Sally Is on a Day Hike at Mt

question 62

Essay

Sally is on a day hike at Mt.Baker.From 9 to 11:00 a.m.she zig-zags up z = f(x, y)where x is the number of miles due east of her starting position, y is the number of miles due north of her starting position, and z is her elevation in miles above sea level.Feeling tired, she decides to continue walking, but in such a way that her altitude remains constant from 11 a.m.to noon to settle her stomach for lunch.At 11:30 a.m., she will be passing through (2, -1, 5)where f_x(2, -1)= 3 and f_y(2, -1)= -2.
What is the slope of her "path" in the x, y plane at this instant? (This "path" is among the level curves in the plane.)

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Definitions:

Compounded Continuously

The theoretical concept where the interest on an investment is calculated and added to the principal continuously, leading to exponential growth.

Compounded Annually

Interest on an investment that is calculated once per year, taking into account the interest that has accumulated up to that point.

Compounded Daily

The process of calculating interest on both the initial principal and the accumulated interest from previous periods, with the compound frequency being every day.

Federal Deposit Insurance Corporation

A U.S. government agency that insures deposits in banks and thrift institutions for at least $250,000 per depositor, per bank.