Secondary Maths questions, give me your maths questions

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I feel like I'm spamming the page but whatever

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a and b are easy,

I'm really not sure with c, the answer gives me a support of 0<y<4 but I just can't see how they got that at all. I probably should've paid attention in class...
 

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Ahhh I couldn't find this thread, but here it is.

one of the few exam questions I nailed.

A ferris Wheel is moving at a rate of one revolution every 4 minutes and has a radius of 10. what is the rate of change when a person is 16 m above the surface. (Ignore units)
 
Nasma

Or anyone else that can help me

How do I find the tangent equation of a curved equation, that is also parallel to another curved equation??

It is calculus, I can take a picture of the whole question if you want. We were learning how to figure our tangent and normal equations. But with most of the questions points or the gradient was given so it would be easy to figure out. However, in this case, none of that is given just two curved equations which are parallel to each other.

Thanks
 
tazzawazza said:
Nasma

Or anyone else that can help me

How do I find the tangent equation of a curved equation, that is also parallel to another curved equation??

It is calculus, I can take a picture of the whole question if you want. We were learning how to figure our tangent and normal equations. But with most of the questions points or the gradient was given so it would be easy to figure out. However, in this case, none of that is given just two curved equations which are parallel to each other.

Thanks
Click to expand...
If you put up the whole question it'll probably explain it better, little confused about what you mean.

You know same gradient = parallel right?
 
bumpity bump.
  1. Bob and Doug are playing the following game. Bob starts by rolling two fair dice; if the sum of his dice is six, then he wins the game. If not, then Doug rolls the dice, and if the sum of his rolls is seven, then he wins the game. If neither player wins the game during the first round, then they repeat the process (with Bob going first) until someone wins a round. What is the probability that Bob wins this game? Is he more or less likely than Doug to win?

I'd imagine it's some kind of series that will converge to give me the probability that Bob wins. Otherwise there's some distribution function that I'm missing.

God I hate probability.
 
treefingers said:
bumpity bump.
  1. Bob and Doug are playing the following game. Bob starts by rolling two fair dice; if the sum of his dice is six, then he wins the game. If not, then Doug rolls the dice, and if the sum of his rolls is seven, then he wins the game. If neither player wins the game during the first round, then they repeat the process (with Bob going first) until someone wins a round. What is the probability that Bob wins this game? Is he more or less likely than Doug to win?

I'd imagine it's some kind of series that will converge to give me the probability that Bob wins. Otherwise there's some distribution function that I'm missing.

God I hate probability.
Click to expand...

I'm assuming you're rolling d6? The inner D&D player in me knows there are plenty of other dice you could roll. Let's assume, for the sake of it, that d6 it is.

P(rolling 6) = 5/36
P(rolling 7) = 6/36

1st roll:

P(Bob wins) = 5/36
P(game continues) = 31/36

2nd roll

P(Doug wins) = P(we're still playing) * P(rolling 7) = 31/36*6/36
P(game continues) = P(we're still playing) * P(not rolling a 7) = 31/36*30/36

3rd roll

P(Bob wins on THIS roll) = P(we're still playing) * P(rolling 6) = 31/36*30/36*5/36
P(game continues) = 31/36*30/36*31/36

4th roll

P(Doug wins on THIS roll) = P(we're still playing) * P(rolling 7) = 31/36*30/36*31/36*6/36
P(game continues) = 31/36*30/36*31/36*30/36

5th roll

P(Bob wins on THIS roll) = P(we're still playing) * P(rolling 6) = 31/36*30/36*31/36*30/36*5/36
P(game continues) = 31/36*30/36*31/36*30/36*31/36

That's probably far enough.

So the probability of Bob winning is the sum of all the probabilities of him winning whenever he gets to roll.

P(Bob wins) = 5/36 + 31/36*30/36*5/36 + 31/36*30/36*31/36*30/36*5/36 +...
= 5/36 * (1 + 31/36*30/36 + (31/36)^2 * (30/36)^2 + ...)
= 5/36 * (1+ 930/1296 + (930/1296)^2 + ...)

Hey presto, a geometric progression where a = 5/36 and r = 930/1296

P(Bob wins) = 5/36/(1-930/1296) = 0.491803

HTH and hope I haven't fluffed up the calculations.
 
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expires said:
Why does F = G.M.m/d/d?
Click to expand...

Um, it doesn't. It's d^2 in the denominator.

As to why, not really a maths question but a physics one. Newton discovered that the force between two objects was directly proportional to the product of their masses divided by the square of the distance between them. The constant G was determined experimentally and found to be the same everywhere.

A fairly good explanation may be found at:

http://www.physicsclassroom.com/class/circles/Lesson-3/Newton-s-Law-of-Universal-Gravitation
 
Norwegian Blue said:
Um, it doesn't. It's d^2 in the denominator.

As to why, not really a maths question but a physics one. Newton discovered that the force between two objects was directly proportional to the product of their masses divided by the square of the distance between them. The constant G was determined experimentally and found to be the same everywhere.

A fairly good explanation may be found at:

http://www.physicsclassroom.com/class/circles/Lesson-3/Newton-s-Law-of-Universal-Gravitation
Click to expand...

Suppose it is better to put it as 1/dxd. I would be good to have superscript so as something squared can be posted unambiguously.

If it is a physics question, doesn't matter, but (quoted from your link) Newton knew that the force that caused the apple's acceleration (gravity) must be dependent upon the mass of the apple.

How could the magnitude of a force removed from the apple (the earth's gravity) be dependent on the mass of the apple for its magnitude. The mass of the apple doesn't cause the earth to accelerate apples towards earth at a rate 9.8 m/s/s does it?. Can you explain that? (Like your username, have a dream of seeing the fjords.)
 
expires said:
Suppose it is better to put it as 1/dxd. I would be good to have superscript so as something squared can be posted unambiguously.

If it is a physics question, doesn't matter, but (quoted from your link) Newton knew that the force that caused the apple's acceleration (gravity) must be dependent upon the mass of the apple.

How could the magnitude of a force removed from the apple (the earth's gravity) be dependent on the mass of the apple for its magnitude. The mass of the apple doesn't cause the earth to accelerate apples towards earth at a rate 9.8 m/s/s does it?. Can you explain that? (Like your username, have a dream of seeing the fjords.)
Click to expand...
The apple exerts the same force on the Earth as the Earth does on the apple. Since G*M(earth)*Mass(apple)/r^2 =Force = mass * acceleration

acceleration(Earth) = G*mass(apple)/r^2

where i have just divided both sides by the mass of the Earth. Notice if I were to calculate the acceleration of the apple I would divide both sides of the equation by the mass of the apple and get the large value of 9.8m/s/s you are familiar with.
 

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Moonwatcher said:
The apple exerts the same force on the Earth as the Earth does on the apple. Since G*M(earth)*Mass(apple)/r^2 =Force = mass * acceleration

acceleration(Earth) = G*mass(apple)/r^2

where i have just divided both sides by the mass of the Earth. Notice if I were to calculate the acceleration of the apple I would divide both sides of the equation by the mass of the apple and get the large value of 9.8m/s/s you are familiar with.
Click to expand...

Doesn't answer the question of dependency though. You read it. The force that caused the apples acceleration is dependent on the mass of the apple.

And can you answer the problem of mathematics within the law.

Just say the earth had a mass of 1,000,000. And the apple a mass 1. We have a a total mass of 1,000,0001. And a mutual attraction factor of 1,000,000. You would expect the two should be the same.

But lets say the earth had a mass of 999,999 and the apple a mass of 2. We still have a total mass of 1,000,001. But the mutual attraction factor is now 1,999,998

Shouldn't the mutual attraction factors be the same for the same overall quantity magnitude if the multiplication of mass was a real part of the gravity of the universe. Take a bit of mass from one, give it to the other, you would expect the mutual attraction factor to be the same. But mathematics says it isn't possible.
 
If you are far away enough a two object system has the same gravitational effect of a point mass (sum of both masses) placed at the center of mass of the system. It wouldn't matter what the distribution of the mass was.

EDIT: It is an interesting point you make though. It is hard to come up with a simple explanation.

Most importantly you want the gravitational force from a box that you cannot see inside of to be independent of whether someone has separated the mass into a different number of pieces at different times.
 
Last edited:
Moonwatcher said:
If you are far away enough a two object system has the same gravitational effect of a point mass (sum of both masses) placed at the center of mass of the system. It wouldn't matter what the distribution of the mass was.

EDIT: It is an interesting point you make though. It is hard to come up with a simple explanation.

Most importantly you want the gravitational force from a box that you cannot see inside of to be independent of whether someone has separated the mass into a different number of pieces at different times.
Click to expand...

The box being the universe. Would love to see someone make the arithmetic work.
12642885_10205778512205147_2099010018518770914_n.jpg



Would also like to know how the the force applied to the apple is dependent on the apple's mass. After all mass is a scalar quantity and can't do much outside of its self.
 
expires said:
The box being the universe. Would love to see someone make the arithmetic work.
12642885_10205778512205147_2099010018518770914_n.jpg



Would also like to know how the the force applied to the apple is dependent on the apple's mass. After all mass is a scalar quantity and can't do much outside of its self.
Click to expand...
That's a good question. Mass warps space and time so it does affect its own neighbourhood.
 
expires said:
The box being the universe. Would love to see someone make the arithmetic work.
12642885_10205778512205147_2099010018518770914_n.jpg



Would also like to know how the the force applied to the apple is dependent on the apple's mass. After all mass is a scalar quantity and can't do much outside of its self.
Click to expand...
I think the modern interpretation of gravity is in terms of two masses swapping virtual particles. The more mass on each side increases the number of virtual particles passed between them.

EDIT: I got my undergrad physics degree but didn't go on to honours which is where your questions are leading.
 
expires said:
The box being the universe. Would love to see someone make the arithmetic work.
12642885_10205778512205147_2099010018518770914_n.jpg



Would also like to know how the the force applied to the apple is dependent on the apple's mass. After all mass is a scalar quantity and can't do much outside of its self.
Click to expand...
Actually Einstein showed that mass actually bends the space and time around it, which is what gravity actually is the result of (general relativity).
 
expires said:
Sounds good.
Click to expand...
I only read up on the whole relativity thing last year (coincidentally the centenary of Einstein's theory of general relativity).

I studied physics at high school and have an engineering degree, but never had any concept of gravity outside Newton's classical mechanics.

Watch a few videos on YouTube. The whole thing is literally unbelievable for a while.
 
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