Provide an appropriate response.
-x = 10u cos 5v, y = 10u sin 5v
A) 500u
B) 250v
C) 250u
D) 500v

Question

Quizplus · Accepted Answer

The given equations are in parametric form, where $x = 10u \cos(5v)$ and $y = 10u \sin(5v)$. To find an appropriate response, we can differentiate both $x$ and $y$ with respect to a parameter (let's say $t$) and then find an expression that relates $x$ and $y$. However, the question seems to be looking for a specific value or relationship, which might be related to the area or some other geometric property derived from these equations. Given the options, none directly relate to the differentiation of $x$ and $y$. However, if we interpret the question as looking for an expression related to the area (a common application of such parametric equations in polar coordinates), we might consider the formula for the area of a sector in polar coordinates, which is $\frac{1}{2}r^2\theta$, where $r$ is the radius and $\theta$ is the angle in radians. Given the form of $x$ and $y$, and without a clear path to directly apply this formula, it seems there might be a misunderstanding or a missing step in the interpretation.Given the options and assuming a possible missing context about deriving a quantity related to $u$ and $v$ from the given parametric equations, none of the options directly follow from the provided equations without additional context or operations. If we were to consider the derivatives or any operation that could lead to a product of $u$ and $v$, or their individual magnitudes, we would need more information or a different approach. The equations as given suggest a relationship in polar coordinates, but the options do not directly correspond to a common result from these equations, such as an area or a length, without further operations.Therefore, without additional context or clarification, it's challenging to provide a detailed explanation for the correct answer based on standard mathematical operations or interpretations of the given equations. The response seems to require an assumption or additional information not provided in the question.

Provide an Appropriate Response