Curve Definition and 1000 Threads

The limit below represents the slope of a curve y=​f(x) at the point​ (a,f(a)). Determine a​ f After finding the f(x) and a, I did this:8(3^2+3h(3)+3h(3)+h^2)-72 dividing by h getting h(8h^2+144) dividing by h; canceling the h's and the plugging in the limit h --> 0 getting 144. But I am...

Homework Statement Find the curvature of the car's path, K(t) Car's Path: r(t) = \Big< 40cos( \frac {2 \pi}{16}t ) , 40sin( \frac {2 \pi}{16}t ), \frac{20}{16}t \Big> Homework Equations K(t) = \frac { |r'(t)\:X \:r''(t)|}{|r'(t)|^3 } The Attempt at a Solution This is part of a massive 6...

Homework Statement Deducing what the area under the stress-strain curve shows. There are four option in the attached image. I can discount work done by considering the units. The remaining ones seem plausible, but only one is true. Homework Equations stress = force / area; strain =...

Homework Statement Igor, the inchworm, is crawling along graph paper in a magnetic field. The intensity of the field at the point ##(x,y)## is given by ##M(x,y)=3x^2+y^2+5000##. If Igor is at the point ##(8,6)##, describe the curve along which he should travel if he wishes to reduce the field...

Homework Statement r(t) = < 2e^t - 5 , e^t +3t^2 , 4t^2 +1> Is a curve that lies within a plane. Find the equation of this plane. The Attempt at a Solution I am not sure if my approach is correct. These are my results: x=2e^t - 5 y = e^t +3t^2 z = 4t^2 + 1 z = 4t^2 + 1...

Homework Statement The equation ## f(x,y) = f(a,b) ## defines a level curve through a point ## (a,b) ## where ## \nabla f(a,b) \neq \vec 0##. Use implicit differentiation and the chain rule to show that the slope of the line tangent to this curve at the point ##(a,b)## is ##-f_x(a,b)/f_y(a,b)##...

Homework Statement Match the parametric equations with the graphs. In this case, I am stuck on this equation: x = cos t y = sin t z = 1/(1+t^2) Homework EquationsThe Attempt at a Solution So far I have: x^2 + y^2 = cos ^2 t + sin ^2 t = 1 I know this is a circle in the xy-plane, and thus...

I'm familiar with galactic rotational curves and there are plenty of graphs depicting such curves, but I'm interested in the rotation curves of entire galactic clusters at the moment and I'm not too good with sifting through what shows up in the search engines. (not a physicist, just a...

Sorry if this is more of a HW question (if so then moderator please move my question. Thanks!) Hi, I'm trying to get an expression for a best fit curve of the combination formula (##_nC_r##). As far as I can tell, the curve is a simple parabolic curve, and its shape doesn't change. It's just...

Find the area bound by the curve y=x^2-16 , the x-axis and the lines x=2 and x=5. i am trying to use the definite integral way ∫_2^5. but i am not getting the right answer. the right answer is 53/3

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 there, I have a motor peak torque, peak power, peak speed, rated torque, rated power, rated speed, torque at max speed. I was able to produce the peak torque curve. But, i don't understand how to create this continuous torque curve here. I have attach a link here, and somehow the continuous...

I am trying to find the slope of the tangent line of this polar equation: r = 4 + sin theta, (4,0) I put the equation into wolfram alpha and it gives me a 3D plot. If someone could help me find the slope of the tangent line, I would really appreciate it. Thank you.

The graph of y = x - 1 CUTS the x-axis at x = 1 while the graph of y = x2- 1 TOUCHES the x-axis at x = 1. The point at which the tangent touches the curve is shown mathematically by having two solutions of x, i.e. x = 1 (twice). Is there some deeper meaning to these two identical solutions for x?

Homework Statement for the line segment c2 , why did the author want to differentiate dx with respect to dy ? and he gt dx = 0 ? I'm curious why did he didnt do so for C3 , where dy= 0 ..Why didnt he also differentiate dy with dx ? dy/dx = 0 ? Homework EquationsThe Attempt at a Solution is...

I know the concepts of conformal mapping and complex mapping but I didn’t see none explanation about how apply this ideia and formula for convert a curve, or a function, between different maps. Look this illustration… In the Cartesian map, I basically drew a liner function f(x) = ax+b...

Can the envelope curve (of a family of curves) intersect a member curve of the family at more than one point? It seems possible. Consider the following. Each blue line is a member curve and the red line is the envelope curve. If we modify each blue line such that it has a protrusion like a...

Is there any experimental evidence that pure energy (massless) can curve spacetime?

Hello everyone, i just finished a course of analysis(2)\vector calculus.Now iI'm interested in doing Gd of curves and surfaces(Do Carmo), and functional analysis(Rudin'sbook), but do not know what may have precedence between the two, on which i should start before you think?

Guys... If there is a bar, half of it is Copper and another half is Steel (Length wise) and both of its ends are at 1000K and I want to know how to find the temperature- length curve. this was an interview Question by the way.

Homework Statement I've got a given Breit Wigner curve of the number of decays at given energies. I've been told by several sources that the width (FWHM) of the curve gives the rate of the reaction. I can't see however how an energy here actually translates into a rate. Homework Equations I...

Homework Statement Homework Equations equation with each part. The Attempt at a Solution I did part a) b) and c) on my own: Part d: I am having trouble at this part. I understand how to draw the heat curve but I am confused on what numbers I should use for the x-axis of the graph. I...

In special relativity we can view spacetime as ##\mathbb{R}^4## with its standard smooth structure, and a metric ##\eta_{ab} = \sum\limits_{\mu, \nu = 0}^3 \eta_{\mu, \nu} (dx^\mu)_a (dx^\nu)_b## where ##\nu_{\mu \nu} = \mathrm{diag}(-1, 1, 1, )##. Given a curve ##\gamma: I \rightarrow...

Homework Statement Consider the parametric curve given by: x=6cos(2t), y=t5/2. Calculate the equation of the tangent to this curve at the point given by t=π/4, in the form y=mx+c. The tangent is given by y= Homework Equations The Attempt at a Solution [/B] the answer that I got was...

why can't it be like this?

The curve y=x^4-2x^3-2x^2-2x has a bitangent. I need to find the equation of this line. First, I started off by computing the slope. Since it touches two points on the curve, their slopes should be the same. So, I have the equation 4x^3_1-6x^2_1-4x_1-2=4x^3_2-6x^2_2-4x_2-2 I got up to the point...

For my Quantum II class I am working on a paper about masers. I am using a naive model (a coupled pair of infinite potential wells), and I would like to find out where I can find a graph of the inversion potential energy curve. This would be a simple one dimensional curve of the potential...

Find the arc length of $$f (x)=(1/3)(x^2 +2)^{3/2}$$ On the interval [0, a] The parametric I got $$y=t$$ $$x=\sqrt{(3t)^{2/3}-2}$$ I proceeded but didnt get the answer of $$a+\frac{a^3}{3}$$

The title space is too short for what I want to ask, so here it is. When determining the area bounded between two functions/curves, you have to know which is the upper curve and which is the lower curve to solve the problem. Currently I only know how to do it by graphing, but I was wondering...

Homework Statement [/B] The problem has to do with sig figs going down to 1. I've checked them multiple times by hand and with sigfig calculators but it is all the same. With 1 sig fig my standard deviation ends up being 0 which I am not sure that is acceptable. It makes sense as the points are...

hi, so my lecturer decides to give me manic depression by sending me on a wild goose chase. what is the general form of a plot of Ψ, Ψr2 and r2Ψ versus r for both Ψ2s and Ψ2p orbital... am not even sure i said it right So far I have only gotten the Ψ2r2 versus r

Hello everyone I'm having some difficulty wit curve sketching this specific function. If some one could walk through the steps and solution so that i can hopefully grab a handle on the concept it would be much appreciated! I can handle the beginner functions, but this one is giving me a hard...

Hi, I'm doing a lot of temperature measurement, and I would like to add a function that could estimate how high the temperature would rise and how long it will take to get there. The calculations would be based on the current temperature relative to the past x measurements. Anyone have any...

Homework Statement A cyclist is initially heading exactly due North. He then initiates a turn to the West, the turn being a quarter circle with radius 12-m. He travels at a constant speed of 5.5-m/s during the turn. What is the direction of this average acceleration, measured anti-clockwise...

There are 2 unknowns in the formula. The time period of rotation and the mass enclosed by orbit is Star. So how could we calculate the expected time period of rotation of stars in a galaxy and thus velocity of stars.

I am having a hard time understand why the frictional force of the tires of the car point to the center of the circle (centripetral force). http://physics.stackexchange.com/questions/138871/why-does-friction-play-the-role-of-centripetal-force-during-the-turning-of-a-car . Here is the...

Homework Statement I did a lab this week measuring periods of swings of a simple pendulum. We need to curve fit the equation T=k*l^n and we got ln(T)=n*ln(l)+ln(k), and we need to plot the data we collected into the linear graph, meaning out y axes is ln(T) and our x axes is ln(l). So far all...

Homework Statement [/B] The normal to a curve at a point P cuts the y-axis at T and N is the foot of the perpendiculor from P to the y axis. If for all P, T is always 1 unit below N, find the equation of the curve.Homework EquationsThe Attempt at a Solution Point T has co ordinates ## (0,y)##...

Ok, first week of first year of undergraduate physics lab and they explain that we want all our graphs to be linear, and in order to do that we can change our x and y axes to be log(x) or y^2 or whatever. They did some simple examples such as y=(k/x)+c and explained that if the x axes is 1/x we...

Homework Statement Show the area under the curve of v(t) is equal to the displacement from t1 to t2 Homework Equations x/t = v The Attempt at a Solution Integrate V(t) = vt dt (v/2)*t^2]t1 to t2 (v/2)*t1^2 - (v/2)*t2^2 Not sure if that is good enough or how toactually show it. To find the...

Hello Forum, In the situation of a car banking a curve there are two forces: weight W and the normal force N. Theta is the banking angle between the road and the horizontal. The vector addition between W and N gives a net force F_net that is directed toward the center. That F_net is the...

Homework Statement I have done a tensile test. Now that remains to do is create a table where the elongation (in mm) is shown at a specific load (in kN). I had two plates that I put through the tensile test. Both of them were 165 mm before the test. After measuring after the test, the first...

Hi, I'm working on some coursework for which I have been modelling a curve to a set of points, and for the final section I am wanting to calculate how close each point is to the curve as a method of comparison between the curves I have calculated. Some of the curves are quadratic, and others are...

I'm trying to create a simple (well, not for me apparently) commission curve based on a few basic parameters. I can do the straight line approach, but I need a little more power. This is for an interactive report I am writing in Crystal Reports. User currently enters Max Commission Rate and...

Because I wasn't able to find it in my calculus textbook, what book I should learn about involute curve?

Hi I have uploaded centrifugal compressor performance curve. I want to know how Mass Flow vs Pressure Ratio curve plotted under different efficiency since efficiency is a constant for a compressor. Please help.

Homework Statement Find the arclength of the curve x = ⅓(y2+2)3/2 from y=0 to y=1. Homework Equations (Please forgive the crazy definite integral symbols - I'm taking a LaTex class tomorrow so hopefully I'll be able to communicate more clearly from then on..!) arclength of curve = ∫ab √ (1 +...

Will epsilon delta test fail if curve changed direction within the +/- delta of the limit point? Is there a scenario where no matter how small we pick delta to be, the frequency of the graph changing directions is always going to be a higher than delta's distance? In that scenario the limit...

Given a parametrized curve ##X(t):I\to\mathbb{R}^2## I am trying to show given a fixed point ##p##, and the closest point on ##X## to ##p##, ##X(t_0)##, the line between the point and the curve is perpendicular to the curve. My only idea so far is to show that...

Simple and basic question(maybe not). How are rotations performed in differential geometry ? What does the rotation matrix look like in differential geometry? Let us assume we have orthogonal set of basis vectors initially. I am looking to calculate the angle between two geodesics. Can this...