question archive The parish has decided to give the Catholic Youth Group an End-Of-Year celebration after their successful winter of activities and charitable projects
The parish has decided to give the Catholic Youth Group an End-Of-Year celebration after their successful winter of activities and charitable projects
Subject:MathPrice: Bought3
The parish has decided to give the Catholic Youth Group an End-Of-Year celebration after their successful winter of activities and charitable projects. The young folk and their chaperones have decided to go to the local amusement park on a beautiful sunny day.
1. One busy Chaperone pours herself some coffee into a paper cup before making her way to the amusement park. The coffee temperature is 350C when the cup is placed on the kitchen counter with room temperature of 20o. The Chaperone is called to the phone for last minute arrangements, and her coffee is forgotten. When she finally returns to her coffee 35 minutes later, the temperature has been decreasing by 1.2% per minute.
a. What type of function best models the cooling of a hot liquid? Explain your choice.
b. What is the mathematical model for this situation? (i.e. - the equation)
c. If the optimal temperature for drinking a hot liquid is 280C, at what time would the chaperone have had to return in order to enjoy her cup of coffee?
2. It is a beautiful sunny day at the fair. The U.V. index for this day is 8, or high, so sunscreen is a must for all people. The effectiveness of sunscreen is indicated by the sunscreen protection factor (SPF). The higher the SPF number the fewer U.V. rays can penetrate to burn the skin. When the protection factor (SPF), s, is known you can determine the percent, p, of the sun's ultraviolet rays that pass through it by using the following mathematical model:
a. What are the asymptotes for this function? Interpret the meaning of the asymptotes based on the scope of the problem.
b. Graph the function.
c. The sunbathers on the beach were using a sunscreen with SPF of 35. What percent of the sun's rays will pass through to skin?
3. The amusement park has a Ferris wheel with a radius of 6 m and it takes 2 minutes to complete one revolution. The bottom of the lowest carriage is 1 m above the ground. Consider the height of a specific carriage as the wheel rotates:
[Marks: a: 2; b: 2; c: 5; d: 3]
a. What are the independent and dependent variables?
b. Sketch the graph of a specific carriage over the first two rotations of the ride.
c. What is the mathematical model for this situation?
d. Determine the height of the carriage at exactly 1 minute, 30 seconds.
4. The young folk decide to ride the Terror Tower as the Chaperones opt to watch from the comfort of the ground! At its maximum height, the ride reaches 65 m above the ground. When one boy reaches the top of the tower, his gum falls out of his mouth. The height of the gum can be given by the mathematical model:
, where t is in seconds and h is measured in meters.
a. Find the average velocity of the gum on the intervals and .
b. Find the instantaneous velocity when t=1.5.
