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Hamster Lord

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need help with these two problems:
40) Circumference=2*pi*radius²
the question asks is the circumference a function of the radius or is the radius a function of the circumference
44) this one is about the general sherman tree. in this problem, the circumference of the tree is 102.6 ft. it says show how to find the diameter without measuring it directly and then find that value to the nearest tenth of a foot.
 

Orion

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need help with these two problems:
40) Circumference=2*pi*radius²
the question asks is the circumference a function of the radius or is the radius a function of the circumference
To be technical, it's both. Since it's an equation, the operations can be reversed to define one in term of the other, and vice versa. If it's got to be one, I'd say it's the circumference defined by the radius.
44) this one is about the general sherman tree. in this problem, the circumference of the tree is 102.6 ft. it says show how to find the diameter without measuring it directly and then find that value to the nearest tenth of a foot.
As mentioned above, C = 2*π*r²
We can re-organise the equation by applying inverse operations to both sides. We want to single out the r on the right hand side, so we want to apply operations that will steadily single it out, while also applying those operations to the left hand side. 2*π can be simplified and used as a constant on its own (tau - τ - which is equal to twice pi, so 6.2831 etc). The right hand side is made by multiplying tau by r², so to get r² on its own, we want to divide the whole lot, part of which will result in tau/tau, which we know would just be 1, and in terms of a multiplication, one is 'invisible'. As said before, we need to apply this operation to both sides, so we're left with
C/(2π) = (2π*r²)/2π
C/(2π) = 1*r²
C/(2π) = r²

Now on the right hand side, the value of r has been squared, so we want to find the square root of r², which will give us r on its own.
So:
sqrt[C/(2π)] = sqrt[r²]
sqrt[C/(2π)] = r

From here, you can just plug in the known values in the right hand side to establish the value of r, therefore:
C/2π = 102.6/6.2831 = 16.3293
sqrt[16.3293] = 4.041 ft radius
 

Luap

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I'm building a poster for my Environment Science AP class on the Japan Nuclear Crisis and I'm failing to find some information. So, maybe I can get some help here (with sources, please).

Firstly, were there any precautions to protect nuclear power plants from tsunamis?

Secondly, how did the tsunami lead to a release of radioactive material?

All I know is that the tsunami flooded the plant, cut the power, and broke some pumps, causing the cooling system to fail.
 

Dogenzaka

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We just got to angular momentum which I hear is a non-intuitive concept to grasp at first, and I'm having trouble.

We've got a problem that says,

A man, mass M, stands on a massless rod which is free to rotate about the center in the horizontal plane. The man has a gun (massless) with one bullet, mass m. He shoots the bullet with velocity Vb, horizontally. Find the angular velocity of the man as a function of the angle, theta, which the bullet's velocity vector makes with the rod.

So you've got a guy standing on one end of a rotating rod, and he shoots a bullet from an angle and starts moving.

My prof told me I have to determine first that the angular momentum in the direction we are moving is conserved. To do this, I must show that external torque in that direction is 0.

Since it's frictionless, the only two external forces acting on the man are gravity and normal force. When I use right-hand-rule and cross product of those two forces with the r displacement vector from the origin of pivot to the man, I get that their torques are in the horizontal axis, which has nothing to do with the direction I'm interested in.

L = r x p, so to determine the direction of angular momentum for the man, I do r x mv which she said the velocity vector was pointed into the board/paper

BeSz9.jpg


So that r x p = angular momentum in the upwards z-direction.

I don't understand why the velocity vector goes into the board? If the man shoots the bullet in that direction, he's going to move outwards from shooting the bullet inwards.

If anybody could clear up this one conceptual misunderstanding for me (which I've been looking all over the internet to try to understand) I would greatly appreciate it.
 

very differentiable
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You're quite right dogen, i guess your lecturer meant that the vector for the bullet was directed into the board, else i don't see how it's possible. Especially as the pivot is frictionless. I'd say the angular momentum of the guy is directed downwards.
 

Dogenzaka

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Just talked to her. She said I was right but it doesn't matter anyway since either way, the angular momentum for that is in the Z-axis (which I knew I just wanted to see why the velocity was in the direction she described).

So much frustration...wasted. Lol.
 

Xickin

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I've got an English assignment where I have to write an Essay comparing 1984 to my ISU Brave New World, so I need help coming up with a good hook-I've got the jist of it but I need someone to look it over please!

If our society continues in its advancement of technology with no regard for human emotions or rights, then eventually our government will take over our lives and we will become a number and not an individual person in society.
 

Taylor

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I've got an English assignment where I have to write an Essay comparing 1984 to my ISU Brave New World, so I need help coming up with a good hook-I've got the jist of it but I need someone to look it over please!

If our society continues in its advancement of technology with no regard for human emotions or rights, then eventually our government will take over our lives and we will become a number and not an individual person in society.

That is not a hook; that is a thesis.
 

Xickin

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Well then how can I grab the readers attention? I thought by mentioning human rights and emotions that it would catch anyones eyes! (PS in case no one has noticed essays aren't my fortey)
 

Nyangoro

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Things like surprising statistics or a real-life example can be hooks. Basically, they're something that jumps out at the reader and makes them think "oh snap, this sounds like serious business, I want to know what this paper is about."
 

Xickin

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O! I got it! How about this!?

In 1917 the Soviet Union formed and became a communist super power up until 1991 when its economy collapsed. In 1934 Adolf Hitler formed the Nazi party, whom started World War 2 and later fell after Hitler's death. These two party's failed because they were unable to control and unionize their peoples and countries; so how did these two fictional governments prevail?
 

Dogenzaka

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O! I got it! How about this!?

In 1917 the Soviet Union formed and became a communist super power up until 1991 when its economy collapsed. In 1934 Adolf Hitler formed the Nazi party, whom started World War 2 and later fell after Hitler's death. These two party's failed because they were unable to control and unionize their peoples and countries; so how did these two fictional governments prevail?

Not quite. It NEEDS to be within the first sentence. If I have to get to the second or third sentence to finish reading the main idea of your "hook", you've already lost me.
 

Dogenzaka

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I'm having a lot of trouble understanding Stokes' Theorem and Surface Integrals. I've done the homework for my course, the optional homework, practice tests, talked to my professor multiple times, etc. and I still can't get through a problem involving them intuitively without screwing up in a fundamental step of logic or understanding. The whole thing is so bizarre to me.

Surface integrals are having a parametrized function of two variables (say u and v) on the u-v plane and matching each of those points to a surface in 3D space on a separate coordinate system, or something like that, right?

Well Stokes' Theorem is messing me up because I still don't quite get how it makes sense. I have some 3D surface and if I project a section of that surface onto the x-y plane in two dimensions or something, I can take the area of that 2D surface, or the line integral of the 3D surface in space, and it is the same as that section of surface area in 3D space? wtf

So I end up having to take a surface, find out what the domain they want me to use, parametrize that, and then either use that or find the curve boundary and parametrize that and take the line integral? It's just so unintuitive to me.

I've tried watching the khanacademy videos which makes more sense but it's still a pretty sour concept with me. Does anybody think they can explain surface integrals or Stokes' Theorem to me better? Or maybe have some additional resources?

Thanks.
 

Amazing

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You have no idea how much these problems are pissing me off. Can you guys give me the formula for these problems?

R=1400 10% per year compounded quarterly for 8 years
Answer in the back of the book: 1st part $67,410.39 2nd part: $22,610.39

R=$800, 9% per year compounded monthly for 4 years
Answer in the back of the book: 1st part$46,016.57 2nd part $7616.57

The problems below are compounded annually
R=$1200 i= 0.075 n=8
Answer in the back of the book: 1st part $13475.82 2nd part $3875.82

R=$17,544 i=0.08 n=6
Answer in the back of the book: 1st part $138,997.66 2nd part $33,733.66
 

Amazing

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^

It isn't Compounding interest that I'm doing it's annuities and right now I'm having a problem doing annuity problem compounding quarterly formula
 

Xickin

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I went to my English Teacher today and said to redo it and take away any specific names or dates, so how about this? (Hook)

When Communism was first introduced into the world not much thought or concern was put into it. As time progressed its idea of a better world, people working side by side and for their government became warped and changed into a society where their higherups become greedy and would do anything to stay in power.
 
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