Systems of Linear Equations

An athlete can burn 9 calories per minute on a stationary bicycle,

11.5 calories per minute on a stair climber

The total amount of exercise is 30 minutes

In the 30 minute workout the athlete burns 300 calories

◦ How many minutes does the athlete spend on each type of exercise equipment?

x=(9) the number of min. on stationary bike y=(11.5) the number of min. on stair climber

x + y =30 (total workout time) 9x + 11.5y = 300 (calories burned)-----------------------------------------------------x + y = 30 (multiply by -9)-9x -9y = -2709x + 11.5y = 300_____________________________________________________________

2.5y = 30 y= 12 minutes on stair climber, therefore x= 18 minutes on bicycle 30 total minutes on equipmenty= 12 x 11.5 = 138 ; x = 18 x 9 = 162: Total

Calories=300

Maximum heart rate◦ R = 220-A◦ A= Persons age◦ B= Beats per minute

◦ (a) Find heart rate for a 20 yr. old and 70 yr. old ◦ (b) sketch a graph of R≤ 220-A◦ (c) Interpret the graph

220- 20= 200 bpm for a 20 year old person 220- 70 = 150 bpm for a 70 year old person

Systems Of Linear Equations with 2 Variables

x+y = 189.000 x-y= 20,000 2x=169,000 x= 84,500 84,500+y= 189,000 Y=104,500

X= 84,500

y= 104,500

chinadaily.com

X=+ 39, 525 Y= 13.75 39,525 divided by 13.75= 2874.5

There were 2,874 deaths in 1912 compared to 39, 525 deaths in 2003

FUNCTIONS

Fat Grams: A cup of milk contains 8 grams of fat.

(a) Give a formula for f(x) that calculates the number of fat grams in x cups of milk.

a) f (x) = 8x (b) What is the slope of the graph of f ? b) m=8 (c) Interpret the slope as a rate of change. c) As the number of cups increase by one,

the amount of fat increases by 8 grams.

Linear Equations

Target Heart Rate: A target heart rate T that is 70% of a person’s maximum heart rate is approximated by T=150-0.7A where A is a persons age.

(a)What is T for a person 20 years old? 60 years old?

T= 150-0.7 (20) T=136

T=150-0.7 (60) T=108

(Age, THR)(20, 136)(30, 129)(40, 122)(50, 115)(60, 108)

(b) Sketch a graph of T ( is greater than or equal to) 150-0.7 A. Assume that A is between 20 and 60.(c) Interpret this graph.

Series and Sequences

Chlorine In Swimming Pools

Initially the pool has chlorine of 3 parts per million

20% dissipates daily

No additional chlorine is added.

Day 1- 3ppm x .80 =2.4 ppm Day 2- 2.4 ppm X.80 = 1.92 ppm Day 3- 1.92 ppm x 0.80= 1.536 ppm Day 4- 1.536ppm x 0.80= 1.228 ppm

This is a geometric sequence with a common ratio of 0.80

The first four terms are: 2.4, 1.92, 1.536 and 1.228. Successive terms are found by multiplying the previous term by 0.80

Rockswold & Krieger, (2009)

Air Filtration

Each air filter removes 80% of the impurities.

How many filters are needed to remove 96% of impurities?

Polynomial function

Heart Rate of an Athlete running a 100- meter race. The race last 10 seconds.

A.) Does P(t)=0.2(t)2+5t+90 model the data in the table exactly?

P(0)=0.2(0)2+5(0)+90=90

The following table list the calories burned by a 140-pound person walking at 4 miles per hour for various lengths of times.

http://www.chinadaily.com.cn/english/doc/2005-05/13/content_441834.htm

McKinley Health Center, (2008). University of Illinois at Urbana-Champaign-Macronutrients: the Importance of Carbohydrate, Protein, and Fat. Retrieved on August 2, 2011 from http://www.mckinley. illinois.edu/Handouts/macronutrients.htm

Rockswold, G.K. & Krieger, T.A.(2009). Beginning and intermediate algebra with applications and visualization.(2nd ed.). Boston, MA: Addison – Wesley

http://www.smartmotorist.com/traffic-and-safety-guideline/what-causes-car-accidents.html