Section 0.3.  How many seconds are in a calendar year?  How can we convert 1 year to seconds?  What other time measurements do you know? ◦ 1 year =

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Presentation transcript:

Section 0.3

 How many seconds are in a calendar year?  How can we convert 1 year to seconds?  What other time measurements do you know? ◦ 1 year = 365 days (non–leap year) ◦ 1 day = 24 hours ◦ 1 hour = 60 minutes ◦ 1 minute = 60 seconds

To change 1 year to seconds multiply by fractions that are equivalent to 1.

Now you know that there are 31,536,000 seconds in 1 year, how would you find the number of second in 5 years?

When quantities are related like this, they are said to be in direct variation with each other. Name two other quantities that are a direct variation with each other.

Another example of direct variation is the relationship between the number of miles you travel and the time you spend traveling. In each case the relationship can be expressed in an equation of the form y = kx, where k is called the constant of variation.

 To qualify for the Interlochen 470 auto race, each driver must complete two laps of the 5- mile track at an average speed of 100 miles per hour (mi/h). Due to some problems at the start, Naomi averages only 50 mi/h on her first lap. How fast must she go on the second lap to qualify for the race?

 What do you know and what might you need to know?  Assign variables to the quantities that you don’t know.  Use a table to organize the information, and include the units for each piece of information. To qualify for the Interlochen 470 auto race, each driver must complete two laps of the 5-mile track at an average speed of 100 miles per hour (mi/h). Due to some problems at the start, Naomi averages only 50 mi/h on her first lap. How fast must she go on the second lap to qualify for the race?

Remember the relationship distance rate time, or d = r t. To qualify for the Interlochen 470 auto race, each driver must complete two laps of the 5-mile track at an average speed of 100 miles per hour (mi/h). Due to some problems at the start, Naomi averages only 50 mi/h on her first lap. How fast must she go on the second lap to qualify for the race?

It takes one-tenth of an hour, or 6 minutes, to do the first lap. You know that the distance for the second lap is 10 miles and the speed for the two laps must be 100 mph. Find the total time for the two laps. What does this tell you?

The time for the second lap must be zero, which is impossible. What would happen if the laps were 60 miles each rather than 5 miles?

Lab assistant Jerry Anderson has just finished cleaning a messy lab table and is putting the equipment back on the table when he reads a note telling him not to disturb the positions of three water samples. Not knowing the correct order of the three samples, he finds these facts in the lab notes. 1. The water that is highest in sulfur was on one end. 2. The water that is highest in iron is in the Erlenmeyer flask. 3. The water taken from the spring is not next to the water in the bottle. 4. The water that is highest in calcium is left of the water taken from the lake. 5. The water in the Erlenmeyer flask, the water taken from the well, and the water that is highest in sulfur are three distinct samples. 6. The water in the round flask is not highest in calcium. Organize the facts into categories. (This is the first step in actually determining which sample goes where.)

Container Source Element Position 1.The water that is highest in sulfur was on one end. 2.The water that is highest in iron is in the Erlenmeyer flask. 3.The water taken from the spring is not next to the water in the bottle. 4.The water that is highest in calcium is left of the water taken from the lake. 5.The water in the Erlenmeyer flask, the water taken from the well, and the water that is highest in sulfur are three distinct samples. 6.The water in the round flask is not highest in calcium.

ContainerBottle Erlenmeyer flask Round flask SourceWellLakeSpring ElementCalciumIronSulfur PositionLeftCenterRight

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur

1. The water that is highest in sulfur was on one end. 2. The water that is highest in iron is in the Erlenmeyer flask. 3. The water taken from the spring is not next to the water in the bottle. 4. The water that is highest in calcium is left of the water taken from the lake. 5. The water in the Erlenmeyer flask, the water taken from the well, and the water that is highest in sulfur are three distinct samples. 6. The water in the round flask is not highest in calcium. Read the statement. Use N for No and Y for Y along with a statement number to indicate special properties about the containers

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur 1.The water that is highest in sulfur was on one end. What is this telling you? N1

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur 2.The water that is highest in iron is in the Erlenmeyer flask. What is this telling you? N1 Y2

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur 3.The water taken from the spring is not next to the water in the bottle. What is this telling you? N1 Y2 N3

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur 4.The water that is highest in calcium is left of the water taken from the lake. What is this telling you? N1 Y2 N3 N4 N3

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur 5.The water in the Erlenmeyer flask, the water taken from the well, and the water that is highest in sulfur are three distinct samples. What is this telling you? N1 Y2 N3 N4 N5 N4

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur 6.The water in the round flask is not highest in calcium. What is this telling you? N1 Y2 N3 N4 N5 N4 N6

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur What do you know about the E Flask holding calcium? What do you know about the bottle holding calcium? What do you know about the other two containers holding iron? What do you know about the Sulfur? Analyze each block. N1 Y2 N3 N4 N5 N4 N6NY NN Y N

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur Analyze another block. N1 Y2 N3 N4 N5 N4 N6 NN NY Y N

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur What do you know so far? Calcium is in the bottle Lake water is not high in calcium Is the lake water in the bottle? N1 Y2 N3 N4 N5 N4 N6 NN N Y YN N YN And that the E flask has either lake or spring water since it cannot have sulfur.

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur From statement 5 we know that E flask cannot contain sulfur or be from the well. Since the Round flask has sulfur the E flask must be from the lake or spring. From statement 4 the water with calcium (bottle) is on the left and to the left of water from the lake and we know that the bottle is not in the center, the E flask is in the center and the from the lake. N1 Y2 N3 N4 N5 N4 N6 NN N Y YN N YN Y Y Now fill in no’s and yes’s. N YN

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur Filling in No‘s and yes’s in the first block N1 Y2 N3 N4 N5 N4 N6 NN N Y YN N YN Y Y Now fill in no’s and yes’s. N YN NN NY From statement 1 the Round flask must be on an end so it is on the right. N N Y

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur N1 Y2 N3 N4 N5 N4 N6 NN N Y YN N YN Y YN YN NN NY N N Y Bottle E Flask Round Flask Well Calcium Lake Iron Spring Sulfur Y Y Y N N N N

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur N1 Y2 N3 N4 N5 N4 N6 NN N Y YN N YN Y YN YN NN NY N N Y Bottle E Flask Round Flask Well Calcium Lake Iron Spring Sulfur Y Y Y N N N NY Y Y N N N N N

Bottle E flask Round flask CalciumIronSulfurWellLakeSpring Left Center Right Lake Well Spring Calcium Iron Sulfur N1 Y2 N3 N4 N5 N4 N6 NN N Y YN N YN Y YN YN NN NY N N Y Bottle E Flask Round Flask Well Calcium Lake Iron Spring Sulfur Y Y Y N N N NY Y Y N N N N N Y Y Y N N NN

1. The water that is highest in sulfur was on one end. 2. The water that is highest in iron is in the Erlenmeyer flask. 3. The water taken from the spring is not next to the water in the bottle. 4. The water that is highest in calcium is left of the water taken from the lake. 5. The water in the Erlenmeyer flask, the water taken from the well, and the water that is highest in sulfur are three distinct samples. 6. The water in the round flask is not highest in calcium. BottleE FlaskRound Flask Well Calcium Lake Iron Spring Sulfur

There are five houses along one side of Birch Street, each of a different color. The home- owners each drive a different car, and each has a different pet. The owners all read a different newspaper and plant only one thing in their garden. ● The family with the station wagon lives in the red house. ● The owner of the SUV has a dog. ● The family with the van reads the Gazette. ● The green house is immediately to the left of the white house. ● The Chronicle is delivered to the green house. ● The man who plants zucchini has birds. ● In the yellow house they plant corn. ● In the middle house they read the Times. ● The compact car parks at the first house. ● The family that plants eggplant lives in the house next to the house with cats. ● In the house next to the house where they have a horse, they plant corn. ● The woman who plants beets receives the Daily News. ● The owner of the sports car plants okra. ● The family with the compact car lives next to the blue house. ● They read the Bulletin in the house next to the house where they plant eggplant. Who owns the zebra? How many different variables? Build a chart with all the variables.

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clue Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clue Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 12

Clue 13 Okra Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clue Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clue Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clue 2 Dog Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clue Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clue Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clean up Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clean up Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

Clue 4 and clean up Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 5 and clean up

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 7

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 3

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 11

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 12

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 6

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 2

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 10

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 15

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 13

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 13

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 12

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse Clue 13 and clean up

Who owns the Zebra? YellowBlueRedGreenWhite CompactVanStation Wagon Sports CarSUV BulletinGazetteTimesChronicleDaily News CornEggplantZucchiniOkraBeets CatHorseBirdDog Zebra

12345 Red Green White Yellow Blue Station Wagon SUV Van Sports Car Compact Gazette Times Daily News Bulletin Chronicle Zucchini Corn Eggplant Beets Okra Dog Bird Cat Horse