What is Line: Definition and 1000 Discussions

The reflection of the line 5x - 7y - 13 = 0 by the line y = -x is ... A. 7x + 5y - 13 = 0 B. 7x + 5y + 13 = 0 C. 7x - 5y - 13 = 0 D. 7x - 5y + 13 = 0 E. 7y + 5x + 13 = 0 This one I totally have no idea. Like, at all.

The point B(3, -1) is reflected by the line g and results in B'(5, 7). The equation of line g is ... A. 4y + x - 15 = 0 B. 4y + x - 9 = 0 C. 4y + x + 15 = 0 D. 4y - x - 15 = 0 E. 4y - x - 9 = 0 Since I didn't know how to approach the problem in a formal, textbook way, I tried to get...

This comes from a line of a proof in my book, and I need help resolving why the equality is true. Suppose that ##M>N##. Why is it true that ##\displaystyle \sup \{\frac{1}{n} (s_{N+1} + \cdots + s_n) ~|~ n>M \} = \frac{n-N}{n}\sup \{s_n ~|~ n > N \}##?

Homework Statement [/B] Consider the line whose shortest distance to the origin is 5 and that is perpendicular to the ray ##\theta= \frac {5*\pi}{7}## for r>0 Find its polar equation ##r=r(\theta)## and ##\theta_1<\theta_2## in the interval ##[0, 2\pi]## such that ##r(\theta)\geq 0## for all...

Homework Statement Write an alternate vector equation for the following line. Change both the point and the direction vector: w⃗ =(4,−1,3)+t(−2,1,7) Homework EquationsThe Attempt at a Solution Did I write a proper alternate vector equation here? I'm still new to vectors in 3-space any tips or...

In a graph , straight line intersects the parabola at(-3,9) & (1, 1) Then the equation is A) x^2-2x+3=0 B) x^2+2x-3=0 C) x^2-3x+2=0 D) x^2-2x-3=0 I know that I can find the answer by substituting the known values to each options, but how to do it the proper way? We need at least three known...

Consider a 3D straight line passing through z-axis. Following two angles are given (available): (1) Angle of the line with the z-axis in X-Z plane (2) Angle of the line with the z-axis in Y-Z plane I want to know the true angle of the line with the z-axis, i.e.,the angle of the line with...

Homework Statement -infinity < r > +infinity Which of the following are equations for the line y=m*x for m<0: a. theta = -arctan(m) b. theta = arctan(m) c. theta = arctan(-m) d. theta = arctan(m) + pi e. theta = arctan(m) - pi f. r = 1/(sin(theta - arctan(m))) 2. The attempt at a solution...

Hello, A low density gas, when heated at a temperature T, emits radiation having a line spectrum, i.e. having only discrete spectral lines. Each spectral line corresponds to a very specific energy transition (jump) for the electron in the atom. Some energy transitions are allowed, some are...

Given m = a/b and the point (a, b), find the equation of the line. I got to use the point-slope formula. y - y_1 = m(x - x_1) y - b = (a/b)(x - a) y - b = (a/b)x - (a^2)/b y = (a/b)x - (a^2)/b + b y = (a/b)x + (b^2 - a^2)/b Is this correct?

Good day, From the first attachment... Why is "D" divided by "D1"? The book is saying that it is for normalizing "D" by the value of "D1". It's not quite clear ! The whole formula is to find the slope of this graph.

Evaluate $\displaystyle \int_C(x+y)ds$ where C is the straight-line segment $x=t, y=(1-t), z=0, $ from (0,1,0) to (1,0,0) ok this is due tuesday but i missed the lecture on it so kinda clueless. i am sure it is a easy one.

I'm requiring help on a circle geometry question I've done. The line L, has equation of y=0, and intersects the circle with (3,0) and radius of 29. Find the points of intersection. My working out: 292 = 841 It's centre is 3,0, Inserting that in circle equation gives (x-3)2+y2 = 841 Solving...

calculate the work done by the force field $F(x,y)=(ye^{xy})i+(1+xe^{xy})j$ by moving a particle along the curve C described by gamma (γ):[0,1] in $R^2$, where gamma (γ)=(2t-1, t²-t)

Hey, What does the vertical line with the "I_b" on the bottom right mean? Link here: https://imgur.com/a/nII9g Thanks, -Yael

Homework Statement The figure shown consists of two rods at right angles to each other and each is uniform of 2m length. D and E are the midpoints of AC and AD Draw the line of action of the weight of the arrangement relative to A, B,C, D and E when it is (a) Suspended from A and in...

Defining dS2 as gijdxidxj and given dS2 = (dx1)2 + (dx2)2 + 4(dx1)(dx2). Find gijNow here is my take on the solution: Since the cross terms are present in the line element equation, we can say that it's a non-orthogonal system. So what I did was express the metric tensor in form of a 2x2...

Homework Statement [/B] Homework Equations - The pressure drop equation. [/B]The Attempt at a Solution

I've noticed that for every prime and every composite number on the number line that is not a perfect power, ( I am referring to positive whole numbers only), that there are infinitely many perfect powers (PPs) that can be generated using that number. This suggests that the PPs should swamp the...

Supposedly the strength of the electric field is is related to the distance between electric field lines. I have two questions about what exactly this means. 1.) What is the distance between electric field lines? Is it just the distance between two points on adjacent electric field lines that...

Hey guys, could anyone tell me if set up this integral correctly? Thanks in advanced!

Homework Statement Hello hello, I am on the second to last question of 6 practice examinations I've been doing! ''There is a transformation matrix T = \begin{pmatrix} 4 & 9\\ 3& 4 \end{pmatrix} They want me to derive the equation of the line onto which the line x +(1/2)y = 0 is mapped by the...

Homework Statement Find an equation for the net electric field at a point, above and between, two infinite line charges, one with line charge density λ and the second with line charge density -λ. The point is a distance R from both line charges, a distance y above the midpoint between charges...

Homework Statement Homework Equations V = IR And R becomes 2(r of one conductor) because of return path. The Attempt at a Solution V minimum is at third junction. At VD Using KVL we get: [/B] Drop at AB = (10 + 20 + 50) * 2 * 0.1 = 16 V Drop at BC = (20 + 50) * 2 * 0.08 = 11.2 Drop at CD =...

Hello, I'm having the damnedest time wrapping my head around a concept of audio electronics: http://whirlwindusa.com/support/tech-articles/high-and-low-impedance-signals/ How exactly does a higher impedance bring down the frequency at which capacitance dominates? My current understanding is...

Hi All, [This thread has been re-started to accommodate modification of the project for the benefit of anyone that isn't a qualified Professional. Specifically the use of a Low Voltage isolated Source.] I want to get the opinion of people with more experience than me, regarding a project I was...

Homework Statement A 50 Ω lossless transmission line of length 0.4λ is terminated in a load of (40 + j30) Ω. Determine, using the equation given below, the input impedance to the line.Homework Equations The Attempt at a Solution Zo= 50 Zl= 50∠36.87 or 40+j30 βι= 144° (this is known due to...

Homework Statement [/B]Homework Equations I think right answer should be A. Long line on no load is like capacitor so due to ferranti effect the terminal voltage is high. Now when alterator is disconnected the terminal voltage will drop to Ef The Attempt at a Solution Book says answer is D. It...

Homework Statement Compute ##\partial_n f## where ##n## is normal to ##f##, and ##f## lies in the ##x-z## plane and is parameterized by $$x(s) = \frac{1}{c} \sin (c s);\\ z(s) = \frac{1}{c} (1-\cos (c s)) $$ Homework Equations ##\partial_n f = \nabla f \cdot \hat n## The Attempt at a Solution...

I notice from the classic electric field line diagram of two positive charges that there is no field line going along the line segment joining those two charges. So I wonder whether that is true or it's just a way that you can't show all the field lines in the diagram but it actually exists. (I...

Homework Statement Consider a cylindrical hole of radius a and infinite length cut into a dielectric medium with relative electric permittivity ε (the interior can be treated as a vacuum). Inside the hole there are two line charges of infinite length with line charge densities λ and −λ...

Homework Statement Homework EquationsThe Attempt at a Solution Line integral of a curve ## I = \int_{ }^{ } yz dx + \int_{ }^{ } zx dy + \int_{ }^{ } xy dz ## with proper limits. ## I = \int_{\frac { \pi }4}^{ \frac { 3 \pi} 4} abc ( \cos^2 t - \sin^2 t ) dt = -abc ## |I| = abc...

Homework Statement A single phase transmission line has 2 parallel conductors 1.5 metres apart. The diameter of each conductor being 0.5 cm. Calculate the line to neutral capacitance for a line 80 km long[/B]Homework Equations CAN = 2(3.14)(permittivity)/Loge [D/r] This gives capacitance per...

So for inductance of transmission line book says formula H = 2 * 10 -7 Loge { [Ds]/[Dm] } I'm struggling to understand self and mutual geometric mean distance. Here is one solved example and for this they've drawn And they say that let a a' form one connection and let b b' form other...

Hi I have a personal art project and I am stuck, because of very limited knowledge. I'd like to project an 1-2 meter white line from 1-3 meter distance. The projected line should be as thin as possible (3-10mm) and as powerful as possible. I created a DIY projector, but my problem is that, the...

1. A certain type of atom has only four energy levels, as shown in the diagram. The "spectral lines" produces by this element are all visible, except for one infrared line. The quantum jump that produces the infrared line is: (see attached file) A) state 4 to 3.B) state 4 to 1.C) state 2 to 1...

Hello, how can you imagine the geometrically meaning of the minus sign in ds2=-dx02+dx12+dx22+dx32, maybe similar to ds2=x12+dx22 is the length in a triangle with the Pythagoras theorem?

This video came up in a Private Conversation I was having with @Grands recently. The level of sophistication and precision of this production line is amazing to me. Thinking about all of the design work and experimentation and fabrication work and optimization that went into it... :smile:

Homework Statement [/B] I would like to ask for Q5b function G & H Homework Equations answer: G: -2pi H: 0 by drawing the vector field The Attempt at a Solution the solution is like: by drawing the vector field, vector field of function G is always tangential to the circle in clockwise...

I have read a few parts in various papers where they refer to tiltered vortex lines in superconductor vortexes, however it is not clear what these lines really mean physically. Can anyone suggest a source or a description to this? Thanks

Hey everyone, I'm trying to plot a straight line for a bipolar junction transistor to find the room temperature, T, using my experimental results for the associated base-emitter voltage, ##{V}_{BE}## and collector current, ##I_C##. Here's the equation that I'm using: $$ I_C = α_F {I}_{EO}...

The voltage value on a wire a distance away from the signal-port (where we apply the initial voltage) has a phase delay because the current takes time to travel down the wire. But how do you visualize this? First we have a voltage at the beginning, and that causes current to flow. Then a...

Hi :) The question is in dutch so i'l translate it. on an ellipse E with vertex P and P' on the major axis and vertex Q and Q' on the minor axis. chose R(x1,y1), the projection of R on the major axis is R' and on the minor axis is R''. Define the perpendicular projection of the intrersection...

Hello, I have some simple 3d data like, point 1: x1 = 5.8573375, y1 = -4.17885, z1 = 2.338175 point 2: x2 = -3.26132, y2 = 1.28276, z2 = 0.931583 I need to be able to extend the line from point 1 through point 2 to some additional distance. There are a few posts on stackexchange, but they...

$\text{Determine the smallest distance between point}$ $$P(1,1,1)$$ $\textsf{ and the line $L$ through the origin $L$ has the direction}$ $$\langle -4,-5,8 \rangle$$ ok just barely had time to post this but was ?? about direction presume going off of this $\textit{Distance between point...

Hey, I have this question I've been trying to figure out in an integration textbook. The part of the question that I'm having trouble understanding is basically this. With the parabola below, find the x coordinate of A, if the line OA divides the shaded area into two equal parts. The area of...

Hello All, I have recently studied about oil atomization and have question regarding return line. According to my understanding, oil pressure has influence on droplet size that is formed after atomization which is obvious , higher pressure means smaller droplet size as the oil is passing thru...

Really basic question. I was talking with my friend and we started to get onto discussing lines when I said in three dimensions a straight line can be curved. He thinks of a straight line as a line with no curve, whilst I see it as the shortest possible distance from A to B, which in 3...

Homework Statement I need to first find phase current in the load and line current from the supply Homework EquationsThe Attempt at a Solution I thought it would be easier to work with a star because then the Ztl would be in series with it... I am not sure how to find the current but my best...

Homework Statement I am studying for an exam and I never know if I am finding line current / voltage or phase current / voltage. How can I tell? I guess I am confused on what "phase" and "line" represent. For example: If I do the voltage divided by the impedance, then this gives me phase...