Need Math Help?

[Proud_Smash_N00b]

I have a problem involving impulse

A model rocket of mass 0.25 kg is launched vertically with an engine that is ignited at time t=0. The engine provides an impulse of 20 N*s by firing for 2 seconds

How do I find the magnitude for average acceleration using this information? Do I find the force and use F=ma, do I make Ft=mv then solve for v then use V=Vnot+at, or do I do something else?

 

[Death]

I have some problems in math for exponents but I am getting the wrong answers...

ABC is a right triangle with Ab perpendicular to Bc, AB = 50 cm, BC = 120 cm. Find the area of the largest rectangle that can be inscribed in ABC with one of its corners at B.

What is the minimum value of the function f(x) = 2^(2x^2 - 2x)

 

[Death]

Anyway know how to solve these?>

 

[AltF4]

ABC is a right triangle with Ab perpendicular to Bc, AB = 50 cm, BC = 120 cm. Find the area of the largest rectangle that can be inscribed in ABC with one of its corners at B.

Firstly, by "largest" I assume, you mean "most area".

The rectangle will then have its opposite corner (from B) on the hypotenuse of the triangle. But where on the hypotenuse? Well, you want it as far away from B as possible, because that will give you the largest rectangle. You could (I guess) use a bunch of complicated calculus to find out exactly where, or you could just use some obvious facts.

The altitude (the line from B to the hypotenuse that forms a right angle) is the longest such line. Thus where the altitude connects, that's your point.

So draw the altitude onto your triangle. Good.

Now solve for that new mini-triangle. You know 2 angles and one side, thus you can solve the whole thing.

Now you have the cross section of the rectangle you need, and the angle at which it grows. So you can find the area.

*jeez, this would be easier with pictures...*

I think I'm getting about 756 cm^2. Is that what you should be getting?

What is the minimum value of the function f(x) = 2^(2x^2 - 2x)

When you do the derivative of an exponential, you just keep the whole thing the same, but then multiply by:

1) ln of the base
2) The derivative of the exponent

So you should get:

2^(2x^2 - 2x) * ln(2) * (4x - 2)

 

[Pr0phetic]

I have a problem involving impulse

A model rocket of mass 0.25 kg is launched vertically with an engine that is ignited at time t=0. The engine provides an impulse of 20 N*s by firing for 2 seconds

How do I find the magnitude for average acceleration using this information? Do I find the force and use F=ma, do I make Ft=mv then solve for v then use V=Vnot+at, or do I do something else?

You should use F=ma to ifnd the acceleration, they made it just a little harder because they didnt say it was by the surface of Earth, lol *****.

Impulse = Ft
(20 N*T) = F(2 s)
F = 10 N

F=ma

You think you can carry yourself from there?

 

[cF=)]

Alt, do you know any program able to solve this kind of equation: I(jw)=wCA∠Pi/2 ?

 

[SuperRacoon]

The following problem has me completely stumped, to be honest I'm not so sure that there is enough information to solve it in the first place, but before giving up, does any one have any ideas about how this might be solved?

The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration -5.65 m/s2 for 4.40 s, making straight skid marks 60.0 m long ending at the tree. With what speed does the car then strike the tree?

 

[AltF4]

Alt, do you know any program able to solve this kind of equation: I(jw)=wCA∠Pi/2 ?

What the heck is that equation? lol. I'm afraid I'm not familiar wit an "I" function which takes 2 inputs? I dunno.

The following problem has me completely stumped, to be honest I'm not so sure that there is enough information to solve it in the first place, but before giving up, does any one have any ideas about how this might be solved?

The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration -5.65 m/s2 for 4.40 s, making straight skid marks 60.0 m long ending at the tree. With what speed does the car then strike the tree?

Well, let's organize what information we're given.

Acceleration (constant) = -5.65 m/s^2
total time taken = 4.4 s
distance traveled = 60 m

What do we need to find? The velocity at a certain time. Namely: v(4.4) IE: The velocity at time 4.4 seconds. So we should use this equation:

v(t) = at + vi

...but we don't know what vi (initial velocity) was! So first we have to find that.

Instead, let's go to our trusty position equation!

x(t) = (1/2) a t^2 + t * vi + xi

if we define the start of the skid marks to be the 0 meter mark (with 60 meters being at the tree) we get:

x(t) = (1/2) (-5.65) t^2 + t * vi + 0

now let's see what happens when we plug the value 4.4 in for time!

60 = (1/2) (-5.65) (4.4)^2 + 4.4 * vi
60 = -54.692 + 4.4 vi
26.066 = vi (initial velocity)


So now we can use the equation:

v(t) = at + vi

plugging in what we just found...

v(t) = at + 26.066

Now what we want to find is v(4.4) right? So just plug that in!

v(4.4) = (-5.65)(4.4) + 26.066 = 1.206 m/s

 

[1048576]

Super Racoon: I just found the following equation on teh interwebz.

d = vt - 0.5at^2, where v represents the final velocity.

Plug in your numbers for d, t, and a, and solve.


Please don't ban me again CK. I tried to avoid flaming and inappropriate language as best I could.

 

[Lixivium]

What the heck is that equation? lol. I'm afraid I'm not familiar wit an "I" function which takes 2 inputs? I dunno.

I'm pretty sure that's a phasor angle not a less than sign.

I have no idea what to do with it though. (Or what "CA" means)

 

[Anonymous.]

omfg

its 12:28 im exhausted somebody help me

true or false: if two infinitely differentiable functions match in their value and all their derivatives at a point, then the functions must be the same?

I have NO clue what this

can you use the definition of a derivative for it?

HELPPPPPP MEEEEEE


wait, i think its false actually

.......


yes?

 

[AltF4]

False. Counterexample:

f(x) = 2x + 2
g(x) = 2x + 1

For both G and F, all derivatives will be exactly the same. And at some point, their value will equal as well.

IE:
f'(x) = 2
g'(x) = 2

f''(x) = 0
g''(x) = 0

f'''(x) = 0
g'''(x) = 0

etc...

Yet they are not the same function.

 

[Anonymous.]

ok and

u have a double integral of a continuous function over a bounded region, and u calculate it by evaluating the integrals one at a time. whose theorem did i just use?

edit: fubini nvm

 

[cF=)]

I'm pretty sure that's a phasor angle not a less than sign.

I have no idea what to do with it though. (Or what "CA" means)

Exactly. I'm given a 100 µF capacitor and I know the voltage takes the following values: v(t) = 40cos(20t - Pi/2). Now, they ask me to calculate the expression of the current through a phasor which is the equation I posted above: I(jw)=wCA∠Pi/2, where I is the current, w is 20, C is 100 µF and A is 40... my problem is, I need to find the imaginary part of this phasor to get the current

 

[Knyaguy]

Algebra II Question:

I am having a little trouble with negative exponents. All I know it that do the reciprocal at one point. Here is an example of a problem I can't do.

(3x²) ^-2
(14y³)^-3

 

[AltF4]

Exactly. I'm given a 100 µF capacitor and I know the voltage takes the following values: v(t) = 40cos(20t - Pi/2). Now, they ask me to calculate the expression of the current through a phasor which is the equation I posted above: I(jw)=wCA∠Pi/2, where I is the current, w is 20, C is 100 µF and A is 40... my problem is, I need to find the imaginary part of this phasor to get the current

Oh, you're talking physics. I was thinking of it in terms of just math, and couldn't wrap my head around it! Anyway, my electromagnetism is rather rusty. I only had one class in it and never used it again ever since. I'm a software guy, not a hardware one I'm afraid.

Algebra II Question:

I am having a little trouble with negative exponents. All I know it that do the reciprocal at one point. Here is an example of a problem I can't do.

(3x²) ^-2
(14y³)^-3

When you see a negative exponent, just put whatever it is on the bottom of a fraction (IE: Take the reciprocal). But if it's already on the bottom of a fraction, then move it back on top. After you've done this, the exponent becomes positive again.

So in your example of:

[(3x²) ^-2] / [(14y³)^-3]

All you need to do is swap the numerator and denominator to make their exponents positive. The top one needs to move down, and the bottom one moves up like this:

(14y³)^3
(3x²) ^2

Note that after swapping them, the exponents become positive. Now you can simplify like usual.

(2744y^9)
(9x^4)

 

[Death]

Oh, God, big math test tomorrow. I just need some help with a few problems.

Solve the equations for z.

(1+i)z = 2 + i

z^2 - 2z + 2 = 0

2iz = 3 -2i ???????

A projectile fired vertically with an initial velocity of v and affected only by the force of gravity g, will have its height h, in metres per second after time t, in seconds, is given by the formula: h = vt - 1/2gt^2. Show that the projectile attains a maximum height of v^2 / 2g at time v/g. WTF??

Prove that the minimum value for (x-a)^2 + (x-b)^2 occurs when x = a+b / 2

 

[Knyaguy]

Thank you AltF4Warrior.

 

[Death]

okay so for: z^2 - 2z + 2 = 0

I get: z = sqrt of -2 + sqrt of 2z???

 

[1048576]

Use the quadratic formula.

(--2 +- sqrt(2^2 -4*2))/2

1+i and 1-i are both solutions.

 

[Death]

Ahh, I forgot all about that. Thanks a lot.

But what about some like (1+i)z = 2 + i? Does the z multiply with both terms? So it would then be: z + iz = 2 + i?

 

[1048576]

yes. That's the Distributive Property. Not to sound rude, but if you hope to have any success with math at all, you need to master that conversion.

A(B+C) = AB + AC

z = (2+i)/(1+i) ................ divide both sides by 1+i
z = (i+2)(i-1)/(i+1)(i-1) ............. multiply the fraction by (i-1)/(i-1) [this is legal because you are multiplying by one and denominator is not zero]
z = (i^2+i-2)/(i^2-1) ............ F.O.I.L.
z = (i-3)/(-2) ................. i^2 = (sqrt(-1)) squared = -1
z =(3-i)/2


Edit: I have a question of my own. Assuming no information is known and there aren't any special powers, what is the appropriate ratio of townies to mafia to ensure both sides have an even chance of winning?

 

[NintendoMan07]

Proofs were always a weak point of mine, and I've always considered myself pretty strong in math, too.

Anyway, the prompt I'm given is:

"Prove or disprove formally: The largest even prime number is 2." (Well, it's one part of a two part question, but I think I'm confident in my answer to the first.)

The thing is, I THINK I know how to go about this... but the word formally is throwing me off. Then again, you don't know my professor/TA, and neither do I. What I was thinking was starting with the definitions of a prime number and an even number, and... go from there. So... could someone tell me if I'm on the right track or completely off-course, and if I'm off-course, could someone explain how else I need to go about this problem?

 

[moogle]

Proofs were always a weak point of mine, and I've always considered myself pretty strong in math, too.

Anyway, the prompt I'm given is:

"Prove or disprove formally: The largest even prime number is 2." (Well, it's one part of a two part question, but I think I'm confident in my answer to the first.)

The thing is, I THINK I know how to go about this... but the word formally is throwing me off. Then again, you don't know my professor/TA, and neither do I. What I was thinking was starting with the definitions of a prime number and an even number, and... go from there. So... could someone tell me if I'm on the right track or completely off-course, and if I'm off-course, could someone explain how else I need to go about this problem?

a) An even number is defined as an integer that is divisible by 2.
b) A prime number is defined as a positive integer that is divisible by exactly two numbers: 1 and itself.

The number 2 satisfies both of these definitions. Note that every positive integer is at least divisible by 1 and itself. Now, there cannot be an integer greater than 2 which satisfies both of these conditions, since an even number that is greater than 2 must be divisible by at least three distinct values: 1, 2, and itself. So 2 is the largest even prime.

That might be too much detail, or it's just enough. Probably the safest way to do a problem like this is to write out the definitions you know and then use them.

 

[AltF4]

Lol, 2 is the ONLY even prime number. So it must also be the largest! You could just as easily have said "the smallest even prime number"

That problem is so easy, I don't even know how I'd go about proving it! It's just... obvious...

 

[1048576]

I'd really like to know the optimal town to mafia ratio for an even game (both sides have an equal chance of winning) assuming no other information is known.

 

[AltF4]

Hmm.... that's a good question. The problem is going to be all the strange special powers. They aren't easily quantified. Let's look at the rules.

And even without that, there's a lot of calculations. The number of calculations is exponential, in fact. Plus we'll have to make some assumptions like mafia only vote for townies. Let's look at a small example...

4 townies, 2 mafia

In order to calculate the "odds" of a victory for either side, you have to calculate every possible path through the game and how they end. Every time a choice has to be made, you split the path and make a new one.

(Bolded means a situation where mafia victory is ensured. No need to calculate further)

Night 1:

3 townies, 2 mafia

Day 1:

2 townies, 2 mafia (60%) OR 3 townies, 1 mafia (40%)

Night 2:

1 townie, 2 mafia OR 2 townies, 1 mafia

Day 2:

1 townie, 1 mafia (66%) OR 2 townies, 0 mafia (33%)


So, the mafia has an advantage of 87% - 13% in that matchup! Wow... Maybe that was a bad example!

I did some more calculations on paper adding some townies, and the odds didn't improve much. Odd. I came up with only a 82% - 18% split in favor of mafia when starting out at with 6 town and 2 mafia. And I got bored calculating any further.

 

[Tom]

Did someone say Mafia?

Sources:
Numbers (Part 1)
"...and They All Lived Happily Ever After."

The following lists probabilities for the town winning in different setups. All are basic games, with Mafia and Townies only, starting with Night and assuming random lynchings and night kills. The numbers probably do not reflect what the actual outcome would be if real games were played, as they don't account for the Mafia giving themselves away through bad logic. Only games with probabilities between 30% and 70% are included (except for 5 players, where 25% is the closest to 50%). Note that the probability for the Town drops when there are an odd number of players to start with.

In most Mafia games, the Mafia is required to kill. What if they weren't?

As you can see from the table of probabilities in Numbers, Part 1, the probability for the Town winning actually increases if the game starts with an even number of players instead of a slightly higher odd number. For example, a game with 8 players (1 Mafia) gives the Town a 54.29% chance of winning, while in a game with 9 Players (1 Mafia), the probability drops to 45.31%. These numbers assume that both the Mafia and the Lynch Mob kill every day, but what if they don't have to? If the Mafia choose not to kill on the first night, it is as if the game has started with 9 players instead of 8; the Mafia has increased its chances by 9%! But, it is then in the Town's best interest to not lynch (for the same reason). By this logic, no one will ever die!

Of course, this holds only in games with just Mafia and Townspeople, where the Mafia is not required to kill; but wouldn't it be interesting to see a game which ended with the Moderator finally giving up and writing "And they all lived happily ever after. The end."?

Obviously, when power roles even as simple as a cop or a doctor are added, the equation shifts towards the town side.

edit: 1048576, do you play Mafia regularly? IRL or on a forum, and are you interested in playing games here at SWF? We run games down in Decisive Games, in Forum Games, if you are interested...

second edit: scatterbrained... I didnt even think... If you are looking to host a game, I would recommend a C9 game for 7 players or an F11 game for 9 players.

 

[AltF4]

Oh, good!

When I was running some of the numbers for Mafia, Tom, I started to see some odd behavior. Like, the town being worse off when I added more townies. I'm glad to see that same behavior in the numbers you posted.

 

[SuperRacoon]

I need some help understanding parametric equations,

So if X(t)=a+d*t is the parametric equation of a line through the point P: (2,-3,1). Where t is the distance from point P. I need to find what a and d are. Also this line is perpendicular to the plan 3x+10y+5z=1.

What do I need to do?

 

[pyrotek7x7]

Could somebody explain logarithms to me? I ran across a logarithm question on the ACT and haven't learned what it is yet (I'm only halfway through PreCalculus right now).

 

[Lixivium]

Could somebody explain logarithms to me? I ran across a logarithm question on the ACT and haven't learned what it is yet (I'm only halfway through PreCalculus right now).

A logarithm is the reverse of an exponent. (NOT the same as a root)

The logarithm of a number with respect to the base is the power you have to raise the base by in order to get the number.

For example:

2^3 = 8
"2 to the power of 3 equals 8"
Then by defintion of a logarithm:
log2 (8) = 3
Meaning, "if you take the log of 8 with respect to 2, you get a power of 3"

Suppose you wanted to know,
"10 to the what power equals 500"?
or
10^(x) = 500

Now 10^2 = 100 and 10^3 = 1000, so x won't be a nice round number, but it must exist, and it will be somewhere between 2 and 3.

Here is where you would use the log function:

log10 (500) = x

You're not supposed to know this number off the top of your head, but if you use a calculator, you will get

log10 (500) = 2.699

This means that 10^(2.699) = 500

 

[Cease Tick]

ABCD is a parallelogram, with diagonals AC and BD intersecting at point E. AB = 5x, BC = 3x - 2.2, BE = 4y - 5.5, ED = 1/2y + 5, and AC = 5y - 2. Find the perimeter of triangle DEC.

...

BE = ED
4y - 5.5 = .5y + 5
3.5y = 10.5
y = 3

ED = .5(3) + 5
ED = 6.5

AC = 5(3) - 2
AC = 13

EC = 1/2 AC
EC = .5(13)
EC = 6.5

BD = ED + BE
BD = 13
AC = 13
BD = AC
ABCD is a rectangle

Angle ABC is a right angle
ABC is a right triangle
(5x)^2 + (3x - 2.2)^2 = 13^2
25x^2 + 9x^2 - 13.2x + 4.84 = 169
34x^2 - 13.2x = 164.16

I'm having a hard time finding x

 

[AquaTech]

This semester I'm taking Calculus, Managerial Accounting, and Business Statistics. BLEH. I'll probably need lots of help. Although I'm not sure how much help you can offer here.

EDIT: Sorry, now I know about the signature violation rules.

 

[Face124]

I've got a good question:

0x0?

 

[Pr0phetic]

Angle ABC is a right angle
ABC is a right triangle
(5x)^2 + (3x - 2.2)^2 = 13^2
25x^2 + 9x^2 - 13.2x + 4.84 = 169
34x^2 - 13.2x = 164.16

I'm having a hard time finding x

Its because the numbers they gave you are ridiculous. Im going to walk you through the steps of solving it with a quadratic eqaution.

Alright so you've gotten up to here

34x^2 - 13.2x = 164.16

Now this problem can't be solved this way, so lets put it in quadratic form.

34x^2 - 13.2x - 164.16 = 0

Now here's the trick part, we hav eto facotr to find two roots of this x. However, they gave yo utricky numbers, so you'll have to use a calculator that can solve for the numbers, but I can still lay it out.

34x^2 - 13.2x - 164.16 = 0 (equation)
(x - 2.4)(x + 2.01176) = 0 (factors)
(x = 2.4)|(x = -2.01176) = 0 (roots)
answer: x = 2.4 (You negate the negative because you can'y have negative length.)

 

[Cease Tick]

Thanks for the help. And 2.4 seems to make sense, because both AB and BC become whole numbers (12 and 5)

 

[Face124]

no-one going to answer my question?

0x0 people.

 

[Knyaguy]

no-one going to answer my question?

0x0 people.

Umm, you can type that into a calculator. Zero zero times is zero

 

[Face124]

Umm, you can type that into a calculator. Zero zero times is zero

Wrong. Nothing times nothing, is anything but zero.

Think about it, if you have no nothings, you have something. Double negative.