Normal Definition and 1000 Threads

Homework Statement 11) The tangent at P on the ellipse \frac{x^2}{a^2}+ \frac{y^2}{b^2}=1 meets the x and y axes at A and B. Find, in terms of the eccentric angle of P, the ratio of the lengths AP and BP. 12) Repeat Question 11 using the normal at P. Homework Equations bx \cos \theta + ay...

Why do people say that RVs that have the normal distribution has a constant variance. What does that mean constant variance.

why do we consider normal line in expressing a plane,say in ##R^3## ,of the form ## ax + by + cz = d ##? What is the logic behind this normal line selection? Plz provide intuitive explanations.Thanks

Hello everyone, I am currently considering a set of random variables, \vec{x} = [x_1,x_2,...x_N] which are know to follow a multivariate normal distribution, P(\vec{x}) \propto \mathrm{exp}(-\frac{1}{2}(\vec{x}-\vec{\mu})^\mathrm{T}\Sigma^{-1}(\vec{x}-\vec{\mu})) The covariance matrix Σ and...

Homework Statement A cup is represented by the surface -(z-1)2 + x2 + y2 = 1 and it is on a table represented by the plane z=0 a) find the angle at which the cup intersects the table b) find the equation of the normal line to the cup at the point (0, √2 , 2) c) find the equation the tangent...

Is there a relatively simple algorithm to compute the area in percentage under the curve as represented by a sigma value? For example; 3 sigma = 99.7 2 sigma = 95 1 sigma = 68.3 Now suppose I wanted to know 2.5 sigma without a table.

My main difficulty is finding E(XY), where if we find it by integrating, we get ∫xy f(x,y) dy dx where f(x,y) is the bivariate normal density function. This integral is a nightmare... are there any tricks to evaluating this integral, or finding E(XY) for that matter?

How do you find a normal vector of a function at a point, such as f(x,y)= ax^y+yx^y^x+b at (X_o,Y_o) where a and b are just arbitrary constants, and the function is an arbitrary function. So I guess, what is the general steps you take to find the normal? I thought it had to do with the...

Homework Statement So, a string with length L and a mass of M is given tension T. Find the frequencies of the smallest three modes of transverse motion. Then compare with a massless string with the same tension and length, but there are 3 masses of M/3 equally spaced. So this is problem #1...

Homework Statement It is known that the IQ score of ten-year-old children in a particular population has a normal distribution with mean 100 and standard deviation 15. (a) What proportion of this population have an IQ score above 115? (b) Mary’s IQ is equal to the 80th percentile of this...

So, I know that there is a Normal force exerted on the book by the table, and, according to Newton's Third Law, the book exerts a force onto the table. However, I have two questions: if I were to push down on the book, would that Normal force increase? What "creates" the Normal force? Is it the...

Homework Statement...

Hey guys, I'm just wondering if it's normal to feel this way. "Depressed" isn't the right word (a bit overdramatic), but I keep seeing people around me with "senioritis" who can't wait to graduate and move on. My fellow students keep talking about how they want to fast-forward time until May...

Homework Statement Find vector normal to z = x^2 + y^2 - 3 at point r = (2, -1, 2) Homework EquationsThe Attempt at a Solution here is the markscheme. I understand how to find the gradient, but i don't understand how they calculated the magnitude. thanks

"A study of long distance phone calls made from the corporate offices of the Pepsi Bottling Group Inc. showed the calls follow the normal distribution. The mean length of time per call was 4.2 minutes and the standard deviation was 0.60 minutes. a.What is the probability the calls lasted...

Homework Statement let's say you have a regular bathroom scale, which we know measures the normal force that it exerts on a person aka. apparent weight. Now let's say that we didn't know that it measured the normal force when a object was on it. Obviously we still know that the only two forces...

Homework Statement Consider a unit sphere centered at the origin. In terms of the Cartesian unit vectors i, j and k, find the unit normal vector on the surface Homework Equations A dot B = AB cos(theta) A cross B = AB (normal vector) sin(theta) Unit sphere radius = 1 The Attempt at a...

Is there a relationship between QM probability and normal distribution ? I'm thinking about drawing probability densities as functions of phase. Thanks

Homework Statement A point moves along the curve y = x3 + x such that the vertical component of velocity is always 3. Find the tangential and normal components of acceleration at the point P(2,10). Homework Equations Tangential Acceleration - aT(t) = v(t) ⋅ a(t)/ magnitude of velocity vector...

Hi, I read somewhere the geodesic distance between an arbitrary point ##x## and the base point ##x_0## in normal coordinates is just the Euclidean distance. Why?! That's the part I don't understand. I know that one can write g_{\mu \nu} = \delta_{\mu \nu} - \frac{1}{6} (R_{\mu \rho \nu \sigma}...

The lengths of a certain species of worm follow a normal distribution. Thirty percent of the worms are at least 16cm long, and 15% of the worms are less than 10cm long. Find, to 2 decimal places, the standard deviation of the lengths of the worms.

Homework Statement How does P(-1<Z<1) equal to 1-2P(Z>1)? (So you can find the values on the Normal Distribution Table) Homework EquationsThe Attempt at a Solution I tried P(-1+1<Z+1<1+1) but ended up with P(1<Z+1<2).

Homework Statement Let ##G## be a group and ##\sim## and equivalence relation on ##G##. Prove that if ##\sim## respects multiplication, then ##\sim## is the equivalence relation associated to some normal subgroup ##N\trianglelefteq G##; i.e., prove there is a normal subgroup ##N## such that...

Hello, given the figure above, how do I get the tangential and normal components of a vector in any plane by integration?

Homework Statement Hi all! I have been blindly drawing normal forces till today and i stumbled on this question. Homework EquationsThe Attempt at a Solution I have drawn 3 normal forces, - Hand - Leg - Center of mass Is there a normal force at the center of mass and is it the sum of the...

I'm trying to get my head around the calculation for coefficient of friction: COF = Friction/Normal force. And what happens if you vary normal force. Am I right in saying: The COF is a constant - every pair of materials has a specific COF which is independent of how hard they are pressed...

Please help with below. is it correct? A 41 kg crate rests on a horizontal floor and a 67kg person is standing on the crate. a. determine the magnitude of the normal force the floor exerts on the crate b. determine the magnitude of the normal force that the crate exerts on the person...

How is the expected frequency column worked out for each interval of trains? 2) My attempt Take the first interval, 60 - 62, I thought about doing this: (62 - mean) / standard deviation (62 - 67.45) / 2.92 = - 1.866 using Z score < - 1.886, from the normal distribution table, I get: 1 -...

I'm having a very hard time understanding the concept of a "Normal Force." The only framework with which I've come to terms with is imagining the Normal Force as the force exerted when object A comes into contact with object B which keeps object B from losing its macroscopic structural...

Here's a few stacks of the milky way I took last week, using an 85mm lens and a static tripod- 3.2s exposures. Two from the region around Cygnus: And a panorama closer to the horizon (12 stacks): This is about 13k x 11k pixels. At 100% the nebulae are still clear: Unfortunately, I...

I'm so impressed with many modular phone concepts including GOOGLE ARA and some other main concepts like "Puzzle Phone"(http://www.puzzlephone.com/), "ZTE Eco Mobius"(http://www.theverge.com/2014/1/8/5289998/zte-shows-off-eco-mobius-modular-smartphone-concept) and "Phone...

Homework Statement A block of mass m is kept on a smooth wedge of angle α and mass M which is in turn kept on a smooth floor. When the system is released from rest, calculate the force exerted by block on the wedge. Homework Equations None. The Attempt at a Solution Let the block a have a...

Why is the normal reaction of an object circulating a planet, equals to the gravitational force minus the centripetal force? I thought both gravitational force and centripetal force are directed towards the centre of the circular path i.e. in the same direction, therefore having, normal reaction...

Homework Statement A 10 N horizontal force is applied to a 50 N block initially at rest on a rough horizontal surface. If the coefficient of static friction is 0.5 and the coefficient of kinetic friction is 0.4, then the frictional force on the block is A 10 N B 20 N C 0 N D...

WARNING. I'm not a physicist! If there was a universe that only had 10000 photons and we observed all of them then ran the double slit experiment would we get a normal pattern or an interference pattern? If we observe a particle is that it forever in the universe that we happen to be running...

[FONT=Courier New]Note: I only need help on the underlined portion of the problem, but I'm including all parts since they may provide relevant information. Thanks in advance. 1. Homework Statement Let S be a subset of a group G such that g−1Sg ⊂ S for any g∈G. Show that the subgroup ⟨S⟩...

Homework Statement The airplane traveling at a constant speed of 50m/s is executing a horizontal turn. If the plane is banked at ##\theta=15## when the pilot experiences only a normal force on the seat of the plane, determine the radius of curvature of the turn. Also what is the normal force of...

I am trying to use the Israel junction conditions for a null surface, but I am running into complications with defining a normal vector for a null surface. As I understand it the normal vector is defined to be perpendicular to the surfaces tangent vectors n\cdot e_i=0, as well as satisfying...

Homework Statement In a children's park, there is a slide which has a total length of 10 m and a height of 8.0 m . Vertical ladder are provided to reach the top. A boy weighing 200 N climbs up the ladder to the top of the slide and slides down to the ground. The average friction offered by the...

I need help understanding normal distribution. I am self studying statistics to help me in my role of teaching excel as a business tool. I understand taking a data set and creating a frequency distribution. I don't understand about normal distribution. Why should any data set regardless of...

As I try to set up equations regarding Newtonian forces, I am looking for patterns in example problems I read. It's really frustrating then when I see different approaches that I can't see a connection to. There are two problems that I've attached that seem to solve - what seems to me about...

Homework Statement Let G = G1 × G2 be the direct product of two simple groups. Prove that every normal subgroup of G is isomorphic to G, G1, G2, or the trivial subgroup. The Attempt at a Solution I tried proving that the normal subgroups would have to be of the form Normal subgroup X Normal...

Homework Statement why the object will fall of when the normal reaction force is less than zero ? P/s : the normal reaction force is in downward direction... How if if the normal reaction force is less than zero ? the normal reaction is in upward direction ? Homework EquationsThe Attempt at a...

Hello, I am returning to college after a ten year hiatus and am taking an online course on edx to try and refresh my knowledge a bit before the fall. I read a few other posts on Newton's Third law, but it seems I am falling short on this one concept. In the case of an object, m_1, which is at...

Homework Statement As you can see , the writer state that the direction of normal reaction force(R) is acted upwards , I have another book state that the normal reaction force (R) is acted downwards , which one is correct ? Homework EquationsThe Attempt at a Solution [/B]

Homework Statement The Particle moves in the plane in a such a way that its polar equation of motion is ## \vec{R}=t\vec{i}+(t^2+1)\vec{j}##. a)What are its normal and tangential components of accelaration any time t ? b)Whats the curvature of path any time t ? Homework...

Homework Statement Find a unit normal to the plane containing a and b. a=(3;-1; 2) and b=(1; 3;-2) Homework Equations \frac{V}{|V|} where V = a+b The Attempt at a Solution (3;-1; 2) +1; 3;-2)=(4,2,0)=V |V| = \sqrt{4^2+2^} = 2\sqrt{5} there fore the unit vector is (\frac{2}{\sqrt{5}}...

A Google image search of "normal blood pressure versus age" came up with charts that I don't understand completely. Consider the following information. Also see, http://www.betterhealthfacts.com/2014/02/normal-blood-pressure-for-men.html It looks like it is normal for blood pressure to rise...

Hey everybody, I went through a discussion with a colleague today about Finite element modeling of composite structures and how to interpret the stress analysis. I understand that for isotropic materials, principal stresses could be used against the allowable stresses to see if failure will...

Hi, ##x(s)=\cos\frac{s}{\sqrt{2}}## ##y(s)=\sin\frac{s}{\sqrt{2}}## ##z(s)=\frac{s}{\sqrt{2}}##, it is a unit-speed helix. Its curvature is ##\kappa=||\ddot{r}||=\frac{1}{2}##. Principal unit normal is ##{\mathbf n}=(\cos\frac{s}{\sqrt{2}},\sin\frac{s}{\sqrt{2}},0)##. So far so good... But the...