Question

1. A detective is called to a crime scene in an apartment. She arrives at noon and finds the thermostat set to 72 degrees F. She also finds a body, which is at 78 degrees F. She examines the area for clues, and then rechecks the body's temperature at 1:00 PM, and finds it to be 75 degrees F. Given that normal (living) body temperature is 98.6 degrees F, at what time did the murder occur?

2. A snowball melts such that its surface area decreases at a rate of 1 square centimeter per minute. How fast is its radius decreasing when its radius is 10 cm?

3. A small child accidentally lets go of their balloon which rises directly up from them at 5 feet per second. By the time they realize their mistake, the balloon is already 45 feet above them. Crying, they make a beeline for their nearby friendly neighborhood Spiderman to ask for help, running at 15 feet per second. It takes them 3 seconds to get to him. Spidey can aim at and web the balloon accurately if its distance to him is changing less than 20 feet per second. Can he save the day?

Answer 1

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