OK, y’all, I trust that you know the formulae for area and circumference of a circle. As I said in class, one way to keep them straight is to remember that area is always given in square units which means that a unit had to be squared. (cm x cm = cm2) So, area is the formula with the squared radius.
You have to complete section 1-9, largely on your own. Treat it like a proof packet which will have to be turned in. Much of it is review from middle school math but I’ll give you tips in case you’ve forgotten the details.
1-7) Basics (Draw a quick sketch for 6 and 7)
8-11.) Read directions. Don’t use a calculator.
12-15) I changed the directions to read “Find the circumference of the circle to 4 significant figures.” Refer to the sheet I gave you in class for help with significant figures. Use a calculator.
16-19.) Draw these out. For some sides, you’ll need the distance formula.
20-26.) Be careful with units. They must be the same. Give two answers, one in each unit given.
27-32.) Again, leave pi in your answer and give the units.
33-36.) Use the pi key on your calculator unless you happen to know pi to 9 decimal places. This time, give the area to 5 significant figures.
37-38.) What’s it going to be – addition or subtraction? You choose. One way is clearly easier for #38 but you can do it either way.
39.) Part c is good general knowledge to have. A square foot is a square with 1-foot sides.
40-46.) SKIP
47-49.) I know these are simple to do mentally but I’d like to see you create solvable equations from formulae. For each of these, follow this algorithm:
a. Top line – formula (No values substituted into the variables yet.)
b. Next line – fill in the parts that you know, making an equation
c. Solve, keeping your = signs lined up.
d. You will need to repeat this twice for 50c.
50.) Use good ole’ common sense for part a and b. For part c, this is an important skill to have. Pay attention to this… it says to “write a formula for the area of a square – “ (A) – “in terms of its perimeter. “- (P) This means that your formula will start with A= and can only have a P for its variable. The s variable will be the bridge from one to the other. Solve for s in the perimeter equation and then substitute what you get into the area equation.
51.) It helps to label each face of a solid with a number in order to draw its net.
52.) Use inches throughout the problem and show the units in each step. As mentioned above, units act just like variables. When you multiply inches by inches, you have inches2. If you divide inches2 by inches, you’ll have inches.
53-54.) SKIP (too easy)
55-56.) Just do it.
57.) Read the rounding part carefully. ( If I round a number to the nearest ten, that number must end with at least one zero. If I round a number to the nearest hundred, it will end with two zeros.)
58.) Good algebra practice. Show the expression that you used to find the answer.
59-62) SKIP
63.) Don’t forget that you’re first finding a diameter. Read carefully to decide whether or not to calculate pi.
64.) Refer to class notes on using your calculator to make tables of values. Specifically:
a.) Are you in FCN mode? You should be.
b.) In this mode, the variable will always be x. Your work will have b’s (for the base) but change them on your paper to x’s.
c.) Write an equation for the height of this corral in terms of the base (x). Hint: There’s 100 feet of fencing available so you will write an equation that looks like this: ______ + h = 100. Look at the picture. Solve this equation for h. (In other words, get h alone.)
d.) We enter equations into the calculator with the y= key. Enter your equation for h. (Clear whatever is on your y= screen.)
e.) Use TBLSET to start at 1 and to make steps of 1. Quit TBLSET. Show your table. (2ND GRAPH) Do you know what the columns represent?
f.) Now you want another column for the area of the corral. You will enter an area equation as y2. You will need to multiply every value of x to its corresponding y1 value. There is not a key for y variables but they’re in there. Find the VARS key. (VARS – YVARS – Y1)
g.) So your y2 equation will be y2 = xy1.
h.) When you press TBL now, you will have three columns. The first is the list of possible integral bases, the second is the corresponding heights if you’re using all 100 feet of fencing and the third is the corresponding areas. Isn’t that cool?!
i.) Find the greatest area and give its dimensions.
LOOKING AT THE TABLE, WRITE ALL THE VALUES ON YOUR CALCULATOR SCREEN WHEN THE HIGHEST AREA IS RIGHT IN THE MIDDLE.
j.) To see the graph, you have to adjust your window. We know that the x-values (the possible bases) range from 0 to 100. Well, not really but that’s a decent range. The area values range from 0 to something around 1400. (I’m not telling.) To set my window (the part of the graph that we can view), I enter the smallest and largest x’s for Xmin and Xmax. Then divide the difference by 10 to get XStep. Do the same for y’s. Reset your window to those numbers.
k.) We’re told to graph the base on the horizontal axis and the area on the vertical. We need to turn off the height equation so we don’t see it when we graph. Just go to the y= screen, highlight the = sign for y1, and press ENTER. This should un-highlight the = sign and turn off this graph.
DRAW A PICTURE OF YOUR GRAPH AND GIVE THE DIMENSIONS OF YOUR VIEWING WINDOW.
PHEW……….. Aren’t you glad that most of this assignment was so easy? This will seem easy to you once you’re halfway through advanced algebra next year.
65.) Awesome question. Easy to answer but harder to comprehend.
66-68.) I like this one too. Don’t be afraid to use variables as if they were numbers. They ARE numbers for us. Of course your answers will have variables in them. For #67, you could look back at your work for 50c and see if it worked.
69.) This is a cool problem. Now that you know the Pythagorean Theorem so well, you can find two squares with radicals in their sides whose areas add up to an 11 X 11 square. Find three squares with integral sides that add up to the 11 x 11 square. I just used guess and check. I didn’t find four squares but I did find more than four that added up to the right answer.
70.) Let’s use four significant digits for the answer. Think carefully about the radius of the two circular ends of the field. This problem isn’t bad, huh?!
