Francesca

The effectiveness of Roman rule can easily be seen in the fact that the fall of Rome led to 1) political chaos and economic collapse in western Europe 2) the rapid rise of a new European empire

16 years ago

1.) Find the producers' surplus if the supply function is: S(q) = q^7/2+3q^5/2 + 54. Assume the supply and demand are in equilibrium at q= 25. 2.) S(q) = q^2 + 12q and D(q) = 900 - 18q - q^2 The point at which the supply and demand are equilibrium is (15,...

13 years ago

Use the definite integral to find the area between the x-axis over the indicated interval. f(x) = 36 - x^2; [-1,13] So, what does be the area between the x-axis and f(x) equal? Thank you for any help! I'm really confused with this problem!

13 years ago

what are the best desciiptions of both push and pull facors?

15 years ago

Can someone please calculate this: 48(-1/2)^6 The answer is 3/2, but I get 3/4. What am I dong wrong?

14 years ago

I want to verify that this is correct: An arithmetic sequence begins, 116, 109, 102 • Determine whether -480 belongs to this sequence, if it does, what is its term number? -480 = 116 + (n - 1)(-7) n - 1 = 85.142. . . So, that means -480 does not belong to...

14 years ago

An arithmetic sequence begins, 116, 109, 102 Find the 300th term of this sequence.

14 years ago

Find the inverse of f: R→R given by f(x) = x³ – 2

14 years ago

Determine the domain and range of: y = 5 – [1/ (1 + x)] So, would the domain be all real numbers except -1? And would the range be all real numbers except zero? I'm really confused. . .

14 years ago

Find g ° f f(x) = {(1, 2), (2,1), (3,1), (4, 4)} g(x) = {(1, 2), (2,4), (3, 1), (4, 3)}

14 years ago

An archer shoots an arrow horizontally at a target 14 m away. The arrow is aimed directly at the center of the target, but it hits 59 cm lower. What was the initial speed of the arrow? So, I am trying to find find v₀x. . .

14 years ago

f: A→B, g :B→A Is g ° f defined? If so, what is its domain and range? Any suggestions?

14 years ago

So, I uploaded the figure in photobucket, and if you type flutegirl516 in the search bar you will see it's the first photo. F:B→C, h:C→B, and G:A→C Is F°h°G defined? If so, what is its domain and range? Yes it is defined. And I thought that the domain and...

14 years ago

Hi, I need help with interpreting a figure. You can find it one photobucket. First, type in flutegirl516 in the search bar and then click on the message that says: "Are you looking for the Photobucket user flutegirl516? Click here to see this user's profi...

14 years ago

Congruence True or False: (give reason) _ __ 2 ∈ 18 (mod 8) Can someone please help with this problem? I'm confused. . . Thanks for any helpful replies.

14 years ago

Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. n³ + 5n is divisible by 6 I really do not understand this to much. This is what I have so far: n = 1, 1³ - 5(1) = 6, which is divisible by 6 Then I really don'...

14 years ago

Use mathematical induction to establish the following formula. n Σ i² / [(2i-1)(2i+1)] = n(n+1) / 2(2n+1) i=1 Thanks for any helpful replies :)

14 years ago

Use mathematical induction to prove the truth of each of the following assertions for all n ≥1. 5^2n – 2^5n is divisible by 7 If n = 1, then 5^2(1) - 2^5(1) = -7, which is divisible by 7. For the inductive case, assume k ≥ 1, and the result is true for n...

14 years ago

Theorem: For every integer n, if x and y are positive integers with max(x, y) = n, then x = y. Basic Step: Suppose that n = 1. If max(x, y) = 1 and x and y are positive integers, we have x = 1 and y = 1. Inductive Step: Let k be a positive integer. Assume...

14 years ago

Find f(1), f(2), and f(3) if f(n) is defined recursively by f(0) = 1 and for n = 0, 1, 2, . . . • f(n+1) = f(n) + 2 So, would it be f(n) = f(n+1) + 2? Or would I just keep it like the original and plug in 1, 2, 3. Thanks for any helpful replies.

14 years ago

Why use mathematical induction to get the sum of a sequence? Also, if there are any websites you can recommend that will be a help too. However, I need an explanation rather than examples. Thank you for any helpful replies.

14 years ago

Solve the recurrence relation a_n = -2a_n-1 + 15a_n-2, n ≥ 2, given a₀ = 1, a₁ = -1. x² + 2x - 15, the distinct roots 3 and -5, so a_n = C₁(3^n) + C₂(-5)^n. The initial condition gives a₀ = 1 = C₁ - C₂, a₁ = -1 = 3C₁ - 5C₂. We obtain C₁ = C₂ = 1/2 and so...

14 years ago

Solve the recurrence relation a_n = -6a_n - 1 + 7a_n-2, n ≥ 2, given a₀ = 32, a₁ = -17. This is what I have figured out so far: polynomial: x² + 6x - 7 distinct roots: 1 and -7 I do not understand how to find C₁ and C₂. How do I complete this problem? Tha...

14 years ago

Is this correct? • Using the Principle of Inclusion-Exclusion, find the number of integers between 1 and 2000 (inclusive) that are divisible by at least one of 2, 3, 5, 7. A = {n| 1 ≤ n ≤ 2000, 2 |n} B = {n| 1 ≤ n ≤ 2000, 3 |n} C = {n| 1 ≤ n ≤ 2000, 5 |n}...

14 years ago

Can someone help? Very confused. . . John Sununus was once the governor of New Hampshire, and his name reminds one of the authors of a palindrome (a words which is spelt the same way forwards as backwards, such as SUNUNUS). How many seven-letter palindrom...

14 years ago

isisDOTpolyDOTedu/courses/discretemath/problemsDOTpdf Link is above can you please take a look? Specifically #21 on pg. 345. [There are 900 3DN], I need help with g-h. Thank you.

14 years ago

A factory makes automobile parts. Each part has a code consisting of a letter and three digits, such as C117, O076, or Z920. Last week the factory made 60,000 parts. Prove that there are at least three parts that have the same serial number.

14 years ago

Gaseous nitrogen has a density of 1.17 kg/m3 and liquid nitrogen has a density of 810 kg/m3. [The relative molecular mass of nitrogen is 28.0] What is the mean volume per nitrogen molecule in each case? What is the mean separation between nitrogen molecul...

14 years ago

Two cars collide head on while each is travelling at 80 km/hr. Suppose all of their kinetic energy is transformed into thermal energy. What is the temperature increase of each car? [You may assume that the specific heat capacity of each car is that of iro...

14 years ago

1.) Express each decimal number as an 8-bit binary number in the 2's complement form and then find the negative of the representation of that number in two’s compliment a.) +18 b) -117 Thanks for any help!

14 years ago

Imagine that you are a system administrator for a company, and that the company operates from two locations Phoenix and Boston. Phoenix has 350 hosts and Boston has 2100. Given that the following class C IP addresses have been assigned to your company as...

14 years ago

1.) Encrypt the hexadecimal message F9E8 using the Rail Fence cipher for binary numbers with 3 Rails. [Give answer in hexadecimal encrypted message] 2.) Decrypt the hexadecimal encrypted message CDEF created by the Rail Fence cipher for binary numbers wit...

14 years ago

How do I solve for negative modular arithmetic? Here is an example: -45 mod 13 = 7, but how?

14 years ago

Find the value of x: 20x ≡ 9 (mod 15)

14 years ago

The balance sheet of Burger King reports current assets of $30,500 and current liabilities of $15,800. Calculate the current ratio of Burger King and detemine whether it will increase or decrease as a result of the following transactions: -Paid $2,030 cas...

13 years ago

Can someone please help me find the derivative of the following: y = (-9e^7x) / (5x+3) Thank you!

13 years ago

Solve for x. .006x^3=8889 x = approx 114, but I don't understand how to get that answer. Can anyone help me solve? Thank you!

13 years ago

how do you solve: 4=1(2)/(x-2) Thank you!

13 years ago

An income-producing property is priced at $600,000 and is expected to generatethe following after-tax cash flows: Year 1: $42,000; Year 2: $44,000; Year 3:$45,000; Year 4: $50,000; and Year 5: $650,000. Would an investor with arequired after-tax rate of r...

12 years ago

Calculate the morality of a solution that contains a 4.0 mol of a solute dissolved in 12.0L of solution

12 years ago

Calculate the pH for each of the following cases in the titration of 50.0 mL of 0.150 M HClO(aq) with 0.150 M KOH(aq). The ionization constant for HClO is 4.0x10^-8. pH before the addition of any KOH? pH after the addition of 25 mL of KOH? Please show the...

10 years ago

A baseball is hit off the edge of a cliff horizontally at a speed of 30 m/s. It takes the ball 3 seconds to reach the ground, with no air resistance. How high is the cliff wall?

10 years ago

What is water treatment? Is it also the same with water filtration? Please answer! Thanks

8 years ago

on an island without squirrels some squirrels are introduced. a mathematical model of the population growth of squirrels on the island is given by the function f defined by f(x)= 1320/(1 + e^(5,1-0.66x)) where x is the time in years after the introduction...

7 years ago

Please suppose that the actual temperature is above 32 degrees F but the wind chill or real feel temperature is below 32 degrees F. Could water still freeze on the roadway surfaces?

6 years ago

Yes this is a multiple question. I think the answer is choice 1 but im not sure. - Francesca

16 years ago

By the way, my friend Jonathon, thinks it's 2. What do you think?

16 years ago

I think it is 1. But i'm not sure if choice 2 refers to the Byzantine Empire, which in that case, I think it would be 2.

16 years ago

I heard of them but i'm not exactly sure about them.

16 years ago

Thank you for responding. Hmm... IDK. . .I'll have to ask if that's a typo on the other end. Hey do you mind seeing if this is correct, and helping with the second part? Consider the geometric sequence that begins -3072 and common ratio –1/2. Find the 13t...

14 years ago

OK thank you!

14 years ago

Thank you!

14 years ago

OK Thank you!

14 years ago

ok thank you!

14 years ago

Well, I am suppose to find the composition of functions from a figure. If you don't mind I uploaded a photo of it on photobucket. Can you take a look, and offer any suggestions for the first problem, so that I can get an idea? Since this forum will not le...

14 years ago

I read the the link you provided previous to posting this discussion, but I was still confused.

14 years ago

I'm using the search bar at the very top right-hand corner, then I enter: flutegirl516. It will say no matches found, but it will say: Are you looking for the Photobucket user flutegirl516? You can also try using the search bar drop down menu and clicking...

14 years ago

ooOo I think I get it now. . .

14 years ago

Ok so g ° f = {(1, 4), (2, 2), (3, 2), (4,3)} There are two 1s in the range of f(x) though (1,2) and (3,1). . .Does that mean anything? Is this correct: Does g ° h = {(1, 2), (2?, 2?), (3, 2), (4, 1)}? For this one there was no 2 in the range of h. Also,...

14 years ago

"There are two 1s in the range of f(x) though (1,2) **I meant to say (2,1)** and (3,1). . .Does that mean anything?" Anyway, scratch this statement of the previous post. . .

14 years ago

Here are the functions from the figures: • f(x) = {(1, 2), (2,1), (3,1), (4, 4)} • g(x) = {(1, 2), (2,4), (3, 1), (4, 3)} • h(x) = {(1, 1), (2, 3), (3, 1), (4, 3)}

14 years ago

So is this correct? g ° f = {(1, 4), (2, 2), (3, 2), (4,3)}

14 years ago

There is something not connecting in my thought process. I'm still confused with g ° h does it = {(1,2), (3,1), (1,2), (4,3)}? I feel way off. . .I am doing something terribly wrong. IDK

14 years ago

Is this correct? g ° h ={(1,2), (3,1), (1,2), (4,3)}

14 years ago

Lol. . .But really Thank You! You are really helping me to understand. I know you are probably annoyed by my silly questions, but I am really starting to get a better understanding. Ok so would h ° h = {(1,1), (2,1), (3,1), (4,1)}? But the h² is throwing...

14 years ago

They appear a little strange. . .how so? The h² does not effect the answer at all? OK so last one f ° g ° h. . .I will attempt now, and check back and see if I am on the right track. . .

14 years ago

Oh it looks strange b/c they all end in zero. Just noticed. . . Is this correct? f ° g ° h = {(1,1), (2,2), (3,1), (4,2)

14 years ago

Hey, I know I said the previous would be the last one but can you check this one too. . . Let f: A→B be a function from A to B. f = {(w, 1), (x, 2), (y, 3), (z, 2)}. Find f^-1. Answer: f^-1 = {(1, w), (2, x), (3, y), (2, z)}

14 years ago

How about this? Let f: A→B be a function from A to B. f = {(w, 1), (x, 2), (y, 3), (z, 2)}. Find f^-1. Answer: f^-1 = {(1, w), (2, x), (3, y), (2, z)} So would this one not have an inverse?

14 years ago

Oh okay we posted at the same time. . .You were such a big help! I really understand this stuff a lot better. Thank you a thousands times!

14 years ago

Also thank you for the time you took out to help me :)

14 years ago

So, if A = (2,4,6) and B = (21,42,52) g : B -> A, wouldn't g = {(21,2), (42,4),(52,6)}? Is g ° f defined because it is one-to-one?

14 years ago

Figured this one out already had to use the equation: x = v₀x√(2h/g)

14 years ago

Can you give an example using numbers?

14 years ago

So, if A = (1, 2, 3) and B = (4, 5, 6) f: A -> B => {(1, 4), (2, 5), (3, 6)} g: B ->A => {(4,1), (5,2), (3,6)} g ° f = {(4,4), (5,5), (6,6), so g ° f = B right? And the domain and range are equal. But I'm still sure how it is defined? When finding the com...

14 years ago

I received that picture from my teacher. . .that's what she says is correct. That's why I am so confused. . .I didn't just make that up. . .So I really don't know what to follow, but I guess if I want to get a good grade I better just go along with the te...

14 years ago

Okay thank you

14 years ago

Thank you for replying. So if this question makes any sense: How do you know I must start with G first? It makes sense because it actually works when I create samples, but it seems that I am working backwards, why is that? But I think I am kind of followi...

14 years ago

So, how would F ° h ° G be defined? It seems the domain is A and the range is C, right? But why does it exist? Does it exist because it can be proven using sample problems or it it because of the figure and the direction of the arrows? IDK. That's what I...

14 years ago

Okay thank you for the clarification :)

14 years ago

So, this would read as : _ __ 2 = 18 (mod 8) Meaning this would be considered true, right?Because 18/8 = 2, and then 8 · 2 = 16, making the remainder 2. This might sound silly, but what does the symbol at the top of the number mean? _ 2

14 years ago

2 ∈ 18 (mod 8) It is true though, right?

14 years ago

Hmmm...I kind of get what you are saying, but why is 18 not a set that does not include 2? Here is an example in the book that is true: _ 55 ∈ 7 (mod 3) _ 7 (the line goes over 7 in the above) Why would this be considered true?

14 years ago

Could you tell me if I am correct in thinking: • With respect to congruence mod 29, 17 ∩ 423 = ∅ (True) • Let a, b, and n be integers with n > 1. Then a ≡ b (mod n) ⇔ a = b (False) •If ac ≡ bc(mod n), and gcd(c, n) = 1, then a ≡ b(mod m) (True)

14 years ago

I think I found something about the overbar _ a <--- equivalence class of a _ b <---equivalence class of b

14 years ago

OK. . .If you don't mind how about the these two too: • With respect to congruence mod 29, 17 ∩ 423 = ∅ (True) •If ac ≡ bc(mod n), and gcd(c, n) = 1, then a ≡ b(mod m) (True)

14 years ago

Yea I was thinking that too, that it is the same thing,but I will double check with the teacher. So,With respect to congruence mod 29, 17 ∩ 423 = ∅ would be considered false, right?

14 years ago

I am too guilty of double posting disregard above 11:51

14 years ago

Last thing I want to ask. . . 5x ≡ 5(mod 25) Is there an easier way to derive to the answer. Because I believed I learned the long version. This is what I know: The possible values are 0, 1, 2, 3 . . .24 5(0) - 5 = -5 not divisible by 25 5(1) - 5 = 0 not...

14 years ago

So, x = 1? Or can it be multiple answers? But what if I have a big equation like: 4x ≡ 320(mod n), n = 592

14 years ago

So, once I reduce it to this:x≡80 (mod 148). Then I have to do the trial and error process? Idk, I get how you got 80, but how did get 228, 376, 524. . .I think I see a pattern though each are incremented by 148. Hmm. . .I have another example that I woul...

14 years ago

So, I worked out a couple. . . 1.) 4x ≡ 2(mod 6) x = 0, 4(0) - 2 = -2 is not divisible by 6 x = 1, 4(1) - 2 = 2 is not divisible by 6 x = 2, 4(2) - 2 = 6 is divisible by 6 x = 3, 4(3) - 2 = 10 is not divisible by 6 x = 4, 4(4) - 2 = 14 is not divisible by...

14 years ago

OK you gave me a lot to think about. . .Thank you so much for your help. Until next time (which may be tomorrow). Thanks again :)

14 years ago

Thank you so much for your response! But I have completed that particular question. However, can you please help with this one? I am confused. . . Use mathematical induction to establish the following formula. n Σ i² / [(2i-1)(2i+1)] = n(n+1) / 2(2n+1) i=...

14 years ago

Any suggestions?

14 years ago

Ok thank you for your helpful response! I have a couple of questions though. . . Is the 15th line suppose to be '(k+1)(k+2)/(22k+3)'? Also, the 16th line = RS, which is what exactly?

14 years ago

Yea that's what I thought. . .Hey if you don't mind helping me further I have been working on this problem for a while and I am a bit stuck. IDK where to go from here or if I am doing it correctly: Use mathematical induction to prove the truth of each of...

14 years ago

Any suggestions?

14 years ago

Thank you for responding. Yes everything is typed correctly. I want to find what is wrong with proof.

14 years ago

No, the question verbatim is "What is wrong with this proof?"

14 years ago

Thank you! So, going back to your counterexample in post 9:52: x=4, y=6, n=max(x,y)=6 Why does it =6? Sorry if this seems like a silly question. . .

14 years ago

Oh okay. . .I get it. . .Thank you so much for your help :)

14 years ago

Here is the solution: The mistake is in applying the inductive hypothesis to look at max(x −1, y −1) . Notice that we are doing induction on n not on x or y. Even though x and y are positive integers, x −1 and y −1 need not be (one or both could be 0). In...

14 years ago

Ok thank for the responses, but there seems to be a contradiction between the two. Wouldn't f(1) = 1 + 2, which equals 3?

14 years ago

The f(n+1) is throwing me off what does that mean?

14 years ago

OK example: f(n+1) = 3f(n) f(1) = 3 f(2) = 6 f(3) = 9 Right?

14 years ago

Oops. . .Sorry disregard previous post. . .

14 years ago

f(n) is defined recursively by f(0) = 1 and for n = 0, 1, 2, . . . Find f(1), f(2), f(3)

14 years ago

Yes, they both follow the same recursive definition. I was just trying the second part on my own to see if I understand. Sorry about the misunderstanding. . .

14 years ago

So, this is how far I got. . .I getting weird numbers. . . -3072(1 - (-1/2)⁹) ------------------- = 1 - (-1/2)

14 years ago

REVISED QUESTION: Why use mathematical induction to prove the sum of a sequence is valid?

14 years ago

Sorry I still don't get it. Can someone please explain?

14 years ago

If you don't mind can you help with this problem? Solve the recurrence relation an+1 = 7an – 10an - 1, n ≥ 2, given a₁ = 10, a₂ = 29. The characteristic polynomial is x^2 - 7 + 10 with characteristic roots 2 and 5. Once again I get confused when I get to...

14 years ago

Oops posted twice. . .Sorry

14 years ago

Thank you so much for your help! I think I am getting the hang of it better. Can you please check: Solve the recurrence relation a_n = -5a_n - 1 + 6a_n - 2, n ≥ 2, given a₀ = 5, a₁ = 19. characteristic polynomial is x^2 + 5x - 6 it has the distinct root 2...

14 years ago

Oh I feel dumb. . . Ok so now a_n = C_1(1)^n + C_2(-6)^n a0 = C_1 + C_2 = 5 (1) a1 = C_1 - 6C_2 = 19 (2) So to find C1 I eliminated it by 6(1) + (2) <--is this allowed? (6C1 + 6C2) = 30 + (C1 - 6C2) = 19 ___________________ 7C1 = 49 C1 = 7 Plug this into...

14 years ago

Idk what happened at 7:24 I think my computer had a glitch or something and it reposted. This one is throwing me for a loop: Solve the recurrence relation a_n = 2a_n - 1 – a_n -2, n ≥ 2, given a₀ = 40, a₁ = 37. Characteristic polynomial: x^2 - 2 + 1 How d...

14 years ago

So the characteristic roots are 1?

14 years ago

How about this: Solve the recurrence relation a_n+1 = -8a_n – 16a_n - 1, n ≥ 1, given a₀ = 5, a₁ = 17. Characteristic polynomial is: x^2 + 8x + 16 with distinct roots -4. Since the roots are equal a0 = 5 = C1(-4)^0 + C2(0)(-4)^0 making C1 = 5, right? But...

14 years ago

So, going back to the previous 9:05. The solution is a_n = 40(1)^n - 3(1)^n, is this correct or way off?

14 years ago

Well a_1 = 37 not 31

14 years ago

Hey thanks a lot for help!

14 years ago

Okay I continued the first problem: |A ∩ B| = [2000/6] = 333 |B ∩ C| = [2000/15] = 133 |C ∩ D| = [2000/35] = 57 |A ∩ D| = [2000/14] = 142 |A ∩ B ∩ C ∩ D| = [2000/210] = 9 1000 + 666 + 400 + 285 - 333 - 133 - 57 - 142 + 9 = 1695 <--Answer

14 years ago

Any suggestions?

14 years ago

To be honest I haven't started yet, but your method sounds like a step in the right direction. . .I'll play around with it for a little and see what I get. . .If you figure out anything post. Hopefully someone who knows something will post cuz I'm lost

14 years ago

Oh okay I think I am following. . .

14 years ago

So, how many seven-letter palindromes contain at most three different letters one of which is S? We would start out with 26^3, but I don't understand how to make sure S will be included as one of the different letters. Any suggestions? Thank you.

14 years ago

Oh ok so there are 13800 that contain at most three different letters one of which is S.

14 years ago

Can you at all help with this? Multiple personality disorder (MPD) is a condition in which different personalities exist within one person and at various times control that person’s behavior. In a recent survey of people with MPD, it was reported that “98...

14 years ago

Ok now I am confused again with 5:08, it seems the same as the first subpart of the problem. They can't be the same answer, for this one: How many seven-letter palindromes contain at most three different letters one of which is S? And for the MPD problem...

14 years ago

Basically for the MPD problem I have to make it more precise.

14 years ago

THANK YOU! :)

14 years ago

588 is the correct answer? But, I don't understand how to get to that number. How did you calculate that? Sorry, that may be a lot to type out

13 years ago

588 is the correct answer!**

13 years ago

Yea I tried doing a google search, but nothing good explaining where to start. Thnx for the reply though

14 years ago

Sorry it's computing in security, so I guess that would fall under computers. . .

14 years ago

Thanks for your help! Also, I am kind of confused about finding the value of x. Example: 9x ≡ 1 mod 10 How do I solve this?

14 years ago

Any help?

13 years ago

Thank you guys!

13 years ago

Thank you!

13 years ago

1.) Find the producers' surplus if the supply function is: S(q) = q^7/2+3q^5/2 + 54. Assume the supply and demand are in equilibrium at q= 25. 2.) S(q) = q^2 + 12q and D(q) = 900 - 18q - q^2 The point at which the supply and demand are equilibrium is (15,...

13 years ago

Thank you!

13 years ago

Also, how would you calculate the IRR? Thank you for any help!

12 years ago

The given are (a) the speed of sound, which is 395 m/s, (b) the velocity of the moving source, which is 12 m/s, and (c) the frequency of the sound both cars are emitting, which is 395 Hz. Let's assume that f{o} is the frequency the observer can hear and f...

10 years ago

Thank you!

8 years ago