Big-Little Principle

What is the Big-Little principle?

5.1A #51

this is just in case if anyone is confused about the diagram, it says that the fence is 35 ft long and shows the fence to include the two triangle bases and another portion left over. it really is the two bases of the triangle that lie on the fence that equals 35 ft excluding that extra portion.

im not sure about you guys but the diagram really confused me!

Assignment #27

Can someone discuss the 5.1A problems with me? I have 5th period lunch.

i like tonights hw!

5.1.61 Question

Can someone walk me through this problem, because when I attempt doing it I get a very messy problem. There is a lot of distributing and I want to know if there is a simpler way to do it.

Tutoring

I know it may be a little too late to help with this upcoming gsp test but I am going to start tutoring on a regular basis. If anyone needs help with anything in our class I would be happy to assist. I will be going at least every Friday and if anyone needs more or needs help on another day, I can offer that as well as long as there is advance warning.

-Fishface

gsp

for the gsp section, are we expected to know how to do some sort of special functions that we might have done in the past? if we do what are they? thanks
melissa

gsp test

Did he say what the GSP test was going to cover? I have been studying the past ones but I'm not sure what is actually on the test.

GSP Test

Just out of curiosity, what sorts of things did you guys put under the "other observations" part of the GSP practice test (the last question)? I put something about the way the graph moved as it went from concave up to concave down and vice versa, but someone probably came up with something more interesting than that...

Round the Room Questions

I am a little confused about how to do number 1 on the "You Still Expect Us to Remember That?" sheet. If any one could explain the process to do these I would greatly appreciate it. It is one of the few things I am a little unsure about, but I am probably just over looking something.

pretest 11b

does anyone understand 11b on the pretest?

pretest

The test days changed to Monday for GSP portion and tuesday is the test.
Can anyone help me on the pretest! um for number 9,10,11b and 13. thanks
when is the pretest due for extra credit?
melissa

Test days

I know that the test is split into two parts, the geometers sketchpad and the regular test, but does anyone know which is on which day? Are the pretests due together?

PS did anyone else think the pretest was harder than the others?

sum of roots

When finding b (the sum of the roots) and the roots are given to you, do u take into acount their signs (negative, positive)? Do you switch the signs or just add them with their original signs?

pretest number 4 and 13

4:
i got confused when i looked at the sign graph for number 4,
for A i thought that the degree was even because when the negative were plugged in they became positive, but i didnt understand why 04 was negative, if the degree were even wouldn't they all be even.
and for b i thought that the leading coeff was neg because if you raised a negative # by an odd degree ud get a neg. number and if you multiply a negative number by a negative number you'd get a positive number.

can someone please clarify how i should look at 4 a and b

13:
how do you start 13?
sarah iqbal

Pretest 11b and 13

If anyone knows how to do pretest problems 10b or 13 i would greatly appreciate any help...

#6 pretest

When you see that one of the zeroes is complex, but the equation is real, you know you have to get rid of that i. You get rid of it with its conjugate. Plug in the two roots given, (x+4) (x-2-5i) and the conjugate (x-2+5i). Expand for the answer.

How to solve number 11a on the pretest

Here is what i did to solve this problem:
First make z = a + bi and w = c + di.
Second, use the distance formula using these two points to get sqrt((a-c)^2+((b-d)*i)^2)
This is the true distance between the points.
Now, do abs(z-w). What this means is the distance from the origin after subtracting these two points. After subtracting them you get a+bi-c-di, or (a-c)+(b-d)i. Simply use the distance formula here to find the distance from zero to get the equation sqrt((a-c)^2+((b-d)*i)^2), which is identical to the equation found when using the distance formula of the two points directly.

I hope that helped... if not ask me to clarify please.

HW

do we have any homework due tomarrow?

Practice Test Issues...

There are a few problems on the practice test that are giving me a hard time:

6. This problem seems like it should be pretty easy, but I'm stuck on it. I tried several different methods, and everytime I tried to solve for b on my calculator, it would say "true" or "false" instead of giving me a value. In my most recent attempt, I defined f(x)=x^3+b*x^2-3*x+d on my calc, and then took f(2+5i) and set the answer [-21b+d-148+(20b-80*i] aside. I then took f(-4) and solved it for d. Since f(-4)=16b+d-52 and f(-4) also equals 0, d equals 52/(16b). I then tried plugging this value in for d in the equation -21b+d-148+(20b-80)*i=0 and solving for b, but my calculator simply replied, "false."

11a. and 11b. This question is daunting, although I should probably give it a second try. I have a feeling it relates to that grid/vector discussion we had in class the other day, and that whole thing went right over my head. If anyone understand this I could REALLY use your help!

13. Like Carrie, I honestly don't know where to begin.

ANY help would be GREATLY appreciated!!

Practice test #10 and #13

For number ten you can see from the graph that {-3, -1, -1, 1, 3, 3} are the roots. I started by turning the roots into factors so I had (x+3)*(x+1)^2*(x-1)*(x-3)^2. From there I'm not sure whether or not to add or subtract anything since the graph has a y intercept not at zero. Also, how would you come up with a second equation for this graph?

For number 13 I don't really know where to start. a≠1 is a solution how would you use that information to start a proof?

4.8, #58

Does anyone understand number 58? I don't even understand what it's asking, otherwise I would post a more specific question about it. Any help would be greatly appreciated!
Casey Blue

4.8# 31, 41

I'm having trouble getting rid of the complex part of the polynomial when i expand an expression based on the roots. Any suggestions on where to go after writing an expression for the polynimial based on the given roots?

supp. prob. 19-24

did we ever get them?

C3 Supplemental Problems for Tonight...

Did Mr. Karafiol post 19-24 of the supplemental problems and/or pass them out in class?

Assn 24 sec 4.4 # 60

I am at a loss. The equation for volume of a cylinder is pi*r^2*h, right. But I do not know how to go from there. Which variable should x represent or how could we get x to be one number.

Storing functions on TI-89

Does anyone know if there is a way to store functions so you can use them even after you start a new problem?

Quiz 2-1 # 3

In number 3 a function is given for widgets sold at x dollars, but then it asks for the revenue in the formula of r(x). I don't understand what the question is asking for. What is the answer and how do you get it?

HW question 37( a & b) (Assignment #23)

i know Mr. Karafiol explained how to prove the answer to 37a during class when we went over homework. But I can't find my notes of his explanation, does anyone else have them?

-thanks

4.4 # 58

For this one I tried using (22+x)500-15x but this number never gave me a max to use as the number of apple trees. Could someone tell me what they did? THanks

-Paul

4.4. Problem 60

I know there has been some confusion with 4.4.60., so I hope I can be of some assistance.

The way I did 60 is as fallows:

I first though of an empty sheet of metal and specific instructions (that being the problem.
We know that the can shall have two genereal shapes cut, in order to form it. These shapes would be circles for the top and base, and a rectangle which will be folded to consruct a cylinder to house the can's content. We know that the can's top must specifically be three tims as thick as the sides and bottom. So the rectangle must be the smae thickness as the base and the top must be the same material except three times as thick.

Now we can start thinking in mathematical reasoning.

Out of the material we should cut:
A Side: Rectangle (length * width)
A Base: Circle (pie*radius squared)
A top: 3 Circles because the top should be three times as thick as the base.(3*pie*radius squared)

Besides this we also know that the can should hold a volume of 355.
The volume of a cylinder is of course (pie*r^2)*height

Now lets get down to business:
The equation for the amount of metal used should be.

(3*pie*r^2) + (1*pie*r^2)+((2*pie*r)*height) = Amount of metal to use

As stated above there should be 3 circle cut: hence 3*pie*r^2
Also there should be 1 circle cut for the base:1*pie*r^2
These expressions give us the top and base.

The amount of metal cut for the side is both important and in question because the height of the rectangle is unknown. We do know that the other side of the rectangle is the circumference of a circlebecause the rectangle should be folded arond two circles to form a cylinder. Hence the expression for the width of the rectangle is 2*pie*r (expression fo the circumference of a circle).

We can solve for the height utalizing information that was given.
We are provided that the volume must be 355 and we know that the volume of a cylinder is (pie*r^2)*height.
There for we solve the equation for height and plug the expression into are equation for the amount of material to be cut.

You should get 355/(pie*r^2)

Plugging height into the equation for material you should get:

(3*pie*r^2) + (1*pie*r^2) + ((2*pie*r)*(355/(pie*r^2)) = Amount that should be cut

Now all that is left is two find the amount cut to minimize amount cut and meet the volume an thickness of top requirements. Simply put, graph the equation and find its maximun in a realistic window.

How do you make a scatter plot?

How do you make a scatter plot?

#60 in 4.4 and #5 in 6.6

I also don't know how to do #60 in 4.4 and also i dont know how to do the models on number 5 in 6.6. thanks melissa

4.4#60

Does anyone have any ideas on how to set up #60 in section 4.4. I know you have to use the formula for the volume of a cylinder but how do you account for the thickness of the metal?
Also, in 4.4 #15 and 17 what is meant in the directions by even and odd multiplicity?

RE: #3 on the Quiz from 11/6/06

Since we got the quizzes back yesterday, I think I'm allowed to post a solution now...

For number 3, we are told that the number of "widgets" purchased is n(x)=200-(x^2/100), and that the price per widget is $x. Since revenue is equal to the number of products sold times the price per product, the revenue here can be given by the equation r(x)=x*(200-(x^2/100)). To find the price that results un the maximum possible revunue, you graph y1=x*(200-(x^2/100)) and find the maximum on the graph. The maximum is at (81.6497, 10886.6), so this means the maximum revenue is $10,886.60 and that the price per widget should be $81.65 (we only had to include the second part to answer the question).

I hope this helps.

response to due date

the rabbit sheet is due either friday in class or monday, he said we'd discuss it on friday but he might not collect it until monday depending on whether or not he wants us to work more on our own

Those Rascally Rabbits!

Does anyone know when the rabbit worksheet is due?

Roots and degree

If you have an equation of, for instance, 5th degree, but only 4 roots, how do you write the equation in root form. Can anyone explain this concept to me?

Quiz

The third problem on the quiz confused me a lot, can someone explain how to do that problem. Please!!!!!!!

quiz

i know some people didnt take it but this is pretty general:

did anyone get a weird answer for the third one?

Using propFrac to Divide Polynomials

So there's this little function hidden in the Algebra menu called "propFrac," and it holds the secret to dividing polynomials. The function itself is designed to reduce expressions, and is the opposite of the "expand" function. The syntax follows the form of "propFrac(EXP/EXP)," and it will return an answer in the form Remainder/Divisor + Quotient.

questions

hey guys, for 4.2 i am not sure how to do number 23, and 45. thanks for ur help! melissa

factor theorem?

Can someone please explain to me how you use the factor theorem?

Will this work?

for number 51 on 4.2, will x(x-5)(x-8)-83 work as the polynomial?

Test question #11

The question asked what transformation in what order, produce the graph of y= the cube root of (8/3x + 1) from the graph of y= the cube root of x. My answer was scale horizontally by 3/8 and then slide left 1 unit, but sliding by 1 unit was wrong. What is the correct answer?

factor theorem confusion

can anyone explain how to do questions 33-37 (odd) and 57 in section 4.2?

supplement #7

can anyone help explain how to answer parts a and c of number 7 of the supplemental problems?

supplement #9, #11

For #9 i set it up as y=(x-315)^2+630. I thought to look for (115,y) on the graph since this is where it would have a width of 400 and to see if y was greater than or equal to 400 because then the cube would fit through. However, I got a concave up parabola and was confused. Any different ideas on how to approach this? Also, for number 11 on the supplement I am confused on how to set it up. Thanks

Karafiol's site is down

I cannot connect to mr. karafiol site, can anyone send me the hw problems for tonight? thanks.
email : goojiu@gmail.com