Question

as katie calculus begins to make her rounds of trick or treat on halloween night, she decides to take a short cut through the cemetery. she is walking at a rate of 3 ft/sec. when she is 30 feet from a tombstone, she notices a ghost 40 feet above the ground rising slowly (dont worry, it is a friendly ghost, i believe the name of the ghost is casper). if the distance between katie and casper is increasing at a rate of 7 ft/sec, how fast is the ghost rising? part 4: which values are given in the original problem? check each correct answer. options: \\(\frac{dy}{dt}\\), x, \\(\frac{dc}{dt}\\), y

Explanation:

1. Analyze the problem: This is a related rates problem in calculus. Let's define variables: Let \( x \) be Katie's distance from the tombstone, \( y \) be the ghost's height above the ground, and \( c \) be the distance between Katie and the ghost.
2. Given values:

• Katie's walking rate: \( \frac{dx}{dt} = 3 \) ft/sec (though \( x \) is given as 30 feet, but in the options, \( x = 30 \) is represented as \( x \) value, \( \frac{dc}{dt}=7 \) ft/sec (rate of change of distance between Katie and Casper), and \( y = 40 \) feet (ghost's height, represented as \( y \) in options). \( \frac{dy}{dt} \) is what we need to find, so it's not given.
• So the given values are \( x \) (30 feet, represented as \( x \) in options), \( \frac{dc}{dt} \) (7 ft/sec), and \( y \) (40 feet, represented as \( y \) in options).

Answer:

The correct options are:

• The option with \( x \) (since \( x = 30 \) feet is given)
• The option with \( \frac{dc}{dt} \) (since \( \frac{dc}{dt}=7 \) ft/sec is given)
• The option with \( y \) (since \( y = 40 \) feet is given)