Normal Definition and 1000 Threads

Homework Statement Find the equation of each of the normal lines to the curve y = x^3 - 4x that is parallel to the line x + 8y - 8 = 0. Homework Equations Differentiation, y - y1 = m(x - x1) The Attempt at a Solution Well, clearly I start by differentiating y = x^3 - 4x to gey...

Hey all. I'm working on a personal programming project where I'm attempting to simulate (to a small degree) a galaxy. And I have come across a decent 2D density map for a spiral galaxy. This map (array actually) defines a 128x128 grid of values between 0 and 255 representing the frequency of...

So, I'm wondering, Suppose a couple years from now, I've applied to physics graduate schools, but I can't get in anywhere due to GPA issues. My physics GPA is decent, if not outstanding(mostly B+'s and B's so far. I'm hoping I can change those into A's next year, when I'm dealing mainly with...

If there are 2 blocks beside each other and a force is applied to the first block, the first block will push the second block has well. This means that the two blocks are in contact. So why isn't there a normal force drawn perpendicular to the side of the second block if it is in contact with...

This might be a bit philosophical, but is this just from experiment? that for a really really smooth surface, people found that the net force on an incline surface is found to be approximately in the direction normal to the incline plane? (approximately because there's no perfectly smooth...

Here are the questions: Here is a link to the questions: Equation of tangent and normal? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement A variable line ax+by+c=0, where a,b,c are in A.P (arithmetic progression), is normal to a circle ##(x-\alpha)^2+(y-\beta)^2=\gamma##, which is orthogonal to circle ##x^2+y^2-4x-4y-1=0##. The value of ##\alpha+\beta+\gamma## is equal to A)3 B)5 C)10 D)7 Homework...

I go through major swings of confidence throughout the day. If I get a compliment from someone or some other kind of validation, I'll feel on top of the world, and then some really small disappointment can sink that confidence into almost depression and a feeling of worthlessness. For...

Homework Statement The number of hours of sunshine in one week in a specific resort is assumed to follow a normal distribution with expectation 43 and standard deviation 17. Family A will spend the first three weeks of the summer at the resort. Family B will spend the LAST two weeks of...

This is a very basic problem which you all must have seen somewhere. But recently an itching doubt has come up to me regarding this problem. Problem: A chain lies on a table with some part of it hanging over the edge. Now if the coefficient of friction is μ, then find out the maximum part...

Homework Statement We have two normally distributed random variables: A = N(129, 29.4) B = N(86, 24.0) What is the probability A is atleast twice the size of B? The Attempt at a Solution P(A > 2B | B = b) or something? I think we are supposed to use the CLT somehow but I don't...

I want to come up with an example of a field extension that is not normal, and seems to be difficult. All extension constructed in some obvious way tend to turn out normal.

If G is a group with subgroups H and K, and if H is normal, then HK=KH, right?...Since we know that N(H) = G. However, since H commutes with K, then H must also be contained in N(K), right?...Since N(K) is the set of elements that commute with K...but I was a bit confused, because we know that...

Homework Statement Let us have lines (x+3)/2 = (y+2)/3 = (z-6)/-4 and (x-5)/1 = (y+1)/-4 = (z+4)/1 Find a normal vector to the plane these two lines are on. The Attempt at a Solution I already know you can solve it by s1 x s2 || n ; where s1 = (2, 3, -4) and s2 = (1, -4, 1) but I am not...

The expositions for a normal probability plot (aka normal quantile plot) (in which observed probabilities are plotted against theoretical probabilities, or sometimes the other way around, to get a rough check as to whether a set of data is normally distributed by checking linearity) are not too...

Homework Statement Hey guys. The title says it all pretty much. We need to find the normal mode frequencies of a driven/forced system containing 3 equal masses connected by 4 springs of equal spring constant k. Homework Equations F=m\ddot{x} Spring potential V = 0.5kx^{2}...

Homework Statement I have a question from my homework. My homework is completed, but I've been running some thought experiments lately and I wish to conceptually discuss this. The problem has to do with a hoop rolling down an inclined plane. I had to find the Normal Force using...

Homework Statement ive reduced a problem down to one last part, and where i need the normal and tangential acceleration components of a moving particle. we are given the following: $$a=xi+yj$$ and $$v=ui+zj$$ where a and v are acceleration and velocity and the x,y,u,z are the components. note...

Homework Statement Show that there is no minimum for the normal distribution function e^(-(x-μ)^2/(2 σ^2))/(sqrt(2 π) σ) Homework Equations The Attempt at a Solution I figured I'd take the derivative and set it equal to 0, but then what?

Hi Everyone! I have two normally distributed random variables. One on the x axis, the other on the y axis, like a complex normal random variable. I'm trying to find the pdf of the angle between a fixed point on the x-y plane(let's say point 1,0) and the vector formed by combining the two...

This is (perhaps) a tricky question regarding the moment of normal distribution. Let f(x) be the pdf of normal distribution with mean (-σ^2/b) and variance σ^2, where b is just a constant. The goal is to solve the integral ∫ x^3 f(x) dx integrating from 0 to ∞. I am stuck. Any...

Homework Statement I have a system of two masses m1 and m2 coupled by two springs with constants k1 and k2. If m1 and m2 are equal what would be the normal modes for this system? Homework Equations Equations of motion for the system: \begin{align*} m_1\ddot{x}_1 &=...

Homework Statement A bar with mass m and length l is attached at one end to a string (also length l) and is swinging back and forth. Find the normal modes of oscillation. Homework Equations L=T-U, and the Lagrange-euler equation, I=(1/12)ml^2The Attempt at a Solution So my idea is this. Use...

EDIT:( Sorry I meant for the title of this to say conjugacy classes of subgroups of Z X Z) I have a question.I am trying to figure out, what are all of the normal subgroups of Z X Z? Well, I know that Z has the following subgroups: the trivial group {0}, itself Z, and then aZ, one for each a in...

Homework Statement Tangent to C at point P(2,7) has an equation of y=3x+1. Point Q also lies on C and is perpendicular to the tangent, show that the X-coordinate is [1/3(2+√6)] Homework Equations curve C has equation y= x3-2x2-x+9 dy/dx = 3x2-4x-1 The Attempt at a Solution gradient of...

Hi everyone, I would like to know if this stament is true or not. I have two variables u,v both of them distributed as normal distribution with mean 0 and variance a^2. Is it true that the expected value of uv is a^2 ? Thanks

Homework Statement X is a normal random variable with mean 1, variance 4. 1. Find P( X(X-1) > 2 ) 2. Find a value 'a' for which P(|X| > a ) = .25 The Attempt at a Solution I had no idea how to start 1. For 2, i got this far then got stuck: P(|X| > a) = 1 - P((X-1)/2 <=...

There is a corollary in our textbook that states "Let G be a group of order 12 whose 3-Sylow subgroups are not normal. THen G is isomorphic to A_4." I attached the proof of this corollary and an additional corollary and proposition that was used for the proof. The 2nd last paragraph is a bit...

I know that every action has a reaction, and I understand that applying a force on a surface yields a "force" from that surface to hold it up, and that it's magnitude and direction are equal and opposite, respectively. But conceptually, what is happening? Defining a force in terms of another...

Homework Statement The 2-oz bead P is given an initial speed of 5 ft/sec at point A of the smooth guide which is curved in the horizontal plane. The horizontal force between the bead and the guide has a magnitude of 3 oz at point B. Determine the radius of curvature ρ of the path at this...

Homework Statement Suppose that F = ∇f for some scalar potential function f(x, y) = 1/2(x2 + y2) Let C denote the positively oriented unit circle, parametrized by r(t) = (cos t, sin t), 0 ≤ t ≤ 2∏. Compute the flux integral of \ointF\bulletN ds, where N is the outward unit normal to C.Homework...

Homework Statement Suppose X is a normally distributed random variable. Suppose also that P ( X > 44.7 ) = 0.33 and P ( X < 46 ) = 0.7123. What is the mean and standard deviation of X ? Homework Equations The Attempt at a Solution P(X<44.7) = 1-P(X>44.7) = 1-.33 = .67 P(X<44.7)...

Homework Statement I am student teaching a class about static friction soon. I am worried a student is going to ask me where Fstatic friction = μ sFnormal comes from. I am not sure how to explain it. Homework Equations The Attempt at a Solution I've always thought of it this...

Hi, i have a curve g:[0,t]->IR² with g(t)=(x(t),y(t)) in a homogenous gravitational field and i want to look at a ball rolling down this curve. therefore i want to derive some equations in order to calculate the normal force and the centripetal force at each point of this curve in order to see...

Hi Homework Statement Let f:\:\mathbb{Z}_{5}^{3}\rightarrow \mathbb{Z}_{5}^{3} be a linear operator and let [f]_{e_{3}}^{e_{3}}=A=\begin{pmatrix}3 & 1 & 4\\ 3 & 0 & 2\\ 4 & 4 & 3 \end{pmatrix} over \mathbb{Z}_{5}. Find a basis B of \mathbb{Z}_{5}^{3} such that...

Homework Statement How can we prove that a subgroup H of Gl_2(Z_3) is normal? These are the elements of H: \begin{pmatrix}1&1\\1&2 \end{pmatrix} \begin{pmatrix}1&2\\2&2 \end{pmatrix} \begin{pmatrix}2&1\\1&1 \end{pmatrix} \begin{pmatrix}2&2\\2&1 \end{pmatrix}...

Hello, i know how to calculate normal line on point but i don't know how to do this problem. "find an equation of the normal line o the parabola y=x^2-5x+4 tha is parallel to the line x-3y=5."

Homework Statement I feel like I am being told that there two different kinds of normal force. 1st. In grade 11 we were always told that normal force on an angle equals m*g*cosθ, where Fn equals the y-component, and θ is the angle between Fn and mg. 2nd. Now in university we are told...

Homework Statement Let's say I'm holding a crate up against the ceiling with a force of 'P', and the crate is stationary. What is the normal force? Homework Equations Newton's 1st law: ƩF=0 The Attempt at a Solution I have three forces acting on the crate - The normal force...

If I am checking whether my data fits a curve C1, I have to check to see whether the residues R1n are normally distributed, which is checking R1n against a normal curve C2, giving me residues R2m; which must be normally distributed, that is, must be checked against a normal curve C3, giving me...

chi-squared dist. converges to normal as df goes to infinity, but... This is surely going to sound naive, but at least this will make it easy to answer. For a chi-squared distribution, if k = the degrees of freedom, then [a] k = μ = (1/2) σ2 [b] as k goes to infinity, the distribution...

Using line equation y = -4058.7x + 16.10 with the experiment pressure measured in kPa instead of atm. I already solved for heat of vaporization thus: (-4058.7K)(-8.314 J/mol \astK)=heat of vaporization = 33444 J/mol = 33.44 kJ/mol. Also, the vapor pressure for normal boiling point...

Homework Statement Hi, guys, I just wondering what's the normal order of A +B Homework Equations if N[A+B]=N[A]+N[B] then I have N[aa^{\dagger}]=N[1-a^{\dagger}a]=1-a^{\dagger}a however we know that N[aa^{\dagger}]=-a^{\dagger}a] what's wrong? The Attempt at a Solution...

Hi, Given that the flow normal to a thin disk or radius r is given by \phi = -\frac{2rU}{\pi}\sqrt{1-\frac{x^2+y^2}{r^2}} where U is the speed of the flow normal to the disk, find the flow normal to an ellipse of major axis a and minor axis b. I can only find the answer in the...

Homework Statement A 2.4-lb slider is propelled upward at A along the fixed curved bar which lies in a vertical plane. If the slider is observed to have a speed of 11.3 ft/sec as it passes position B, determine (a) the magnitude N of the force exerted by the fixed rod on the slider and (b) the...

Homework Statement In the steel structure shown, a 6‐mm‐diameter pin is used at C and 10‐mm‐diameter pins are used at B and D. The ultimate shearing stress is 150 MPa at all connections, and the ultimate normal stress is 400 MPa in link BD. Knowing that a factor of safety of 3.0 is desired...

Prove that the field Q(√2,√3,u) where u^2=(9-5√3)(2√2) is normal over Q. I'm supposed to show that this field is the splitting field of some polynomial over Q. u is clearly algebraic over Q. Do i just take the higher powers of u and try to find the minimal polynomial over Q or is there a...

Homework Statement A box is lifted by a magnet suspended from the ceiling by a rope attached to the magnet as illustrated in Fig 3.65. Draw free body diagram for the box and for the magnet so the picture is basically there is a ceiling , and the rope hanging from the ceiling to the...

Homework Statement The tires on a car are capable of exerting a maximum frictional force of 1753 lb. If the car is traveling at 75 ft.s and the curvature of the road is ρ=560 ft, what is the maximum acceleration that the car can have without sliding? Homework Equations ƩFn = man The...

Homework Statement A biologist interested in the mass of Chickadees (Poecile atricapillus) in North Glenmore Park collects the 3 samples shown below: Sample 1: 9 individuals with a mean mass of 13.23 grams Sample 2: 16 individuals with a mean mass of 9.64 grams Sample 3: 13 individuals...