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Sveta_85 [38]
3 years ago
7

Of the students in Mrs. Henderson's class, 3/5 participate in an after school sport. Of these,1/2 play lacrosse. What fraction o

f the students play lacrosse?
Mathematics
1 answer:
charle [14.2K]3 years ago
4 0
3/5 participate in after school sports...
of these, 1/2 play lacrosse......1/2 of 3/5..." of " means multiply..
1/2 * 3/5 = 3/10....so 3/10 play lacrosse
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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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Step-by-step explanation:

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Tristan's balance at the end of the month was $189.32.

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<em>Additional comment</em>

It can be tedious to enter these numbers correctly into a calculator. Many folks prefer a calculator that provides a "tape", a record of the amounts and operations the calculator uses in the computation. Alternatively, you can put the numbers in a spreadsheet and use the SUM function to do the addition for you. That, too, makes it easy to check that numbers have been entered correctly.

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The image below shows step-by-step on how to solve it.

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Step-by-step explanation:

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