Pink Poogle Toy Forum

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

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

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

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?

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?

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

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.

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:



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?

Alright, who here is good at bio?



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.

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.

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.



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."

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

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

Nice catch though. :)

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?