r'+1 1+3…

A: 23 b. Consider the parametric equation x=t+3t and y=t2-4t. Differentiate x=t+3t with respect to t…

Q: For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). X = 3t – 4t +…

A: a x = 3t2 -4t +2 y = t3 -2t2 + 2t -5  dy/dx and d2y/dx2 =? dx/dt  = 6t -4 d2x/dt2 = 6 dy/dt = 3t2…

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: Given that x (t) = 3 sin t, y(t) = 2 cos² t, convert the parametric equations into the Cartesian…

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Q: Consider the following parametric equation. - 5(cos 0 + 0 sin 0) %3D y = 5(sin 0 – 0 cos 0)

A: Given,         The parametric equations are x=5cosθ+θsinθ and y=5sinθ-θcosθ

Q: Find T(t) and then find a set of parametric equations for the tangent line to the helix given by…

A: Consider the equation of helix given by r(t). Find the value for t , derivative at t and modulus of…

Q: Consider the parametric equations below. x = t?, y = t3 X =

A: Given data:     The first parametric equation is: x=t2. The second parametric equation is: y=t3.…

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: Find parametric equations for the line tangent to the helix r(t) =(sqrt(2)cos t)i + (sqrt(2) sin t)j…

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Q: Consider the following. x = sin(t), y = csc(t), 0 < t < A/2 %3D %3D (a) Eliminate the parameter to…

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Q: The x and y coordinates of particle P, executing simple harmonic motion, are [x = A cos wt, y = A…

A: Given statement is "The x and y coordinates of particle P executing simple harmonic motion, are…

Q: Graph the parametric equations below (x(t) = 3 cost + cos 3t ly(t) = 3 sint - sin 3t

A: To graph the parametric equations.

Q: If x(t) = 7 sint+ 9 and y(t) = 8 cos t + 3, eliminate the parameter to write the parametric…

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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: By eliminating the parameter t, sketch the following parametric equations x y = 6 cos t.. 6 sin tand…

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Q: For the following parametric equation determine d'yldx2 in the indicated value of the parameter 37 x…

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Q: Given the parametric equations x= 2t + sin 2t and y=2- cos 2t , where t is the parameter, dy = dx A…

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Q: By eliminating the parameter t, sketch the following parametric equations x = 5 sin tand y = 6 cos…

A: Both the given equations are x=5sinty=6cost Take squares of both the equations and add them…

Q: For the parametric equations x = cos(t), y = 3 sin(t), find the equation of the tangent line to the…

A: Given that the parametric equations of a curve is                               x = cos (t) ,   y =…

Q: 26 Given the parametric equations x=4cos? r and y = 5sint. Find dy when t= dx

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Q: 2. Given the parametric equation: x= 4 cos (t), y=9 sin (t), 0 <t< 2n, a) sketch the curve and…

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.