Find the Jacobian of the Transformation $$x = 5 \alpha \sin \beta , y = 4 \alpha \cos \beta$$

question 54

Multiple Choice

Find the Jacobian of the transformation.
$$x = 5 \alpha \sin \beta , y = 4 \alpha \cos \beta$$

• A)
• \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = 9 \alpha\)
• B)
• \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = 36 \alpha\)
• C)
• \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - 20 \alpha\)
• D)
• \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - 20 \alpha \sin \beta \cos \beta\)
• E)
• \(\frac { \partial ( x , y ) } { \partial ( \alpha , \beta ) } = - \alpha\)

Recognize the role and types of financing available to small businesses.

Comprehend how small businesses impact the U.S. economy.

Identify reasons for business failures and successes.

Gain insight into the structure and benefits of different business ownership types, including sole proprietorships, partnerships, and corporations.

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Definitions:

Administrative Agency

A government body responsible for the oversight and implementation of specific regulations and statutes within its area of authority.

Substantial Evidence Test

A legal principle that a decision must be supported by sufficient evidence that a reasonable person could accept as adequate to support a conclusion.

Proof Beyond A Reasonable Doubt

The highest standard of proof required in criminal trials, ensuring that there is no reasonable alternative to the conclusion that the defendant is guilty.

Rational Basis

A standard of judicial review that requires laws or actions to be reasonably related to a legitimate governmental interest.