Points Definition and 1000 Threads

Hey! :o We have the function $f(x_1, x_2)=2-x_1-x_2$ and we want to check if it has maxima or minima under the constraint $x_1^2+x_2^2=8$. Since we cannot solve for one variable at the equationof the constraint, we have to use the Langrange function, right? (Wondering) I have done the...

I am looking for some general guidance on questions of the form: "Using a ## \Delta ## complex, compute the homology groups of the quotient space obtained fromt the 2-sphere ##S^2## by identifying three of its distinct points." Similarly I have a question about a torus with two points...

Two questions about Lagrange points. (1) According to Wikipedia, "libration is a perceived oscillating motion of orbiting bodies relative to each other," whereas the Lagrange points are, with respect to two bodies, null points for a (real or hypothetical) third body with respect to the sum...

Hello I have two points: B(1,3) and C(2,6). I need to find a point A on the y-axis, from which BC is "seen" at an angle of 90 degrees. I tried using Pythagoras theorem and got: \[y^{2}-6y+10=y^{2}-12y+40+10\] but it doesn't give the correct answer, which is (0,5) or (0,4). What am I doing...

What is the x-intercept of the line that passes through points (-3,7) and (6,4) in the standard (x,y) coordinate plane?

Homework Statement [/B] A uniform cylinder with radius r is rolling down an incline without slipping as shown in diagram below. It's angular acceleration is α and acceleration of it's center of mass C is a. What will be the linear acceleration of point of contact P and another point Q on the...

Homework Statement A rigid ring is fixed with three bearings evenly spaced around its circunference, which allow it to rotate but not to displace in the radial direction. An external force is applied in a fixed point P of the ring which moves with the ring. The bearings have friction. These...

Find the critical points and test for relative extrema. List the critical points for which the Second Partials Test fails. f (x, y) = x^(2/3) + y^(2/3) Solution: f_x = 2/[3 (x)^1/3] f_y = 2/[3 (y)^1/3] f_xx = -2/[9 x^(4/3)] f_yy = -2/[9 y^(4/3)] f_xy = 0 I set f_x and f_y to 0 and found...

Find the critical points and test for relative extrema. List the critical points for which the Second Partials Test fails. f (x, y) = x^3 + y^3 Solution: f_x = 3x^2 f_y = 3y^2 f_xx = 6x f_th = 6y f_2xy = 0 I set f_x and f_y = 0 and found the critical points to be (0, 0). Is this...

Find the critical points and extrema of the function g (x, y) = sqrt {x^2 + y^2 + 1}. Can someone get me started here? I also would like the solution steps. I said solution steps not the solution. Do it like this: Step 1... Step 2... Step 3...etc...

Homework Statement This problem is taken from S L Loney Coordinate geometry exercise (ch 2)[/B] Prove that a point can be found which is at the same distance from each of the four points ## \bigg(am_1,\dfrac{a}{m_1}\bigg),\bigg(am_2,\dfrac{a}{m_2}\bigg),\bigg(am_3,\dfrac{a}{m_3}\bigg) ## and...

Homework Statement In Figure Q22, the empirical junction diode equation is : (eqn is in the picture attached) for both diodes D1 and D2, where VT = 26 mV at room temperature, n = 1, IS = 3.5 x 10-14 A, R1 = 600 Ω, R2 = 300 Ω, R3 = 200 Ω, VS = 9 V. Calculate the Q-points ID = _____ mA and VD =...

Homework Statement Let γ : [0, L] → Rn be arclength parametrized. Show that the distance between the endpoints of the curve can at most be L, and equality can only hold when γ is a straight line segment. Thus, the shortest path between two points is the straight line segment connecting them...

Lets suppose that two points A and B are very close together compared to their distance from an observer who is very far. Suppose the distance from observer to point A is DA and to point B is DB. How precisely we can find the distances separately.

Homework Statement Two pairs of charges are shown in Figure 1. Homework EquationsThe Attempt at a Solution I originally thought that the electric field past point 7 (i.e. points 8,9, 10) was the solution. However, this is wrong. I then considered point 1, yet that was wrong too. I even...

I'm a computer science student. I'm currently learning electronics so that I can program embedded devices effectively. I'm reading from the free book at allaboutcircuits.com. Why is the voltage between two points on a wire in a closed circuit equal to zero? Note that between these two points...

From Courant's Differential and Integral Calculus p.13, In an ordinary system of rectangular co-ordinates, the points for which both co-ordinates are integers are called lattice points. Prove that a triangle whose vertices are lattice points cannot be equilateral. Proof: Let ##A=(0,0)...

When it comes to analytic geometry, I am little confused about the use of vectors. For example, throughout high school, one works in ##\mathbb{R}^2##, and geometric objects such as lines are described using equations relating two variables, the x and y coordinate, such as y = 2x + 1. However...

So, I got the following problem: I want to write my equation the way you can see it in the picture: I am actually running this: \ begin{align} \begin{split} ... \ end{split} \ end{align} My problem is, that I can not set multiple align points. I need one point to attach the first 4 lines to...

So we just recently did accumulation points in my maths class for chemists. I understood everything that was taught but ever since I was trying to find a reasonable explanation if the sequence an = (-1)n has 2 accumulation points (-1,1) or if it doesn't have any at all. I mean it's clear that...

Homework Statement Given an ellipse ##\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1## , where ##a \ne b##, find the equation of the set of all points from which there are two tangents to the curve whose slopes are (a) reciprocals and (b) negative reciprocals Homework Equations Equation of a tangent...

Homework Statement A projectile is fired with a velocity v such that it passes through two points both at a distance h above the horizontal. Show that if the gun is adjusted for maximum range, the separation of the points is d = (v/g)(√v2-4gh) Homework Equations y = -gt2/2 + vsinθt x = vcosθt...

Can someone explain how this is possible? it makes no sense to me. You wouldn't walk along the track surrounding a soccer field if you wanted to get to the other end... you would walk straight across the grass to reach your destination. Why did Einstein propose this?

Does anyone know of any solutes (such as sodium chloride) that have VERY high melting points (preferably 1800C or higher)? They don't have to be water soluable but they need a solvent that can disolve them.

I want to make a 2D plot of points with different x, y coordinates and have colors depending on a separate variable. I have make column vectors for x and y coordinates and another column containing 1 or -1. I would like to represent the points with 1 as red and -1 as blue points. I have codes as...

Homework Statement Draw the third view and the points on each view. In the first picture you have what the exercise has given us and in the second what I have drawn. I have turned the page so that the first view is the one on the left, the horizontal one is the one on the right. Is that OK...

Homework Statement This is a simple circuit diagram from the class were we derived the equations for the equivalent resistance of parallel resistor connection. I have a quick question about this though.. Is the voltage between points ##A,B## the same as voltage between points ##C,D## and...

Homework Statement [/B] Hi, I seem to have this issue with solving the a system of 3 equations when trying to find the critical points for a 3 variable function. Homework EquationsThe Attempt at a Solution It always keeps happening. I keep getting stuck when solving these equations. Every...

Say that there lies k points upon a straight line. My question is this: what is the total amount of lengths between these points? To elaborate, say k is 2; there are two points and so there is only one length between the two points. How many lengths would there be with k > 2? What is the...

Homework Statement i'm not sure how to calculate the shear stress at point F and point G . I know that shear stress has formula of $$ \tau = VQ/It $$ The maximum shear force that i calculated earlier is V = 205kN , Ixx = 2.1x10^-4 for Q at $$\tau$$ at F , i have...

Homework Statement In the figure below, what is the potential difference Vd - Vc between points d and c if E1(of 1st battery) = 4.7 V, E2((of 2nd battery) = 1.4 V, R1 = R2 = 11 Ω, and R3 = 6.7 Ω, and the batteries are ideal? http://farm6.static.flickr.com/5053/5469093809_53c7fe57f4.jpg...

The pattern above will continue for all values of the harmonic sequence. Will a destination point be reached for any value of θ where 0 ≤ θ < 2𝜋? (I know it won’t for θ = 0) Is there a function which contains the set of all destination points?

Hey! :o I want to find the $\lim\sup$, $\lim\inf$ and the limit points of the following sequences: 1. $a_n=(-1)^n\frac{3n+4}{n+1}$ 2. $a_n=\sqrt[n]{n+(-1)^nn}$ 3. $a_n=\left ( \frac{n+(-1)^n}{n}\right )^n$ 4. $a_n=(-1)^{\frac{n(n+1)}{2}}\sqrt[n]{1+\frac{1}{n}}$ I have done the following...

Is there a way to calculate the freezing and boiling point of water that has different levels of CO2 in it?

Homework Statement Given the points P0 = (0,a), P1 = (b,0), P2 = (0,0), write the parametric equation of a circle that intersects the 3 points. Assume that b > a and both are positive. Homework Equations X = h + rcos(t) Y = k + rsin (t) r = √((x-h)2 + (y-k)2 Cos (t) = (x-h)/r Sin (t) =...

Homework Statement In this notes , i don't understand how the Q=(Ay) of the is considered ... Homework EquationsThe Attempt at a Solution I think the both Q at part C and part B should be = (60)(15)(mm^2) ... i have redrawn the structure , i am not sure whether it is correct or not... From...

dear all i need the help in understanding the following points: 1- In E&M, what is happening (physically) at anomalous absorption?, and how is this explained by the form of permittivity (real and imaginary parts)? 2- why did the "electric displacement" call that way?

Homework Statement Given the points ##A (1, -1, 0)## and ##B (4, 0, 6)##, find the point ##P## of the line ##s## so that the triangle ##ABP## is a right triangle in ##B##. Calculate the area of the triangle. ##s : \begin{cases} x = 1 + 4t \\ y = 2 - 3t \\ z = 3 \end{cases}## ##\vec v_s = (4...

Homework Statement If a, b and c are coplanar vectors related by λa+μb+νc=0, where the constants are non-zero, show that the condition for the points with position vectors αa, βb and γc to be collinear is: λ/α + μ/β + ν/γ = 0 Homework Equations Dot product Cross product Tripple product Vector...

Homework Statement Calculate the resistance of the network shown below: (a) between A and B, (b) between A and C. Answers: (a) 3 Ω, (b) 4 Ω 2. The attempt at a solution (a) I would say that the resistance is 4 Ω between A and B. (b) For A and C the resistance is: (1/4 + 1/4)-1 = 2 Ω. In...

I would like to prove that if $\|f\|_p = 1$ then $f$ is extreme point of unit closed ball in $L^p[0,1]$. [here $1<p<\infty$] I suppose we should try to prove it by contradiction. That is, if $f \in L^p$, with $\|f\|_p=1$, is not extreme, then exists $g,h \in L^p$ with $\|g\|_p,\|h\|_p \leq 1$...

Homework Statement For the moment about B , Cy(0.8) +Ay(0.8) + Cx(0.6) = 0 , right ? Why the author only give ,-Ay(0.8) = 0 Is it wrong ? Homework EquationsThe Attempt at a Solution

I found in Thompson "From Error-Correcting to Sphere Packing and Simple Groups" this on page 131 How do you compute m/n in a finite field? Take the equivalence class 5 given above. Why does 2/5 and 18/22 give 5? thanks

So I have a function f(x,y,z)=3+4(x^2)-9(z^2)-4xy-12yz. I need to find if (0,0,0) is an optimal number. I know I have to get it into the form of 3+(___)^2+(___)^2+(___)^2 or 3-(___)^2-(___)^2-(___)^2 to find if it's a max or min. But I've been working on this all day to no avail. Any help would...

Homework Statement I'm looking at an electric field plot around four (4) + and - point charges in free space. There are several points where the electric fields come together and make right-angled turns (in the limit). Is there a name for these points? Especially is there a traditional name for...

I was studying the Van Allen Belt, and I get it except for the mirror points (see picture). What would cause the particle to be deflected or turned around? Seems to me it would just continue towards the Earth getting tighter and tighter around the field line...

Hello! I have some concentrical spheres with many points inside. And I need to plot the total mass of points in each shell (so between 2 spheres) versus the radius of that shell (defined as (r1+r2)/2, where r1 and r2 are the radius of the 2 spheres forming the shell). I have 10 shells so my plot...

Homework Statement Consider the path r(t) = <10t,5t2,5ln(t) defined for t >0. Find the length of the curve between (10,5,0) and (20,20,5ln(2)) Homework Equations L= ∫ab |r'(t)|dt The Attempt at a Solution r'(t) = <10, 10t, 5/t> t values are 1 and 2 based on the x values for the points...

Hi, I have (probably) a fundamental problem understanding something related critical points and Lagrange multipliers. As we know, if a function assumes an extreme value in an interior point of some open set, then the gradient of the function is 0. Now, when dealing with constraint...

Homework Statement [/B] I am trying to answer two questions: 1. Solve part (b) in the image above by hand. 2. What are the differences between transfer function (a) and transfer function (b). Homework Equations cos(Im(s) / Re(s)) = ζ The Attempt at a Solution 1. For part one given the...