For the set of parametric equations, find the derivative, and indicate points of horizontal and vertical tangency. x = 2t + 9t2 + 17 dy/dx= %3D y = 4t - 18t2 + 24t 29 Points of horizontal tangency: Points of vertical tangency:

Q: The function y=f(x) is given in parametric form by the equationsx=t+cost,y=1+sint,where t∈(0,2π).…

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Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = 2t3 -…

A: Topic- application of derivatives and tangent equation

Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

A: Given data: First curve xy=3. Second curve x2=9y.

Q: Find the slope of the tangent line to the parametric equations: x = 3t2 - 3, y = 2t + 1 at t = 1. %D…

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Q: Give the parametric curve: x = t3 - 6t2 y = t2 - 2t Find an equation for the line tangent at the…

A: We are given: x=t3-6t2y=t2-2t For Finding the equation of the tangent line , we will have to find…

Q: - Find dx2 for the curve defined by parametric equations x = t³ and y = e'.

A: Differentiate given parametric equation

Q: A particle follows the trajectory x(t) = t3 + 2t, y(t) = 20t – t2 with t measured in seconds and…

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Q: Find the Cartesian equation of a curve defined parametrically by 5t and y =10t for all real values…

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Q: Determine the x - y coordinates of the points where the parametric equation x = 3 sint y = 3 cost 0≤…

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Q: Find the points on the parametric curve c(t) (3t2 - 5t, t3 - 10t) where the tangent line has slope…

A: Given curve is Firstly, we find dy/dx

Q: The equation of the tangent line to the parametric equations, x =t +sint, y 4t-cost att 0 is y = -1…

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative…

Q: Parametric Equations Parameter - V, y = V1

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Q: The parametric equation of a curve is given by x= cost, y= sint− cost, 0 ≤ t ≤ 1 . Without…

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Q: Find parametric equations for the given curve. y = 4x2 - x

A: The given curve is y = 4x2 - x

Q: Find the slope of the curve whose parametric equation is given by y = t³ + t²+ 1/t and x = t⁴ + 3t²…

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Q: Given the curve with parametric equations, find the slope and the equation of the tangent line at…

A: Here we have to find the Slope of tangent line at indicated points . We are given parametric…

Q: find the slope of the parametric curve x=-6t-5, y=3t^3, at the point t=3

A: To find the slope we have to find dy/dx For that we find dx/dt and dy/dt first

Q: Give the parametric curve: x = t3-6t2 y = t2-2t Find an equation for the line tangent at the point…

A: Given parametric curves:

Q: Find the second derivative in terms of t for the parametric equations below- x=t² -t+2 y =t -3t

A: Given that, the parametric equations are x=t2-t+2 and y=t3-3t Find the first derivative in terms of…

Q: Determine all points on the parametric curve {x= 2t^3−24t y=t3−6t^2+9t−4 where the tangent slope is…

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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 an equation of the tangent plane to the surface at the given point. 2 x2 + 2z?ey - x = 33, P =…

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Q: Find the parametric equation for the line tangent to the r(t)=sinti+(t2-cost)j+etk curve t=0 at the…

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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…

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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…

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Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: find the equations of the tangent and normal to the curve expressed in parametric form at the point…

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Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: compute using the parametric equations I= cost, y = sin t, te (-x, 0) Write as a function (i) of t.…

A: Using chain rule,

Q: A curve C is defined by the parametric equations x(t) y(t) = 8t³ – 2t² + 4. Write the equation of…

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Q: of the points where the parametric equation y = 3 cost 0≤t≤ 2T will have a horizontal tangent.…

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Q: Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the…

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Q: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

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Q: Find parametric equations for the semicircle x2 + y2 = a2, y > 0, using as parameter the slope t…

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Q: A curve is given by parametric equations x = sec²t and y=csc² t. dy Find and d²y dx² dx in terms of…

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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 of the tangent line to the curve defined by the parametric equations x(t) = t3 +…

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Q: 3x + xy? 2y + x?y dy dx

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

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Q: The parametric equations of a curve are given by 1 = In (Vi +1) and y= cosh(2t). dy when t = 1. dr…

A: According  to question given thatx=ln(t+1)y=cosh-1(2t)

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

A: To find dy/dx and d2y/dx2.   Slope is given as = dy/dx.

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

A: The solution is given as follows:

Q: x = +4r2 +4t +1 y =1+3 at the point P(1, 1).

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Q: An airplane is flying in the direction 25° west of north at 800 km/h. Find the component form of the…

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Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x2 +?…

A: Given      x2 + z2 = 25 and y2 + z2 = 25 at the point (3,-3,4) Let    f(x,y,z) = x2 + z2 - 25  and…

Q: ) Find the equation of the tangent line (in terms of x and y) to the parametric curve at the given…

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Q: Given the parametric curve: x = t3-6t2 y = t2-4t What are all the points that the curve passes…

A: Given: the parametric curve:

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.