5(a) Determine the orthogonal trajectories of the family of electric field lines described by the family (x – c)³ + y² – c² (3x – c) = x³. %3D -

Q: 1. Find the first differentiation of this equation: a. y = (Sx2-3)a b. y = (4x2 – 7)3 c. y Sx+6…

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Q: 2) Find the derivatives of a) y = 7 - 6x-x² b) y - ³x 8 √x

A: Given :(a)y=7-6x-x2(b)y=-8x

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

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Q: 3) A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the…

A: To calculate the local linearization of the temperature at t = 1.

Q: Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) =…

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Q: Solve the pollowing: () (^) 2+j =j(xtjy) X = ? y=? (1) (2+j)(3-j2) = a+jb () (x-j2y) -(y-j«)-2tj a:?…

A: (a). Given  2+j1-j = j(x+jy)⇒ 2+j1-j×1+j1+j = -y+jx⇒ 2+2j+j-11+1 = -y + jx⇒ 12+32j = -y + jxBy…

Q: a) Suppose you are given model with two explanatory variables such that: Y₁ = a + B₁x₁i + B₂x₂₁x +…

A: Given: yi=α+β1x1i+β2x2ix+ui To find: Coefficients

Q: Determine which of the following pairs of functions are linearly independent. 1. f(t) = 3t, g(t) =…

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Q: Determine the magnitude and direction of the largest change 2 2 (x² + y²)z at the point M (1, -2,1).…

A: Introduction How sharply a curve rises determines its magnitude. It is simplest just examine the…

Q: Please find the requested derivative of the following functions. s²-4st+t² = 4, find 25 ds dt - ds…

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Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: L(x) = b) Use the linearization to approximate 125.1 ~

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Q: Determine which of the following pairs of functions are linearly independent. NO_ANSWER f(x) =e5 "…

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Q: Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(0) =…

A: The linear dependency of functions can be evaluated using the value of the Wronskian of those…

Q: say f(3)=5, f'(3)=-2 and let g(x) =xf(x/2) find the linearization of g(x) at x=6

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Q: 3. Find the derivative of the function f(x, y, z) = xy + yz + zx at the point (1,-1, 2) in the…

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Q: Find y as a function of a if y(1)=2, y(1) = 1. y = r²y" + 7xy +9y = 25,

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Q: Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(x) = cos² r independent on the…

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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.