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.
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)...
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.
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.
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.
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.
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)?
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...
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?
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
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?
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)?
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?