Give the family of orthogonal trajectories of y^2=Cx^5+5.

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A: Given:  The family of curves: 3x2 − y2 = C

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A: Given curve is y2=Cx3.

Q: 10. y = Ce 2x

A: We have to find  orthogonal trajectory

Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

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A:

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A: Given,          y=ax2+4ax+4a, where a being paarameter.

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A:

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A:

Q: Find the orthogonal trajectories to the family of curves:

A: Consider the given equation. x2=C-12y2lny2-1 Find the derivative of the function with respect to x.…

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A: In auto regressive model, the value of future variable is predicted using past values.

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A: Solution is given as below:

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A: we have to define "hyperbolic" trajectories

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Q: .2 7. y= cx

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Q: Please use the conjugate gradient method to solve min구 + z. (): with the starting point r1)

A: We will convert the minimising function into matrix form to apply the conjugate gradient method.

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A: To find out the critical points and denote it's nature.

Q: i Explain. Reducible the working procedure of Equation to Homogencous. form.

A: Given: Procedure of equation Reducible to Homogeneous form.

Q: Define Orthogonal Trajectories ?

A: Definition of Orthogonal trajectories:        Given a family of curves , an orthogonal…

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Q: Please answer number 5 determine the equation of the orthogonal trajectories of the following…

A: Given that        ex + e-y = C1 Here we have to find the equation of the orthogonal trajectories.

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A:

Q: Find the orthogonal trajectories of the functen X + ce-X which is . passing Thieugh (-2.0)

A: We need to find the orthogonal trajectories of the function y=x+ce-x, which is passing through (-2,…

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.