In basic physics problems, it's convenient to apply unrealistic scenarios to the situation.
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The Math Help Thread
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In basic physics problems, it's convenient to apply unrealistic scenarios to the situation.
There are some implicit assumptions in physics problems, a constant gravity is one of them. At the end of the day, Physics needs to fit in the reality, and that, in a way, differentiates physics from math. It also helps you get a general sense of the problem. I will solve the problem as it is, but add a postscript to it.
Practice problems.
When I studied for the Calc 3 final, I just endlessly did practice problems. There is a standard procedural form, but the way to solve specific questions requires practice.
GiantEnemyGoomba
Member
Could someone explain why the answer is 0 J and not 3 J. I thought to find the work I could just dot the force and position vectors into each other, but I guess I'm misinterpreting the values of the vectors. At x=1 it looks like the force vector should be 3 N times the x unit vector and the position vector should be 1 m times the x unit vector.
Yeah, but at the same time a lot of simplifying assumptions are made, hoping that it simplifies the model without steering off too much from data. It's very useful to do so if a)if doing so causes barely a noticeable difference to the scenario you are applying to and are aware of the limitations of such a model, b)as a spring board for more complicated problems, basically start simple in order to understand things better, hence often times for undergraduate class, for example, the kinematic problems being worked on doesn't include air resistance even though it makes a lot of difference.
Omega Ultimus
Member
Could someone explain why the answer is 0 J and not 3 J. I thought to find the work I could just dot the force and position vectors into each other, but I guess I'm misinterpreting the values of the vectors. At x=1 it looks like the force vector should be 3 N times the x unit vector and the position vector should be 1 m times the x unit vector.
Are you getting the 3 N from subtracting the 5 N/m^4 from 2 N/m? If so, you can't, as they're different units; that's why you're given the x^4 and x, to multiply against and get the Force function in terms of N. I'm not even sure if m^4 is an actual measurable unit.
Anyway, just take the integral of the function from 0 to 1. Since you have only one direction (the horizontal) the particle is moving in, this is much easier. That'll give you 3 J.
Could someone explain why the answer is 0 J and not 3 J. I thought to find the work I could just dot the force and position vectors into each other, but I guess I'm misinterpreting the values of the vectors. At x=1 it looks like the force vector should be 3 N times the x unit vector and the position vector should be 1 m times the x unit vector.
You have to do some integral in this case. W = Int F*dx from 0 to 1. The reason being that the force changes continuously as the object moves in space.
Rhomega Beta
Member
Ok, I have a 4:3 monitor that's about 18" diagonally. How big a 16:9 monitor would I need to get to have about the same height?
Omega Ultimus
Member
On mobile so I can't quote what you need, so check out the Wikipedia page (https://en.m.wikipedia.org/wiki/Aspect_ratio_(image)). Use the first formula listed.
From Pythagorean theorem, we know that the hypotenuse d (d for diagonal) is related to the width w and the height h of the first monitor by,
w / d = 4 / 5
h / d = 3 / 5
We are given that d = 18", so we can solve for the width and, in particular, the height of the monitor.
Now, can you write down a second set of equations that relate the width, the height, and the diagonal of the widescreen monitor?
Right, I'm aware that E[x^2] and E[x]^2 aren't the same. Rather, I didn't understand why E[x^2] isn't equal to E(X^2|A)P(A) + E(X^2|B)P(C) + E(X^2|C)P(C). I was incorrectly assuming E[X^2|A] would just be λ^2.
Icyflamez96
Member
Use the given information and a calculator to find theta to the nearest tenth of a degree, if 0 < theta < 360.
sin theta = -0.3092 with theta in QIII
So from what I understand, you input a sequence into your calculator to get a degree value, i'm just not sure what sequence it is you input.
It's a simple thing but I can't find a source online that tells me how to do this.
sin theta = -0.3092 with theta in QIII
So from what I understand, you input a sequence into your calculator to get a degree value, i'm just not sure what sequence it is you input.
It's a simple thing but I can't find a source online that tells me how to do this.
Can't say for sure without seeing the calculator, but there is probably a sin^-1 or arcsin button that will take the sine value and return the corresponding angle measure. You probably also need to make sure your calculator is set to degrees rather than radians. Once you get the angle, you may need to adjust it to match the given quadrant.
Icyflamez96
Member
Ah yes I got it. I tried inverse sin at first but I kept getting syntax errors so I must have made a mistake somewhere else. Thanks.
Edit: Wait, it worked for the next problem which had me use inverse cosine, but for the particular I posted above.... This is what I get
sin^-1(-0.3092) = -18.01
That already sticks out as being weird to me since it's giving me a negative angle measure, and it's saying it's not the right answer.
Edit 2: Oh okay since it lands in QIII, I have to do 180 - (-)18. Alright, got it.
Edit: Wait, it worked for the next problem which had me use inverse cosine, but for the particular I posted above.... This is what I get
sin^-1(-0.3092) = -18.01
That already sticks out as being weird to me since it's giving me a negative angle measure, and it's saying it's not the right answer.
Edit 2: Oh okay since it lands in QIII, I have to do 180 - (-)18. Alright, got it.
I have a question on building a function. I'm making a game and all of my tile objects are stored in a dictionary. The dictionary needs a key for input to access the tile, so my key is an equation that takes the tiles xyz position. My question is how can I create an optimal/minimum equation such that any xyz position within some range -R to R yields a unique output key? Was playing around with my system earlier and by luck was teleporting to a tile that I shouldn't had and realized that the positions output the same key. I've fixed it so it works, but I'm interested in seeing if theres a simpler way to do it. Say I set my range from -20 to 20. I made my equation
T = (x + 20) + (y + 20) * 40 + (z + 20) * 800.
I add 20 so each (num) term is positive. Is there a better way to do this?
T = (x + 20) + (y + 20) * 40 + (z + 20) * 800.
I add 20 so each (num) term is positive. Is there a better way to do this?
I feel like any function that does what you're looking for would be less efficient than having a coordinate object with x,y,z or simply using a delimited string as the key like "1,2,3" for x,y,z.
Well I've used them before and something like a 3d array would have a ton of wasted space as there's only a few tiles on screen at a time compared to the maximum there could be. With this I just throw a position into a key calculator function and then it generates the unique key for that object. What did you have in mind?
Hmm I'll look into this.
Thanks.
NamikazeBurst
Member
I have a Chemistry question, so I hope someone here can help.
When the following reactions occurs at 25 degrees C, the value of K_p is 2.15. At what temperature must this reaction occur to ensure exactly 90% of the reactant is consumed?
PCl_5 (g) <=> PCl_3 (g) + Cl_2 (g)
Delta H_rxn = 60900 J/mol
I tried getting the new K_p by multiplying the pressures of the products by 0.9, and the pressure of the reactant by 0.1, and then dividing the 2.15 by the resulting 8.1, and putting this into the van't Hoff equation, but that didn't give me any of the possible answers.
Edit: Am I not supposed to divide the old K value by the coefficient in the left side of the K_p equation? Just taking 8.1 as the second K_p gives me one of the answers.
When the following reactions occurs at 25 degrees C, the value of K_p is 2.15. At what temperature must this reaction occur to ensure exactly 90% of the reactant is consumed?
PCl_5 (g) <=> PCl_3 (g) + Cl_2 (g)
Delta H_rxn = 60900 J/mol
I tried getting the new K_p by multiplying the pressures of the products by 0.9, and the pressure of the reactant by 0.1, and then dividing the 2.15 by the resulting 8.1, and putting this into the van't Hoff equation, but that didn't give me any of the possible answers.
Edit: Am I not supposed to divide the old K value by the coefficient in the left side of the K_p equation? Just taking 8.1 as the second K_p gives me one of the answers.
Digital synth is basically digital filters with various characteristics, right?
MisterLuffy
Member
I have a question: A package of dishes (mass 50.0 kg) sits on the flatbed of a pickup truck with an open tailgate. The coefficient of static friction between the package and the truck's flatbed is 0.340, and the coefficient of kinetic friction is 0.190.
a) maximum acceleration the truck can have so that the package does not slide relative to the truck bed: 3.34 m/s^2
b) acceleration of the package to the ground: 1.86 m/s^2
c) maximum acceleration the truck can have such that the package does not slide relative to the flatbed: 2.47 m/s^2
d) When the truck exceeds this acceleration, what is the acceleration of the package relative to the ground?
I need help with part d. I've kept getting the wrong answers for that one.
a) maximum acceleration the truck can have so that the package does not slide relative to the truck bed: 3.34 m/s^2
b) acceleration of the package to the ground: 1.86 m/s^2
c) maximum acceleration the truck can have such that the package does not slide relative to the flatbed: 2.47 m/s^2
d) When the truck exceeds this acceleration, what is the acceleration of the package relative to the ground?
I need help with part d. I've kept getting the wrong answers for that one.
spelltropy
Member
I'm trying to show for a field F that the polynomial ring F[x1,x2,...,xn] is not a principle ideal domain for n>1.
I think (x1,x2,...xn) is not a principal ideal in this case - is this true? How would i prove it or is there a simpler way?
I think (x1,x2,...xn) is not a principal ideal in this case - is this true? How would i prove it or is there a simpler way?
I think so?
The basic theory is simple enough, so whichever book you can get your hands on will do just fine. You don't even need to read the whole book, if you just want to code for it.
We are asked to simplify the term
(x^8 * y^4 * z^4)^(1/8)
By the properties of exponentiation, we can distribute the power to each of the terms in the product. That is,
(x^8 * y^4 * z^4)^(1/8)
= (x^8)^(1/8) * (y^4)^(1/8) * (z^4)^(1/8)
Furthermore, when a term raised to a power is once again raised to a power, the result is the same as if the term were raised to the product of the powers. We get,
(x^8)^(1/8) * (y^4)^(1/8) * (z^4)^(1/8)
= x^(8 * 1/8) * y^(4 * 1/8) * z^(4 * 1/8)
= x^1 * y^(1/2) * z^(1/2).
In summary,
(x^8 * y^4 * z^4)^(1/8) = x * y^(1/2) * z^(1/2).
Allonym
There should be more tampons in gaming
Hmmm, thanks! I thought that but there are a limited number of entires you can put before you aren't able to submit answers anymore. So thanks again
Stumpokapow
listen to the mad man
Khan Academy videos, but a better solution would surely be that the college you're enrolling in has a Math Skills class designed to cover this material.
Why is Real Analysis so damn hard? How can I prove that the gamma function is well-defined? How can I show that the theorem of Picard-Lindelöf is usable on a differential equation about free fall with air resistance? *sigh*
It's gonna be a long weekend.
It's gonna be a long weekend.
Icyflamez96
Member
Can someone tell me how the heck this isnt right.
Stumpokapow
listen to the mad man
well for one thing, it's asking for your answer to have a parameter that includes time t and you don't
DeployThatPizza
Member
Where is time in that equation? It asks you to put your answer in terms of time.
Icyflamez96
Member
I thought it had something to do with that, but the tutorial for this type of question left it as theta for the answer. Dumb tutorial.
I got it.
I got it.
ThanksVision
Member
Is anyone here proficient with graph theory? I've got a problem I am struggling with, but I'd rather dig into it over PMs. Feel free to shoot me a message if you're interested!
Step 1. Easy to verify it's correct for case n=1;
Step 2. Assuming it's correct for case n=n_0, i.e., person #1 remains till the end. For case n=n_0+1, after one round of elimination, person #1 remains and the case reduces to n=n_0, therefore, person #1 remains till the end.
Stumpokapow
listen to the mad man
This is more generally (for any number n people, and any k where every kth person is removed each round) called the Josephus problem. You may find more formal inductive proofs out there by searching for it by name.
DragonKnight
Member
(Problem-Just for reference)
I have included my Matlab code. When I run the code I receive an incomplete gamma function, which prevents me from plotting my graph. Any Matlab experts see where I may have an error? Thank you very much!
I have included my Matlab code. When I run the code I receive an incomplete gamma function, which prevents me from plotting my graph. Any Matlab experts see where I may have an error? Thank you very much!
I'm not familiar with the problem, but think that you would want to (1) specify the bounds of integration and (2) specify the bounds of x for plotting.
In Matlab, you would type (I'll consider simpler examples),
syms t x;
% Create the definite integral F(t), of f(x) = x^2 from 0 to t
F = int(x^2, x, 0, t);
% Plot the definite integral of x^2 from 0 to t, for various values of t between 0 and 10
ezplot(F, 0, 10);
DragonKnight
Member
Thanks for getting back to me. My goal is to plot the function y or time vs x or concentration using the equation given. When I try to take the integral of the given equation I get an incomplete gamma function which prevents me from plotting the equation. I am trying to figure if the equation I inputted into Matlab was the right way to do it. I tried entering my limits as you have suggested and it just gave me a straight horizontal lines which is what I suspected it would do. Unfortunately it doesn't show the behavior of the function. Any other information? Thanks again!
If you evaluate (1+1/sigma) = 2.0526 in the last integral, you can get a plot. (no guaranty it's correct.)
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