# MATHEMATICS

Mathematics

The purpose of this group project is to solve a small real-world question using algebra. Group projects can also help students develop a host of skills that are increasingly important in the professional world (Caruso & Woolley, 2008; Mannix & Neale, 2005)
Please form a group of 2-6 students and work together on this. Individual work is not accepted. You only need to turn in one group work (remember to put every group members name on it). Show all steps, reasonings, and computations. You may use a calculator or computer software (e.g. MS Excel) in your work.

IMPORTANT
Use any math skills youve learned so far from this class or from your previous algebra classes. Algebraic work with an approximated answer will receive higher score than advanced calculus work* with an exact answer. The purpose is not to learn any new techniques but to explore concepts were learning using whats already available. If you ask an instructor or an engineer friend for help, be sure to tell them to explain using algebra or “Calculus up to our Ch 4.8 in our text”.(* By “advanced calculus work” we mean any calculus techniques that have not been discussed in our MATH 150, even if you have taken Calculus before.)

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Can you ask a tutor? Yes. Can you google this? Yes. But in the end every group member should be able to explain your work by themselves.

Grading
How many points you earn depends on the quality of your work and how close your solution is. Try to state the magnitude of the complexity of this problem (i.e. why cant we find the exact solution with just a few lines of work?) Draw your conclusion based on the assumptions made.

Some General Grading Criteria
Let p be your percentage error rounded to the 10th decimal. Let gbe your grade for this project.
If p4.187%, then g5/10
If p[0.286%, 4.187%): g will be around 6/10, depending on your work. If you do not carefully justify your steps you may get a 5/10 or lower.
If p(0.0287%,0.286%]: g will be around 7/10, depending on your work.
If p(0.00287%,0.0287%]: g will be around 8/10, depending on your work.
If p0.00287%and you fully explain how you arrive at your approximation, you will get g9.
If you use anything that we have not learned yet (and even you have learned it before coming to this class) you will likely earn a much lower grade than you expect!
Fuel Economy and Weight

Since fuel economy depends on a lot of factors, for simplicity we will only consider the factors of distance and the weight the car carries. Our goal is to calculate or estimate how far a car can travel with a fixed amount of fuel.

Taking distance, fuel quantity, and weight as the only variables, we assume everything else held constant (including the moving velocity at all times, road condition, tire condition, weather condition, speed limit, etc.) and we assume that the quantity of fuel consumed is directly proportional to the distance traveled and the weight the car carries (e.g. the longer the distance traveled, the more fuel consumed; the heavier weight the car carries, the more fuel consumed.) We further assume the density of fuel is 6 lb/gallon, and at any positive speed and any given moment, the car can travel 25 miles per gallon of fuel for every 1000 lb it carries.

Suppose a driverless car (total weight of the car without fuel: 1000 lb) has just been filled with 15 gallons of fuel, find the maximum distance this car can travel.

If you think the above description has too much information, just think about this question:
How far can a car travel with 15 gallons of fuel given its
fuel economy is 25 miles per gallon taking weight into consideration?
For this question you then find you need more information.

And you can challenge one by asking this simpler (harder?) question:
How far can a car travel with 15 gallons of fuel?

Objectives: Ratio, Proportion, Unit Analysis, Linear Modeling, Mathematical Modeling, …, etc.

The purpose of this group project is to solve a small real-world question using algebra. Group projects can also help students develop a host of skills that are increasingly important in the professional world (Caruso & Woolley, 2008; Mannix & Neale, 2005)
Please form a group of 2-6 students and work together on this. Individual work is not accepted. You only need to turn in one group work (remember to put every group members name on it). Show all steps, reasonings, and computations. You may use a calculator or computer software (e.g. MS Excel) in your work.

IMPORTANT
Use any math skills youve learned so far from this class or from your previous algebra classes. Algebraic work with an approximated answer will receive higher score than advanced calculus work* with an exact answer. The purpose is not to learn any new techniques but to explore concepts were learning using whats already available. If you ask an instructor or an engineer friend for help, be sure to tell them to explain using algebra or “Calculus up to our Ch 4.8 in our text”.(* By “advanced calculus work” we mean any calculus techniques that have not been discussed in our MATH 150, even if you have taken Calculus before.)

Can you ask a tutor? Yes. Can you google this? Yes. But in the end every group member should be able to explain your work by themselves.

Grading
How many points you earn depends on the quality of your work and how close your solution is. Try to state the magnitude of the complexity of this problem (i.e. why cant we find the exact solution with just a few lines of work?) Draw your conclusion based on the assumptions made.

Some General Grading Criteria
Let p be your percentage error rounded to the 10th decimal. Let gbe your grade for this project.
If p4.187%, then g5/10
If p[0.286%, 4.187%): g will be around 6/10, depending on your work. If you do not carefully justify your steps you may get a 5/10 or lower.
If p(0.0287%,0.286%]: g will be around 7/10, depending on your work.
If p(0.00287%,0.0287%]: g will be around 8/10, depending on your work.
If p0.00287%and you fully explain how you arrive at your approximation, you will get g9.
If you use anything that we have not learned yet (and even you have learned it before coming to this class) you will likely earn a much lower grade than you expect!
Fuel Economy and Weight

Since fuel economy depends on a lot of factors, for simplicity we will only consider the factors of distance and the weight the car carries. Our goal is to calculate or estimate how far a car can travel with a fixed amount of fuel.

Taking distance, fuel quantity, and weight as the only variables, we assume everything else held constant (including the moving velocity at all times, road condition, tire condition, weather condition, speed limit, etc.) and we assume that the quantity of fuel consumed is directly proportional to the distance traveled and the weight the car carries (e.g. the longer the distance traveled, the more fuel consumed; the heavier weight the car carries, the more fuel consumed.) We further assume the density of fuel is 6 lb/gallon, and at any positive speed and any given moment, the car can travel 25 miles per gallon of fuel for every 1000 lb it carries.

Suppose a driverless car (total weight of the car without fuel: 1000 lb) has just been filled with 15 gallons of fuel, find the maximum distance this car can travel.

If you think the above description has too much information, just think about this question:
How far can a car travel with 15 gallons of fuel given its
fuel economy is 25 miles per gallon taking weight into consideration?
For this question you then find you need more information.

And you can challenge one by asking this simpler (harder?) question:
How far can a car travel with 15 gallons of fuel?

Objectives: Ratio, Proportion, Unit Analysis, Linear Modeling, Mathematical Modeling, …, etc.