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reason i say quadratic is because if a 10cm is $5, and a 20cm take four times the amount of raw materials, then it should cost four times the amount of a 10cm pizza. thus, it would cost $20.

it seems to me that it would be quadratic.

well as we doubled the diameter, the raw materials quadrupled.

now the second part of this question says that suppose that the price of each pizza will be directly proportional to the amount of raw materials you use. if you were to model your pricing structure as "price as a function of diameter", then would you expect that model to be linear, quadratic, or...

Homework Statement T or F? a pizza with 20cm diameter will require approximately half of the raw materials of pizza of diameter 40cm. explain your answer. Homework Equations The Attempt at a Solution my thinking is this, if we take the area of both pizzas, then we get 100(pi)...

thanks! i appreciate everyone's help.

hold on, if i plug in 1 for x, wouldn't i get 0 = 1?

the way i see it is that for any value i plug in for x (except 1), the left hand side will always give me a complex answer which does not equal 1.

if x < 1 then i will also get a complex solution here...therefore, i will always have a complex solution to the equation for any value of x except 0?

it seems to me that stating that the equation will give a complex answer when x>1

i'm not quite sure what it is the question is looking for ...

thus, sqrt of 1-x will always give us a complex answer?

i need some time to think about the reasoning here...i'm not quite sure i see it.

i see...then, may I use the same reasoning for part (d)?

well my thinking for part ii is that since (x-3) is always smaller than (x), then we would have a small number minus a big number which would give us a negative solution...thus, since the equation is equalled to 5, there must be no solution.

the only reason i can think of is that she's not really changing the orginal equation. she is only simplying it.

Homework Statement I am having trouble with question 4(c)... part i and ii... Homework Equations The Attempt at a Solution would it be okay for her to write iff between each line? I do not see why not but I cannot find the proper reasoning.

i got a[x+(b/2a)]^2 - [(b^2)/4a] + c where h=-(b/2a) and k=c-[(b^2)/4a]

Homework Statement Can someone assist me with number 3 please... Homework Equations The Attempt at a Solution I went ahead and rewrote f(x) in vertex form in terms of a,b, and c but I'm having a hard time writing down how f can be thought of as a transformation of g.

I did look at b and her math is correct but it's the reasoning that I am not seeing. I would have just taken the original 4 scores, added the fifth score, and divided by 5.

can someone help me out on #3 please. I can't see the reasoning behind her work.

you are correct that she "should" get 4 and 11 but i guess it doesn't matter since her process and reasoning is incorrect. unless the professor made a mistake in typing this question...thank you both for your input.

that makes sense as far as explaining her misunderstanding...but what about the property of fields/integral domains that her mistake is related to?

Homework Statement Mindy solves the problem (x+4)(x-3)=8 by setting x+4=8 and x-3=8, thereby getting the solutin x=4 from both equations. she checks her answer by substituting x=4 into the original equation and finds that it works. She concludes that this quadratic equation has only one...

also, how can i identify an isomorphism from H onto G? can i just say phi(a+b)=10^(a+b)=10^a times 10^b = phi(a) times phi(b). therefore, log (a+b) = log(a)log(b)?

I'm sorry, but I still do not see how this applies to logarithms...how do logarithms apply in showing that R+ maps to R?

1. Homework Statement [/b] The set of positive real numbers, R+, is a group under normal multiplication. The set of real numbers, R, is a group under normal addition. For the sake of clarity, we'll call these groups G and H respectively. Prove that G is isomorphic to H under the isomorphism...

so now, if I want to show that (x^3)^2 is congruent to +/-1 (mod 7) would my work be correct? (please see the attachment).

so how is this for an answer?: since 7 is a prime and the gcd(x,7) =1, then by Fermat's Little Theorem, x^(7-1)=x^6 is congruent to 1(mod7)

it states that if (a,p)=1 then a^(p-1) is congruent to 1 (mod p)

Homework Statement I'm suppose to prove that if (x,7)=1, then x to the 6th is congruent to 1 mod 7. Homework Equations The Attempt at a Solution Now, i have the proof by induction when (a,p)=1 but how do i apply this to prove it when a=x and p=7?

Homework Statement Let w be a primitive cube root of 1. show that 1, w,w^2 are the three cube roots of 1. Homework Equations The Attempt at a Solution I'm not quite sure how to even start this. any help will be greatly appreciated.

Homework Statement Let Z and W be complex numbers. If /Z/ and /W/ are rational and /W-Z/ is rational, then /(1/Z)-(1/W)/ is rational. Homework Equations The Attempt at a Solution How do I represent Z and W as rational complex numbers?

correct, but how do i show that?

I'm having trouble with number three. I know Viete's relations are X1+X2+X3, X1X2+X1X3+X2X3, and x1x2x3 for a cubic equation.

We are not using any books in this class. Everything is based off of lectures only. This is why I am having trouble.

Homework Statement I was able to do number one but can someone help me with 1(b) and 1(c)? I'm not too sure what they're asking. Homework Equations The Attempt at a Solution

Homework Statement Can someone help me out with number two please? I'm not sure what exactly it's asking me to do. Homework Equations The Attempt at a Solution

wow that's toughy

Well that's where I'm stuck. Since it says "rim of a wheel", my only guess is that it is moving along the x-axis. If this is the case, then it produces a cycloid right?

Can someone help me get started on number one please?

Homework Statement If the order of G is p^2 and p is prime, then show that G is either cyclic or isomorphic to ZpXZp... Homework Equations The Attempt at a Solution Any hints here will help!

Homework Statement let p be a prime number and let G be a group with order p^2. the task is to show that G is either cyclic or isomorphic to Zp X Zp. a. let a, not equal to the identity,be an element in G and A=<a>. What's the order of A. b. consider the cosets of A: G/A={A,g2A,...gnA}...

Homework Statement If G is a finite groups whose order is even, then there exists an element a in G whose order is 2. Homework Equations The Attempt at a Solution does this mean that a^2 is the identity? how can i prove this? Also, would't this make G cyclic?

Homework Statement (1 2) (1 4 5) (2 3 4) (2 5)= (1 4) (3 5) Homework Equations The Attempt at a Solution Can someone explain to me how to do this permutation? I know it's the easiest thing to do but i just went blank! how did my professor get (1 4) (3 5)?

could you maybe give me a few examples? It makes sense but the proof is a bit rough for me.

Homework Statement LET G BE A FINITE GROUP WHOSE ORDER IS DIVISIBLE BY THE PRIME P. SUPPOSE P^M IS THE HIGHEST POWER OF P WHICH IS A FACTOR OF |G|AND SET K=(|G|/P^M), THEN THE GROUP G CONTAINS AT LEAST ONE SUBGROUP OF |P^M|. I have the proof but can someone explain it in simpler terms...

Homework Statement If M and N are positive integers >2, prove that ((2^m)-1) is not a divisor of ((2^n)+1) Homework Equations The Attempt at a Solution Is this correct? I use the well-ordering principle. Let T be the set of all M,N positive integers greater than 2 such...

I consulted with my study partners and we agree that what you have is correct. But we didn't get exactly what you got so we had to make some corrections. thanks for your help.

Homework Statement Prove that they are no integers a,b,n>1 such that (a^n - b^n) | (a^n + b^n). Homework Equations The Attempt at a Solution Do I solve this by contradiction? If so, how do I start it?