The homework help thread...(SERIOUS)

[smbrown3706]

I get 1 % extra credit in AP stats if I can prove these two equations are equal, algebraically. They are the two formulas for variance in a discrete frequency distribution.
σ^2= ∑[(x-μ)^2*p(x)]
σ= ∑[x^2*p(x)]-μ^2

Any help would be greatly appreciated!

Here's my go. σ^2 = ∑[(x-μ)^2*p(x)] = E[(x-μ)^2] = E(x^2-2μx-μ^2) = E(x^2) - E(2μx) - E(μ^2) = E(x^2) - 2μ^2 - μ^2 = E(x^2) - μ^2 = ∑[x^2*p(x)]-μ^2

Do you mean to say σ= ∑[x^2*p(x)]-μ^2 or σ^2= ∑[x^2*p(x)]-μ^2? If it's the latter, then this solution looks acceptable, otherwise I've no idea how standard deviation ∑[x^2*p(x)]-μ^2.

If you need explanation I'd be free to provide, but if you've been paying attention good then you can see how these transformations occurred.

[smbrown3706]

What are the bounds of the sum and what variable is being summed?

Bound is i=1 to n

[ANDYMAYNE]

1. Standing on a bathroom scale, a 70kg person is riding in an elevator that accelerates at 2.0 m/s^2 up. What is the scale reading during this acceleration?

2. A 30kg child is standing on a bathroom scale while riding in an elevator that accelerates downwards at 2.0m/s^2. What is the scale reading during this acceleration?

3. Two twins, with a mass of 20kg each, are standing on one bathroom scale in an elevator going upwards at a constant speed of 3.0 m/s. What is the reading on the scale?

4. A 90kg person stands on two bathroom scales (one foot on each scale) in an elevator that is going downwards at a constant speed of 2.0m/s. What is the reading of each scale?

I'd be grateful if you even answered just one.

[BandApart]

1. Standing on a bathroom scale, a 70kg person is riding in an elevator that accelerates at 2.0 m/s^2 up. What is the scale reading during this acceleration?

2. A 30kg child is standing on a bathroom scale while riding in an elevator that accelerates downwards at 2.0m/s^2. What is the scale reading during this acceleration?

3. Two twins, with a mass of 20kg each, are standing on one bathroom scale in an elevator going upwards at a constant speed of 3.0 m/s. What is the reading on the scale?

4. A 90kg person stands on two bathroom scales (one foot on each scale) in an elevator that is going downwards at a constant speed of 2.0m/s. What is the reading of each scale?

I'd be grateful if you even answered just one.

the scale measures the normal force(the perpendicular force of contact between two objects). when standing on a scale, consider the sum of forces in the y direction:

SUM FORCES=ma
N-mg=ma
N=mg+ma or

N=m(g+a)

[Cell-Tech]

1. Standing on a bathroom scale, a 70kg person is riding in an elevator that accelerates at 2.0 m/s^2 up. What is the scale reading during this acceleration?

Sum of the forces equals ma.

mg goes down, normal force, n, goes up.

n-mg = ma --> n = m(g+a)

normal force is what the scale reads.

Number 2 is the same concept except acceleration is negative since it's going down.

If you're have no acceleration like in problems 3 and 4 the scale would just read the weight.

[benchpresschick]

honestly, just keep practicing it. had to memorize monologs from Julius Caesar senior yr, just go one line at a time tbh.

Ughh. I was hoping that wouldn't be the answer.. Haha.

[ANDYMAYNE]

What? I don't get it. Walk me through a problem using those formulas step by step.

[erebus197]

Force is mass time acceleration yes? So without the additional acceleration the force on the scale is just his weight (mg). However, when there is acceleration his mass will push down more on the scale if going up. If going down he will feel lighter.

If going up, you add the acceleration to that of gravity. If going down, you subtract it. N is normal force btw, maybe that was causing some confusion. Normal force is the force that the surface pushes back, stopping you from falling through.

So F(scale reading)=mass(gravity+additional acceleration) for the first problem.

[release]

What is the fastest way to graph curves without a calculator?
Book has a bunch of important points and intervals that i should remember (and are important to the graph's shape) but is very time inefficient.
I'm hoping to "ballpark" the graph (not have to take first/second derivatives and find out where they are pos/neg because it's time consuming).

[SportbikerKid]

If anybody is good with Fourier Transforms, they should message me or post on this thread. I NEED HELP BRAHS!!!!!

[Ballad]

Can anyone show me the algebra for getting the derivative of |x - 2|? The derivative function is piecewise I believe... not sure how to do this.

|x + h - 2| - |x - 2|
--------------------
________h

What do I do from here? :|

[SportbikerKid]

Can anyone show me the algebra for getting the derivative of |x - 2|? The derivative function is piecewise I believe... not sure how to do this.

|x + h - 2| - |x - 2|
--------------------
________h

What do I do from here? :|

there is discotinuity at x=2 so find the derivative for x-2 whereas x>2 and for -1*(x-2) for x<2

[Jacob15728]

there is discotinuity at x=2 so find the derivative for x-2 whereas x>2 and for -1*(x-2) for x<2

I think he means using the limit definition thing. It would be really hard to do it the way Ballad set it up, so you have to make the function a piecewise then set up the derivative formula for each piece.

|x-2| = {x-2 if x>=2, 2-x if x<2

Now we can say

d/dx |x-2| = {lim h->0 [(x+h-2)-(x-2)]/h if x>2, lim h->0 [(2-x-h)-(2-x)]/h if x<2

= {lim h->0 (h/h) if x>2, lim h->0 (-h/h) if x<2

= {1 if x>2, -1 if x<2

[Cell-Tech]

Can anyone show me the algebra for getting the derivative of |x - 2|? The derivative function is piecewise I believe... not sure how to do this.

|x + h - 2| - |x - 2|
--------------------
________h

What do I do from here? :|

EDIT: Never mind didn't realize your original function was absolute value x-2 so forget what I said lol

I didn't really read it but I think the other answers you got involved calculus. I'm assuming from your question you're not in calculus and they just gave you the definition of a derivative and just use algebra to figure it out.

you set it up correctly if | | are supposed to be parenthesis and not absolute value bars. so the parenthesis around x+h-2 don't matter and we can get rid of the parenthesis around x-2 if we distribute the negative sign giving you x+h-2 -x +2 in the numerator. x's and 2's cancel, so just h

So what you end up with is h/h which is 1

So the derivative is just one, and if you do know calculus you know that is the correct derivative.

[SportbikerKid]

EDIT: Never mind didn't realize your original function was absolute value x-2 so forget what I said lol

I didn't really read it but I think the other answers you got involved calculus. I'm assuming from your question you're not in calculus and they just gave you the definition of a derivative and just use algebra to figure it out.

you set it up correctly if | | are supposed to be parenthesis and not absolute value bars. so the parenthesis around x+h-2 don't matter and we can get rid of the parenthesis around x-2 if we distribute the negative sign giving you x+h-2 -x +2 in the numerator. x's and 2's cancel, so just h

So what you end up with is h/h which is 1

So the derivative is just one, and if you do know calculus you know that is the correct derivative.

This is wrong

[Cell-Tech]

This is wrong

Did you not read my edit?

[guitargoalie]

has anyone read James Joyce's "Portrait of the Artist as a Young Man" ? I read it but didn't understand it well, I have to draw similarities between that and an essay called "the good life" which says in order to live a good life you must have love, knowledge and benevolence. Any ideas

[release]

EDIT: Never mind didn't realize your original function was absolute value x-2 so forget what I said lol

I didn't really read it but I think the other answers you got involved calculus. I'm assuming from your question you're not in calculus and they just gave you the definition of a derivative and just use algebra to figure it out.

you set it up correctly if | | are supposed to be parenthesis and not absolute value bars. so the parenthesis around x+h-2 don't matter and we can get rid of the parenthesis around x-2 if we distribute the negative sign giving you x+h-2 -x +2 in the numerator. x's and 2's cancel, so just h

So what you end up with is h/h which is 1

So the derivative is just one, and if you do know calculus you know that is the correct derivative.

you have to take the derivative for x>2 and x<2
x>2 , the derivative is 1
x<2 , the derivative is -1

[orieo56]

the derivative is 1,-1

abs signs only mean u have to consider the positive and negative of each, meaning it spilts into 2 equations. in this case they narrow down to 1,-1, pretty simple

EDIT: im not really sure what the _______h was at the bottom so i ignored it lol

[13uck]

Tomorrow I have to interview a Director of Human Resources at the call center that I work at for an assignment in my business class and was wondering if anyone can help come up with questions to ask her?

[the0dude]

pay attention in class is my advice

[HeavilyBeastin]

This one has to do with the conics of parabolas.

A semielliptical archway is to be formed over the entrance to an estate. The arch is to be set on pillars that are 10 feet apart and is to have a height (atop the pillars) of 4 feet. Where should the foci be placed in order to sketch the arch?

[ANDYMAYNE]

PHYSICS

Two boxes are sitting side by side on a frictionless surface. The box on the left has a mass of 11 kg, and the box on the right has a mass of 17 kg. If a 50 N force pushes on the 11 kg box from the left, what is the force exerted on the 17 kg box by the 11 kg box?

A 30kg child is sitting on a 2.0kg swing that is hanging on two ropes. What is the tension in each rope?

how do I solve these? step by step explanation please. DO not send me to a googled link.

[Daniel0]

Can anyone give me examples of production and consumption externalities which you meet in everyday life? (Economics)

Thanks in advance

[smbrown3706]

Can anyone give me examples of production and consumption externalities which you meet in everyday life? (Economics)

Thanks in advance

Production, positive externality: Working on removing debris from a trail (we just had a major storm here in New England) creates a positive externality for those who use the trail.
Consumption, negative externality: Driving a car consumes gasoline, producing toxic byproducts, which seep into the water, poisoning the water for a creature that comes along and drinks it.

[Dulba]

This is a review and i don't remember ****, please help me fill in the table. I really just don't know how to find R1



1 2

3 4 R4 is 950

[Cell-Tech]

PHYSICS

Two boxes are sitting side by side on a frictionless surface. The box on the left has a mass of 11 kg, and the box on the right has a mass of 17 kg. If a 50 N force pushes on the 11 kg box from the left, what is the force exerted on the 17 kg box by the 11 kg box?

A 30kg child is sitting on a 2.0kg swing that is hanging on two ropes. What is the tension in each rope?

how do I solve these? step by step explanation please. DO not send me to a googled link.

so the force of 50N is acting on a total mass of 28kg. 50/28 m/s^2

Now let's look at the 17kg box by itself. The only force acting is the one exerted by the 11kg box so F = 17(50/28) = 30.357 N

For the second one (32)(9.8)/2

This is a review and i don't remember ****, please help me fill in the table. I really just don't know how to find R1



1 2

3 4 R4 is 950

Too messy can't read the table lol

[Sneds]

The quadratic equation x^2+2kx+2(k+4)=0 has distinct real roots.

(a) Show that k^2-2k-8 > 0

(b) Hence, find the possible values of k

[Cell-Tech]

The quadratic equation x^2+2kx+2(k+4)=0 has distinct real roots.

(a) Show that k^2-2k-8 > 0

(b) Hence, find the possible values of k

Our quadratic equation is x^2+2kx+2(k+4)=0 and it has distinct real roots. What this means is the discriminant, b^2 -4ac >0

The discriminant is (2k)^2-4(2(k+4)) --> 4k^2 -4(2k+8) --> 4k^2 -8k-32 > 0

divide both sides by 4:

k^2 -2k -8 > 0 so part a is done

Now for part b just find the roots.

(k -4)(k+2) = 0

k = 4 and -2

Now just find the intervals where the equation is positive which is x>4 and x<-2

[KevinMK0831]

A playground is being designed where children can interact with their friends in certain combinations.

If there is 1 child, there can be 0 interactions.
If there are 2 children, there can be 6 interactions.
If there are 3 children, there can be 15 interactions.
If there are 4 children, there can be 27 interactions.

How many interactions will there be for 7 children?
Answer
108
60
81
105
1 points
Question 2

A playground is being designed where children can interact with their friends in certain combinations.

If there is 1 child, there can be 0 interactions.
If there are 2 children, there can be 3 interactions.
If there are 3 children, there can be 9 interactions.
If there are 4 children, there can be 18 interactions.

Which recursive equation represents the pattern?
Answer
an = an – 1 + (n – 1)3
an = an – 1 + 3(n – 1)
an = an – 1 + 3(n – 1)
an = an – 1 + (3n – 1)
2 points
Question 3

Shirley purchased a plot of land for $19,500. The land appreciates about 3.9% each year. What is the value of the land after five years?
Answer
$23,302.50
$23,610.89
$15,982.75
$19,818.94
3 points
Question 4

Luke purchased a motorcycle for $8,765. It depreciates about 5.3% each year. What is the value of the motorcycle after five years?
Answer
$6,442.27
$6,675.78
$8,573.14
$11,347.33
3 points
Question 5

The yearly attendance at a local movie theater is 56,000 and grows continuously at a rate of 4.2% each year. What is the approximate attendance at the movie theater in nine years?
Answer
57,789
77,168
81,724
81,096
3 points
Question 6

The number of customers that visit a local small business is 51,200 and has been continuously declining at a rate of 3.8% each year. What is the approximate number of customers that visit the business in 14 years?
Answer
29,766
87,159
30,076
33,690