Homework Help Thread

[Alex]

o.o

I have holiday homework, though a couple of parts have stumped me - I wasn't here when it was taught, and the book isn't helping.

d) Solve the equation 3 sin (2x) = 1.5 using algebra to find the exact values of x.

Er. Help. What do I do? O.o

[Universal Senja]

I think this is how you do it... o_o

-------
Divide both sides by 3

sin (2x) = 1.5/3 = 1/2
-------
Take the inverse sine of both sides

2x = sin -1 (1/2)
2x = 45
-------
Solve for x

x = 22.5

[.neko.]

Ok, we're doing review in Chemistry this week and I cant figure out/remember/find how to do this question in my old text book. If someone with some knowledge of high school chemistry could explain what Im supposed to do I think I can solve it on my own.

1330 mL of gaseous hydrogen were at STP. The pressure was reduced at a constant temperature. The new volume was 1520mL. What was the new pressure in mm Hg?

Boyle's Law states that, assuming constant temperature, initial P*V must equal final P*V.
That is, P1 * V1 = P2 * V2.

Initial pressure, P1 = 760.0 mmHg (STP means pressure is 1 atm = 760 mmHg).
Initial volume, V1 = 1330 mL.
Final pressure, P2 = ?
Final volume, V2 = 1520 mL

Solve Boyle's Law for your unknown, P2, and plug in the known values.

P2 = (P1*V1)/V2
P2 = (760.0 mmHg * 1330 mL) / (1520 mL)

Notice the units mL cancel, leaving you with P2 = <b>665 mmHg</b>.

Hey thanks . I just realized I forgot all about this lol, I managed to figure it out, but I appreciate your help.

[Ammer]

I'm trying to learn a lesson I missed in Calculus and I can't seem to understand how to solve the book solved this problem,

Factor x^3-x^2-14x+24.

Solution
Possible values for p are +/-1, +/-2, +/-3, +/-4, +/-6, +/- 12 and +/- 24.
f(1) = 1 - 1 - 14 + 24 does not equal 0
f(-1) = -1 - 1 + 14 + 24 does not equal 0
f(2) = 8 - 4 - 28 + 24 equals 0
Therefore (x-2) is a factor of f(x)

Thye problem I'm having is, is with the part bolded in red. The book says that, the only possible values for p are divisors of the constant term in f(x) and I don't know what that means! Anyone know?

[.:Requiem:.]

Science...

I've been doing homework all night and my brain is fried for these...

A certain element contains 80 percent of an isotope of mass number X and 20 percent of an isotope of mass number Y. Is the atomic mass of this element closer t X or to Y?

[Alex]

I'm trying to learn a lesson I missed in Calculus and I can't seem to understand how to solve the book solved this problem,

Factor x^3-x^2-14x+24.

Solution
Possible values for p are +/-1, +/-2, +/-3, +/-4, +/-6, +/- 12 and +/- 24.
f(1) = 1 - 1 - 14 + 24 does not equal 0
f(-1) = -1 - 1 + 14 + 24 does not equal 0
f(2) = 8 - 4 - 28 + 24 equals 0
Therefore (x-2) is a factor of f(x)

Thye problem I'm having is, is with the part bolded in red. The book says that, the only possible values for p are divisors of the constant term in f(x) and I don't know what that means! Anyone know?

Erm. We did this a few weeks ago, but I can't remember how to explain it.

Basically, when you're trying to find out the factor of f(x) (eg. f(1), f(-1), and so on), the value you try has to be a factor of the 'constant' in the equation - in this case, 24.

I don't know if that helps, because I don't have my notes with me, but hopefully it made it a bit clearer

[shapu]

Science...

I've been doing homework all night and my brain is fried for these...

A certain element contains 80 percent of an isotope of mass number X and 20 percent of an isotope of mass number Y. Is the atomic mass of this element closer t X or to Y?

Mass number = number of protons + neutrons in a particular atom.

Isotope = A type of a particular atom that has a particular atomic mass number. One example is Carbon14. Carbon 14 is an isotope of Carbon, that has 6 protons (because that's the atomic number) and 8 neutrons. Carbon12 is another isotope of carbon - with six protons and six neutrons.

So let's do a thought experiment. Assume that this element has 5 protons, and two isotopes - one with mass 14 (isotope x, 9 neutrons) and one with mass 15 (isotope y, 10 neutrons).

Calculating atomic mass is simple - you take the ratio of each weight, times that weight, and add them up.

So, we'd take .8X + .2Y, or .8(14)+.2(15), which is 11.2+3, or 14.2 - closer to X.

No matter what weights you use, you'll get the same result - atomic mass is closer to X than to Y.

Last edited by shapu on Mon Sep 26, 2005 4:19 pm, edited 1 time in total.

[Yoshi]

I'm trying to learn a lesson I missed in Calculus and I can't seem to understand how to solve the book solved this problem,

Factor x^3-x^2-14x+24.

Solution
Possible values for p are +/-1, +/-2, +/-3, +/-4, +/-6, +/- 12 and +/- 24.
f(1) = 1 - 1 - 14 + 24 does not equal 0
f(-1) = -1 - 1 + 14 + 24 does not equal 0
f(2) = 8 - 4 - 28 + 24 equals 0
Therefore (x-2) is a factor of f(x)

Thye problem I'm having is, is with the part bolded in red. The book says that, the only possible values for p are divisors of the constant term in f(x) and I don't know what that means! Anyone know?

Hmm...I learned this in Math 11, not Calculus. O_o

Yeah, Alex is right. P is in the rule (x-p) such that if f(p)=0, then (x-p) is a factor of f(x). Note that it's x-(p), not x-(-p) or anything like that. It's taken by factoring out the constant.

So factor out 24 and you get all the values you just highlighted in red. Then you go through all those values until you find something that equals 0. Because this is a cubic function, use long division:

Code:

      x²+ x- 12
     ______________
x-2 ) x³- x²-14x+24
      x³-2x²
       -------
          x²-14x
          x²- 2x
         ----------
            -12x+24
            -12x+24
           --------
                  0


Then use the quadratic formula on the quotient above to find the other two factors. Which in this case ends up as x= -4, 3.

So (x+4)(x-2)(x-3) would be your answer.

[Ammer]

I'm trying to learn a lesson I missed in Calculus and I can't seem to understand how to solve the book solved this problem,

Factor x^3-x^2-14x+24.

Solution
Possible values for p are +/-1, +/-2, +/-3, +/-4, +/-6, +/- 12 and +/- 24.
f(1) = 1 - 1 - 14 + 24 does not equal 0
f(-1) = -1 - 1 + 14 + 24 does not equal 0
f(2) = 8 - 4 - 28 + 24 equals 0
Therefore (x-2) is a factor of f(x)

Thye problem I'm having is, is with the part bolded in red. The book says that, the only possible values for p are divisors of the constant term in f(x) and I don't know what that means! Anyone know?

Hmm...I learned this in Math 11, not Calculus. O_o

Yeah, Alex is right. P is in the rule (x-p) such that if f(p)=0, then (x-p) is a factor of f(x). Note that it's x-(p), not x-(-p) or anything like that. It's taken by factoring out the constant.

So factor out 24 and you get all the values you just highlighted in red. Then you go through all those values until you find something that equals 0. Because this is a cubic function, use long division:

Code:

      x²+ x- 12
     ______________
x-2 ) x³- x²-14x+24
      x³-2x²
       -------
          x²-14x
          x²- 2x
         ----------
            -12x+24
            -12x+24
           --------
                  0


Then use the quadratic formula on the quotient above to find the other two factors. Which in this case ends up as x= -4, 3.

So (x+4)(x-2)(x-3) would be your answer.

I understand what you're saying but isn't 8 a factor of 24? Why wasn't that included?

[fzun]

Alright, who here is good at bio?

The word part eu- means "true," pro- means "before," and kary- means "nucleus." With this information, explain why the words prokaryote and eukaryote are good terms for the orgasnisms they describe. What do the terms suggest about the evolution of these organisms?

Yeah, I haven't a clue XD

edit: And looking ahead at the rest of the assignment I found two more that I don't have a clue either.

3. What characteristic of eukaryotic cells gives them a greater capacity for specialization than prokaryotic cells have? Explain your answer.

4. Livestock in the western United States often die after eating a locoweed, such as Astragalus toanus. The chemical that the plant contains is also poisonous to plants. How does locoweed keep from poisoning itself?

[M. Bison]

o.o

I have holiday homework, though a couple of parts have stumped me - I wasn't here when it was taught, and the book isn't helping.

d) Solve the equation 3 sin (2x) = 1.5 using algebra to find the exact values of x.

Er. Help. What do I do? O.o

Senja, arcsin(1/2) is 30 degrees, not 45.
Aside from that, though, Senja's mostly right on this one. I just wanted to clarify a few things.

2x = arcsin(1/2)
Your teacher might prefer the answer in radians (they almost always do), and if that's the case, it would look like this:

2x = π/6
x = π/12

However, your teacher asked you for exact values of x that satisfy the equation. Because 25π/12 is just as valid an answer, you must account for it (and all the infinitely many) answers as well.

1/2 is positive, and the sine function is positive on the first and second quadrant, thus:

x = π/12 + k*2π, for all integers k
or
x = 11π/12 + k*2π, for all integers k

If that last step was unclear, let me know and I'll explain it in greater detail.

EDIT:
Fuzn, I've always hated biology, and consequently I don't know/remember too much. Take this answer with a grain of salt. Prokaryotes are organisms, usually single-celled, whose cells don't have a nucleus. Eukaryotes are organisms with cells that DO have a cell nucleus.

Prokaryotes were the first organisms to appear on Earth (as their cell structure in general is much simpler than that of Eukaryotes...and evolution had to run its course before things would get that complex). It would be my guess than, that Prokaryotes means roughly organisms that existed before other organisms had cell nuclei? Like I said, I'm just guessing.

Eukaryotes DO have a cell nucleus, and you might be able to get away with bending the Latin for "true" to mean roughly "with" in English.

[shapu]

Alright, who here is good at bio?

The word part eu- means "true," pro- means "before," and kary- means "nucleus." With this information, explain why the words prokaryote and eukaryote are good terms for the orgasnisms they describe. What do the terms suggest about the evolution of these organisms?

Yeah, I haven't a clue XD

EDIT:
Fuzn, I've always hated biology, and consequently I don't know/remember too much. Take this answer with a grain of salt. Prokaryotes are organisms, usually single-celled, whose cells don't have a nucleus. Eukaryotes are organisms with cells that DO have a cell nucleus.

Prokaryotes were the first organisms to appear on Earth (as their cell structure in general is much simpler than that of Eukaryotes...and evolution had to run its course before things would get that complex). It would be my guess than, that Prokaryotes means roughly organisms that existed before other organisms had cell nuclei? Like I said, I'm just guessing.

Eukaryotes DO have a cell nucleus, and you might be able to get away with bending the Latin for "true" to mean roughly "with" in English.

No, you can go with "True." Eukaryotes have a nucleus that stores DNA and allows the products of transcription (RNA) to exit the nucleus and create proteins. So, they have a "true center," which is what nucleus means.

Prokaryotes are recognized to be simpler than eukaryotes, so they must have come before nuclei evolved. That's my read on it, anyway.

edit: And looking ahead at the rest of the assignment I found two more that I don't have a clue either.

3. What characteristic of eukaryotic cells gives them a greater capacity for specialization than prokaryotic cells have? Explain your answer.

4. Livestock in the western United States often die after eating a locoweed, such as Astragalus toanus. The chemical that the plant contains is also poisonous to plants. How does locoweed keep from poisoning itself?

3. Another way of reading the question might help. What's the main difference between the two? Think about how this difference allows for more complexity and, therefore, specialization.

4. If you're learning about cellular organisms, you've probably also learned about how amoebas eat. If you haven't, look up the word "vesicle."

[Yoshi]

I understand what you're saying but isn't 8 a factor of 24? Why wasn't that included?

Oh, didn't see that. It should have been...seeing as +/- 3 was already in there. Someone left out the +/- 8.

[Universal Senja]

Senja, arcsin(1/2) is 30 degrees, not 45.

Er, yeah. You're right Bison. I don't know how I missed that. :\

Nice catch though. :)

[fzun]

Alright, who here is good at bio?

The word part eu- means "true," pro- means "before," and kary- means "nucleus." With this information, explain why the words prokaryote and eukaryote are good terms for the orgasnisms they describe. What do the terms suggest about the evolution of these organisms?

Yeah, I haven't a clue XD

EDIT:
Fuzn, I've always hated biology, and consequently I don't know/remember too much. Take this answer with a grain of salt. Prokaryotes are organisms, usually single-celled, whose cells don't have a nucleus. Eukaryotes are organisms with cells that DO have a cell nucleus.

Prokaryotes were the first organisms to appear on Earth (as their cell structure in general is much simpler than that of Eukaryotes...and evolution had to run its course before things would get that complex). It would be my guess than, that Prokaryotes means roughly organisms that existed before other organisms had cell nuclei? Like I said, I'm just guessing.

Eukaryotes DO have a cell nucleus, and you might be able to get away with bending the Latin for "true" to mean roughly "with" in English.

No, you can go with "True." Eukaryotes have a nucleus that stores DNA and allows the products of transcription (RNA) to exit the nucleus and create proteins. So, they have a "true center," which is what nucleus means.

Prokaryotes are recognized to be simpler than eukaryotes, so they must have come before nuclei evolved. That's my read on it, anyway.

edit: And looking ahead at the rest of the assignment I found two more that I don't have a clue either.

3. What characteristic of eukaryotic cells gives them a greater capacity for specialization than prokaryotic cells have? Explain your answer.

4. Livestock in the western United States often die after eating a locoweed, such as Astragalus toanus. The chemical that the plant contains is also poisonous to plants. How does locoweed keep from poisoning itself?

3. Another way of reading the question might help. What's the main difference between the two? Think about how this difference allows for more complexity and, therefore, specialization.

4. If you're learning about cellular organisms, you've probably also learned about how amoebas eat. If you haven't, look up the word "vesicle."

3. Well the main reason my book mentions is that eukaryotes have a cell membrane around the nucleus but I don't see how this would affect it really. My book does a bad job of explaning things x_x.

4. Actually, my teacher hasn't talked to us about amoebas at all. I've heard of them. They're a unicellular organism, correct?