Line Definition and 1000 Threads

Homework Statement Let A = (1,2,5) and B = (0,1,0). Determine a point P of the line AB such that ||\vec{PB}|| = 3||\vec{PA}||. Homework EquationsThe Attempt at a Solution Initially, writing the line in parametric form\vec{AB} = B - A = (0-1,1-2,0-5) = (-1,-1,-5)\\ \\ \Rightarrow \vec{v} =...

I'm trying to code a script for a character in my game. This will tell the character if the player is in front or behind them. Basically I know the coordinates of the character and their angle of rotation (if rotated 45 deg, that is where they are looking) Perpendicular to their angle is a...

I am assuming that this line integral is along the straight line from $\displaystyle \begin{align*} (0,0,0) \end{align*}$ to $\displaystyle \begin{align*} \left( 5, \frac{1}{2}, \frac{\pi}{2} \right) \end{align*}$, which has equation $\displaystyle \begin{align*} \left( x, y, z \right) = t\left(...

All transmission lines have a characteristic impedance which is different based on their length and voltage and frequency (for AC lines) , Also all transformers and their primaries have a different impedance based on the turnsratio, core steel type etc factors. Now I read that for any given line...

Homework Statement A two dimensional force field f is give by the equation f(x,y)=cxyi+x^6 y^2j, where c is a positive constant. This force acts on a particle which must move from (0,0) to the line x=1 along a curve of the form y=ax^b where a>0 and b>0 Homework Equations Find a value of a(in...

Homework Statement A random sample of size ##n## from a bivariate distribution is denoted by ##(x_r,y_r), r=1,2,3,...,n##. Show that if the regression line of ##y## on ##x## passes through the origin of its scatter diagram then[/B] $$\bar y \sum^n_{r=1} x_r^2=\bar x\sum^n_{r=1} x_r y_r$$ where...

On page 9 of my David Cohen Precalculus textbook (3rd Edition), the following property is given: The distance between a and b is | a - b | = | b - a |. Question: Can we say that | a - b | = | b - a | because distance is always positive? Note: a and b are real numbers.

Homework Statement A line charge with uniform charge distribution and linear charge density ##\lambda## lie along z-axis from ##(0,0,-d)## to ##(0,0,+d)##. Find electric field due to this charge along z, x-axis and potential at ##(0,0,2d)##, ##(\sqrt{3}d, 0,0)## and ##(3d/2, 0 , d)##...

Homework Statement I am trying to study for an exam and a section in the book on pressure on a plane is shown in the attached picture. I am trying to understand how equation15.16 was derived. I know normally the line of action is found using moments so this seems to be a short cut but I...

Our street electric power lines have frequency of 50 Hz or 60 Hz.. what would happen if you increase the frequency higher to radio frequencies or microwaves.. would current still flow? and can you make it as antenna for emergency transmission?

Sorry if this is the wrong place to post this, but I wasn't sure where exactly to put it. When we calculate the force on a closed loop of current-carrying wire in a uniform magnetic field, We calculate the line integral of the loop to be 0. However, when we evaluate the line integral for an...

"The saturation line for a given substance is the combination of temperature and pressure where 100% vapor exists. At any point below this line, there will be a mixture of vapor and liquid, until a point is reached when only the liquid phase exists." I don't understand above passage from...

Homework Statement Homework Equations Summs: $$1+2+3+...+n=\frac{n(n+1)}{2}$$ $$1^2+2^2+3^2+...+n^2=\frac{n(n+1)(2n+1)}{6}$$ The Attempt at a Solution $$\Delta x=\frac{b}{n}$$ $$S_n=f\left( \frac{\Delta x}{2} \right)\Delta x+f\left( \Delta x+\frac{\Delta x}{2} \right)\Delta x+...+f\left(...

∴1. Homework Statement Find an equation for the plane that contains the point (1,-1,2) and the line x=t, y=t+1, z=-3+2t? 2. Homework Equations The Attempt at a Solution I don't know what I am doing wrong but everytime I try to do these plane questions my amswer is always the opposite sign of...

Homework Statement [/B] "Absorption spectra of gaeous HCl show a line at 3.5 μm which results form molecular vibration (oscillation from interatomic distance)" How do I get the frequency of vibration from this? Homework Equations ? If I knew this, then I could probably solve the problem The...

Homework Statement How to rotate a triangle over a line? I have provided a attachment for it? Homework Equations Y= mx +c I don't know the eq for reflection The Attempt at a Solution My plan is find the eq of line. I have got points for the end points of the line but i don't know how to...

I'm trying to construct an analog delay (series of low pass filters) and demonstrate the properties of a transmission line (reflection, attenuating etc.) using a multisim simulation (my attempt attached below). But on the oscilloscope I don't get any kind of reflection. What should I do...

Hi, I am trying to draw circles at the end points of a line but circle centre is not exactly on the end point of the line. Can somebody please guide me. import java.applet.Applet; import java.awt.*; import javax.swing.*; public class JCircle extends Applet{ int x1=30; int y1=30...

I am sorry if this sounds very basic, but I am really troubled on what to title an email regarding a request to join a research group! Any ideas or guidelines?

I am looking at a proof from a book in fluid dynamics on time differentiation of fluid line integrals - Basically I am looking at the second term on the RHS in this equation $$ d/dt \int_L dr.A = \int_L dr. \partial A / \partial t + d/dt \int_L dr.A$$ The author has a field vector A for a...

Homework Statement Evaluate the following line integrals, showing your working. The path of integration in each case is anticlockwise around the four sides of the square OABC in the x−y plane whose edges are aligned with the coordinate axes. The length of each side of the square is a and one...

Homework Statement The problem is your typical N-body simulation, implemented using Python and Numpy. The implementation specifically calls for using the Euler-Cromer method. For this particular case I used the Sun and the first 4 planets of the solar system. Essentially the problem is I'm...

Hii... I have to couple the noise into a communication cable for analyzing the performance of the communication. I am using a function generator which will generate a white noise of 1-2V(rms) and I have a current transformer to couple this to the communication line. The current transformer has...

Homework Statement Find the line tangent to the curve f(x)=0.5x2+3x-1 which is parallel to the line g(x)=x/2+0.5 Homework Equations f'(x)=x+3 The Attempt at a Solution I know it involves taking the derivative of f(x) and using it somehow, but I don't know where to go from there.

Homework Statement We have the hyperbola, the focal stuff of which is on the Abscissa axis. $$x^2 - 2y^2 = 4 $$, and we have a line $$3x - 4y = 2$$, and we need to understand if this two crazy stuff will intersect, or be tangent, or nothing like the previous one. Homework Equations I don't...

Homework Statement For what values of c is there a straight line that intersects the curve ##y = x^4+c x^3+12x^2-5x+2## in four distinct points ? Homework Equations Concept of concavity, Vieta's formulas (link) The Attempt at a Solution Suppose a straight line ##y = mx+b## intersects this...

The set of real numbers satisfying the given inequality is one or more intervals on the number line. Show the intervals on a number line. (A) |x - 4| < 4 (B) |x + 5| >= 2 For (A), I did the following: -4 < x - 4 < 4 I now add 4 to each term. 0 < x < 8 On the number line, I would need to...

The set of real numbers satisfying the given inequality is one or more intervals on the number line. Show the intervals on a number line. (A) |x| < 2 (B) |x| > 0 For (A), I must plot -2 < x < 2 on the number line. In interval notation it is written (-2, 2). Is this right? For (B), we have...

Show the approximate location of the irrational number [(3 - sqrt{5})/2]^(1/2) on a number line without a calculator. Then use a calculator to confirm your approximation. I can find the approximate location using a calculator. How is this done without a calculator?

Homework Statement A 400 kV transmission line has a length of 500 km and a reactance of 0,4 Ω/km. How much power can you transmit, if the power angle (the angle between the voltages of the beginning and the end) is limited to 25 degrees? What would then be the line’s boundary power limit for...

So I'm making an ~200ft long zip line with the top being anchored to a tall tree in my backyard. My problem is I need an anchor for the bottom. Can I use a 6"x6"x12' plywood buried 4 feet in the ground with a guy wire anchored to a 4"x4"x4' 2.5 feet into the ground? What would you say I should...

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

Hi All, Which are the ways one can geometrically obtain, given a line segment AB with length x and an unitary segment OC, a line segment with length 1/x ? Straight edge and compass are allowed (also some auxilliary curve). Best wishes, DaTario

Hey guys, what is the vacuum at the Karman line (100km straight up). I found conflicting sources on this. Wikipedia links to a calculator that states it is ~2.4*10^(-4)T, while another chart I found says it is in between 1.09 and .0075 Torr...

This isn't homework, nor is it an exercise problem; merely a question about a diagram. Re: B.Schutz book "A First Course in General Relativity" 2nd Edition, (Asian print version), page 5, Figure 1.1 "A spacetime diagram in natural units". From section 1.4 Spacetime diagrams: A world line is...

Homework Statement Find the equation of the tangent line to the curve ##\ xy^2 + \frac 2 y = 4## at the point (2,1). Answer says ##\ y-1 = -\frac 1 2(x-2)## And with implicit differentiation I should have gotten ##\frac {dy} {dx}= -\frac {y^2} {2xy-\frac {2} {y^2}}## Homework Equations ##\...

I've been looking for that in various applied electromagnetics books but none of them cover that subject even on the internet the only website I saw it mentioned was in this forum I guess I'd like a book with a level a little above for example cheng or balanis

I hope someone can explain this to me. In the definition of Euler angles, the body-fixed-azimuthal angel γ is measured from the nodal line that defines the intersection of the body-fixed-XY plane and the space fixed-xy plane to the body-fixed-Y axis. This is the green line in this image from...

Anyone know how to get a vertical line between two columns ? Like here in AMSTeX

That pesky 3.5 keV line just won't go away. The authors note that it's compatible with dark matter composed of 7.02 keV sterile neutrinos. If such is the case, the Majorana mass scale of the seesaw mechanism needn't coincide with the GUT scale (if such a scale even exists).

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...

Homework Statement The potential difference between the surface of a 2.2 cm -diameter power line and a point 1.9 m distant is 3.8 kV. What is the magnitude of the line charge density on the power line? Express your answer using two significant figures. Homework Equations V =...

Homework Statement so I have this text file that I'm reading line by line and here is an example of a line: root pts/1 01-19 13:41 (10.0.0.48) Homework EquationsThe Attempt at a Solution How can I extract the terminal and timeframe only? I tried echo $line | cut -d : -f2, 4 and...

Pick any three points on the line y = (x/2) + 3. 1. Reflect each point in the line y = x. Do I simply exchange the x and y coordinates of the chosen 3 points? 2. Show that the 3 reflected points all lie on one line. I need one or two hints here. 3. What is the equation of the line for part...

Show that the points (a, b) and (b, a) are symmetric about the line y = x. Solution: Let m = slope m = (a - b)/(b - a) I know the slope of y = x is 1. Must I now show that the line y = x passes through the midpoint? If so, how is this done when the slope is not a number (as in this example)?

The point P is located on line segment AB in such a way that AB/AP = AP/AB. In words: P divides line segment AB into two segments such that the ratio of AB to the longer segment is equal to the ratio of the longer segment to the shorter segment. (A) Show that this ratio is equal to (1/2)(1 +...

The slope of y = x is 1. Why is this the case?

Show that the slope of the line passing through the two points (x, x^2) and (x + h, (x + h)^2) = 2x + h. Must I use m = delta(y)/delta(x)?

This link is yet another detection of a 3.5 KeV line in long exposure X-ray astronomy observations. It seems that this line is really there, since it has been seen in multiple objects with multiple instruments. I haven't seen any convincing explanations of this line as being due to atomic...

I'm not proficient here, nor skilled, but it is it one of most important calculations in sport. Every point on Mile start line means all run 1609.344m by hitting tangent at various points on 1st bend Every guy has to hit a tangent at assumed different parts of bend ( 36.80m is shortest...