Determine the Largest Set on Which the Function Is Continuous $F ( x , y ) = \arctan ( 10 x + 8 \sqrt { y - 5 } )$

question 33

Multiple Choice

Determine the largest set on which the function is continuous. $F ( x , y ) = \arctan ( 10 x + 8 \sqrt { y - 5 } )$

• A) \(\{ ( x , y ) \mid y \geq 5 \}\)
• B) \(\{ ( x , y ) \mid y \leq 0 \}\)
• C) \(\{ ( x , y ) \mid x \geq 1 \}\)
• D) \(\{ ( x , y ) \mid x \geq 0 \}\)
• E) \(\{ ( x , y ) | y \geq 3 , | 10 x + 8 \sqrt { y } \mid \leq 1 \}\)

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Definitions:

Break-Even Quantity

Break-even quantity is the number of units that must be sold for total revenues to equal total costs, at which point the company makes no profit but also incurs no loss.

Discounted Payback

A capital budgeting technique that calculates the amount of time needed to recoup an investment based on the present value of its cash flows, accounting for the time value of money.

Variable Cost

Overheads that see variation directly aligned with output quantities.

Operating Leverage

The degree to which a company can increase its profits by increasing sales, highlighting the fixed versus variable costs structure.