its_victoria08

Ok, this is the only other question on this review I can't seem to figure out how to do.

"Determine whether the following mappings are 1-1 (injective) and/or onto (surjective). Justify your answers.

ii) alpha is a mapping from positive real numbers to all real numbers where alpha(x) = x - sqrt(x)

I believe it is 1-1 (injective) because every positive real number gives a real answer, but I don't know how to prove my response. I started with...

Assume alpha(x1) = alpha(x2), then show x1 = x2. So, then x1 - sqrt(x1) = x2 - sqrt(x2), but I don't know where to go from there in manipulating the function.

And I don't think the mapping is onto (surjective), but I have no clue where to start on proving my response.

Thanks.

I've been going in circles with this question for days. Any thoughts or help is much appreciated.

If gcd(a, b) = p, and p is a prime number, prove that gcd(a^2, b^2) = p^2. [Hint: let gcd(a^2, b^2) = d and let q be a prime divisor of d.)

I know that if gcd(a^2, b^2) = d, then d|a^2 and d|b^2, and if q is a prime divisor of d then q|d where d = nq, for some integer n. Also, if gcd(a, b) = p, then p|a and p|b, but none of that seems to help me any.

I completely understand the concept of this topic. When using the Washer Method and Shell Method for the same problem, you should get the same answer. With the same function/parameters with a different axis of revolution, I did it with both methods and got the same answer for both.

However, when the axis of revolution was changed, I am getting different answers using each method. Here's my processes... any help or thoughts about what I'm doing wrong would be greatly appreciated.

Given for both methods: Using the region bound by y = -x + 3 and y = 1, find the volume of the solid generated by revolving the region about the line x = 2 using the Shell Method and then the Washer Method.

Shell Method:

(i) Take vertical strips. (ii) Cylinder with height f(x) = - x + 3, thickness Δx, and width/length 2π(2 - x) [cylinder has radius 2 - x, so circumference is 2π(2 - x)].

V = ∫[0, 2] [2π(2 - x)(-x + 3)]dx = 2π ∫[0, 2] [(2 - x)(-x + 3)]dx = 2π ∫[0, 2] (x^2 - 5x + 6)dx = 2π[(1/3)x^3 - (5/2)x^3 + 6x] [0, 2] = (28/3)π

Washer Method:

(i) f(y) = -y + 3, g(y) = 0, h(y) = 2 (ii) Inner radius of washer: h(y)- f(y) = 2 - (-y + 3) = y - 1 (iii) Outer radius of washer: h(y) - g(y) = 2 - 0 = 2

V = ∫[1, 3] [π(2)^2 - π(y - 1)^2]dy = π ∫[1, 3] [4 - y^2 + 2y - 1]dy = π ∫[1, 3] (3 - y^2 + 2y)dy = π[3y - (1/3)y^3 + y^2] [1,3] = (16/3)π

I've done both of these about 3 or 4 times each and keep getting the same answers, and yet, I know they are wrong because the washer and shell methods are supposed to give the same answer. Any help would be greatly appreciated!

I understand this theorem, but there is one usage of it that I am uncertain of. Any explanation is appreciated.

Given F(x) = [1, x] ∫ √(1 + t^4)dt, find F '(x).

I know that F '(x) = √(1 + x^4) by the first fundamental theorem. But then it says to find d/dx[ [1, 2x^3] ∫ √(1 + t^4)dt ] -- in case that's not clear, the derivative of the integral from 1 to 2x^3 of √(1 + t^4) dt. I don't think you can just substitute 2x^3 in for x like previously... so, I tried splitting it into two added integrals, the first from [1, x^3] and the second also from [1, x^3], but I'm not sure that's allowed.

Anyway, if you could explain what to do if the integral is not from [n, x], but to something like [n, x^3] or whatever, I'd be very grateful.

Thanks in advance!

I have a Dell Latitude D505. I do not need comments on whether I have a good laptop or not. That's not the point.

I heard a tiny pop sound, and after that, my laptop is not recognizing the power cable. I don't think it's the cable. I've tried restarting the computer. Any suggestions?

Last month, we had a band trip in Dallas and I was supposed to be on my "empty" pills during that weekend. So I wouldn't have to deal with it, I skipped to the next month's pack instead of having my period.

I know that doing this once or twice in a row is OK, as I've spoken to my gynecologist about doing it, but I have a question and the doctor's isn't open today.

Can purposely skipping a month while on the pill cause the next month's period to be delayed?

The Bible has been undergoing the test of proof, and actually... it's amazing how much these men from so long ago knew, even while the ideas of their time periods were so incredibly different.

I was an atheist too, and I want to know:

What parts of the Bible are you confused with?

Which books don't make sense to you?

Where are the exact "contradictions" you claim are present?

How many of you have actually read the Bible itself (not chosen scriptures pasted onto a website)?

I know how I rationalized atheism before, so I am curious how others do it.

(Don't worry. I won't send you e-mails or IMs trying to convert you. This is merely a poll of sorts.)

If you would like, please read these two websites for more information:

Checkable Biblical Accuracy Table: http://www.doesgodexist.org/Charts/CheckableBiblic...

Examples of Scientic Accuracy of Bible:

http://www.pb.org/pbdocs/bibleac.html

Do you have any favorites? Any in your RSS feed? What are they about?

Think honestly about this before you respond because I want accurate answers. Just tell me how you would react. And don't try to say you'd freak out if you really wouldn't. Be honest.

Let's say you have an 18 year old daughter who is a senior in high school. She gets good grades, is very trustworthy and you know she would never do anything to betray you. She comes to you and says she really needs to have a serious conversation with you. She discloses that there is a boy she wants you to meet. He's 19, is a sophomore in college, and is the ideal gentleman. But, she tells you that he lives in another state and she met him online. She tells you that a few weeks prior, he drove 8 hours and stayed with her and her sister's house without you knowing. And now, this boy wants to talk to you (your husband) to get permission to date your daughter. He will drive 3 hours from where he is working in a nearby city.

Would you agree to speak to him? How would you feel and why? Thanks.

I'm doing a project in a class where I will be training my dwarf hamster, Gizmo, to go through a maze. The problem is, I can't find a food she is excited to eat!

Cheese doesn't work, and neither do those little yogurt bits they sell at pet stores.

I have celery and carrots. Which do you think she'd prefer?

I'm looking at buying a pet mouse. No, not a rat.

I would like to know an average starting price that would include cage and other necessities.

Also, does the cage have to be completely closed in (plastic) or can it be on of the metal barred cages? I saw a "mouse cage" at petsmart, but it was a metal barred one. It seemed like the mouse could get out...

I am pretty good in math (taking Calculus right now) and adults are always telling me that I should be an engineer...

What are the different types of engineers?

Is it really mostly math?

I had always thought that in high school, all of the baby spoon-feeding would stop. I thought that teachers wouldn't ask for assignments over and over again, and I believed that students would be held accountable for their own school and homework.

However, as a high school senior this year, I find this has not been the case. I have had teachers that would allow students to turn in assignments over 4 weeks late, and the only penalty was an automatic 30 point reduction. (In my school, a 70 or higher is passing.) This year, as a senior in high school, my AP Government teacher is requiring a notebook, spiral, and folder for her class and will be giving "notebook grades", to basically make sure that we keep up with our work! Shouldn't we know how to do this on our own by now? I mean, come on! We're seniors! College is just around the corner and no college professor is going to give "notebook grades".

Is my high school the only one sabotaging their students' college futures?

I have blisters (each about the size of the pad of my pinky finger) on each of my baby toes. They hurt really bad and one has seemed to get bigger.

My dad told me not to open it and let the liquid out or it will hurt worse... but it's getting so big that I think it's going to break just by me walking on it.

I bought those Band-Aid brand Blister Band-Aids... they are helping to keep them clean, but I want them to heal faster.

I have marching band practice on Monday and was hoping to get them feeling at least a bit better by then.

Thanks for any help.

On July17th, I had my first pap smear.

I just got a letter in the mail from my gynecologist that said "abnormal cells on pap (HPV negative)" and told me to come in between November and January for another pap smear.

It's HPV negative, so what else could the abnormal cells be?

It's driving me nuts.

I'm a virgin, and have only given oral twice, to two different guys. One was about 4 years ago and the other was last year. I don't want a lecture on what I've done, because trust me, I regret it enough as it is... but what could the abnormal cells be?

Oh, and if you are gynecologist or have experiences this, how weird would it be for me to call the office and ask? My doctor is very busy (always booked up for 2 months at a time), so I feel bad wasting her time.

I am a terrible cook. I usually eat alone, so would prefer recipes that can be either made for a single person, or make great leftovers.

Oh, and as the question says, I'm very picky. All meats except ground beef are out, and "strange" veggies aren't wanted either. I like beans and pasta and the normal fruits and veggies. I'm mostly looking for lunch/dinner recipes.

Thanks in advance.

I like eating fruit like strawberries, but they seem to go bad in a few days. I don't eat them quickly enough.

Is there a way to make fruit last longer? Especially bananas and strawberries.

We have a D-Link router (yes, I know, very stupid choice) that will lose the IP address every month or so.

We've tried doing the power cycle and that doesn't work. Sometimes, if we let it set alone long enough with the main computer off, it finds it... but it can take up to 8 hours for that to work.

Any suggestions? Dont' tell me to buy a new router... just try to help me get this one to work!

My niece is 2 years and a few months old and she has aproblem with my dad.

When she sees my dad she says "mad at you" for no reason. She won't give him hugs and when he tries to give her kisses she cries. But when he's going to bed or leaving, she'll say "I love you".

He isn't the disciplinarian when she's here... I am. I get onto her and she still loves me and prefers me over him.

She does the same thing with my sister's boyfriend. She used to adore him when he first began living with them (about 8 months ago), but now, she does the same thing as she does with my dad.

What are some reasons that a two year old would be doing this? Could it be because they are men?

Oh, and don't say she's been sexually abused, because she hasn't. I know this for a fact because my dad's never been alone with her and neither has my sister's boyfriend.