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juin [17]
3 years ago
11

Find the slope of a line through the following pair of points:

Mathematics
1 answer:
Zinaida [17]3 years ago
6 0
No slope i believe. good luck!
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Suppose a change of coordinates T:R2→R2 from the uv-plane to the xy-plane is given by x=e−2ucos(5v), y=e−2usin(5v). Find the abs
anzhelika [568]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The solution is  \frac{\delta  (x,y)}{\delta (u, v)} | = 10e^{-4u}

Step-by-step explanation:

From the question we are told that

        x =  e^{-2a} cos (5v)

and  y  =  e^{-2a} sin(5v)

Generally the absolute value of the determinant of the Jacobian for this change of coordinates is mathematically evaluated as

     | \frac{\delta  (x,y)}{\delta (u, v)} | =  | \ det \left[\begin{array}{ccc}{\frac{\delta x}{\delta u} }&{\frac{\delta x}{\delta v} }\\\frac{\delta y}{\delta u}&\frac{\delta y}{\delta v}\end{array}\right] |

        = |\ det\ \left[\begin{array}{ccc}{-2e^{-2u} cos(5v)}&{-5e^{-2u} sin(5v)}\\{-2e^{-2u} sin(5v)}&{-2e^{-2u} cos(5v)}\end{array}\right]  |

Let \   a =  -2e^{-2u} cos(5v),  \\ b=-2e^{-2u} sin(5v),\\c =-2e^{-2u} sin(5v),\\d=-2e^{-2u} cos(5v)

So

     \frac{\delta  (x,y)}{\delta (u, v)} | = |det  \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] |

=>    \frac{\delta  (x,y)}{\delta (u, v)} | = | a *  b  - c* d |

substituting for a, b, c,d

=>    \frac{\delta  (x,y)}{\delta (u, v)} | =  | -10 (e^{-2u})^2 cos^2 (5v) - 10 e^{-4u} sin^2(5v)|

=>   \frac{\delta  (x,y)}{\delta (u, v)} | =  | -10 e^{-4u} (cos^2 (5v)   + sin^2 (5v))|

=>  \frac{\delta  (x,y)}{\delta (u, v)} | = 10e^{-4u}

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3 years ago
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Find the sum of the data values, and divide the sum by the number of data values.

Find the absolute value of the difference between each data value and the mean: |data value – mean|.

Find the sum of the absolute values of the differences.

Divide the sum of the absolute values of the differences by the number of data values.

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Answer:

easy

Step-by-step explanation:oklook

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