Curve Definition and 1000 Threads

http://imageshack.com/a/img824/2641/1cpe.png The black curve I drew there represents the load curve in 5th gear. Why is it that at 5500 rpm(160kph), I have a lesser fuel consumption(270g/kWh) than at 4000 rpm(280g/kWh)? Intuitively,if I produce more power at 180kph(ie 5500rpm),I should...

Homework Statement Deside curve tangent in point x=-π/4 Homework Equations f(x)=1/3sin(3x-π/4) y=f(x) The Attempt at a Solution f`(-π/4)=-1 using the tangent equation y=kx+m y=-1*(-π/4)+m y=1/3sin(3(-π/4)-π/4) ≈3.33*10^-14 3.33*10^-14=-1*(-π/4)+m f(x)≈-1*(-π/4)+0,79 is...

determine the point on the graph of: y = x3 - 4 x2 in which the tangent line has the minimum slope. answer (4/3, -128/27) ok my original idea was yo derive the curve first 3x2-8x But when I equal to 0 I get x= 3/8 The curve would be the main and the constrain y = mx I tried and i couldnot...

Find the curve coordinates of the point nearest to P in the curve 5x2 -6xy +5y2 = 4 P = (0,0) oK x2 + y2 =D2 But how can i solve for x or y ? Maybe by expliciting derivative

A particle moves along the curve $$9x^2 + 16y^2 = 144$$ a)Find a parametrization of the curve which corresponds to the particle making one trip around the curve in a clockwise direction starting at (4,0) so I know that $$cos^2t + sin^2t = 1$$ which is a circle. I also know that $$x^2 + y^2 =...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement A town wants to build a banked curve to join to large roads. The maximum speed they would like cars travel on this curve is 51m/s. The angle of the banked curve is to be 19o and the radius is to be 1.8x102 m. a) What does the coefficient of static friction need to be...

[b]1. (a) Find the slope of the tangent line to the curve y=x-x^3 at point (1,0) (i) using the 1st definition of a limit: lim(x->a)- (f(x)-f(a))/(x-a) (ii) using the 2nd equation of a limit: lim(h->a)- (f(a+h)-f(a))/hThe Attempt at a Solution In my attempt I got two different values (the same...

Find the exact length of the curve $0 \le x \le 1$ $$y = 1 + 6x^{\frac{3}{2}}$$ <-- If you can't read this, the exponent is $$\frac{3}{2}$$ $$ \therefore y' = 9\sqrt{x}$$ $$\int ^1_0 \sqrt{1 + (9\sqrt{x})^2} \, dx$$ $$= \int ^1_0 \sqrt{1 + 81x} \, dx$$ $$ = \int^1_0 1 + 9\sqrt{x} \...

A little bit confused. Find the exact length of the curve $$y = \frac{1}{4}x^2 - \frac{1}{2}\ln x$$ $$1 \le x \le 2$$ Using the formula: $$y = \sqrt{1 + (\frac{dy}{dx})^2} \, dx$$ I obtained this: $$\int ^2_1 \sqrt{ \frac{1}{2} + \frac{x^2}{4} + \frac{1}{4x^2}}$$ Now my problem is...

Hi, my problem is this; I am designing a cable camera system to film downhill pursuits. I need to calculate how much tension is required to hang a cable over a 100m span with no more that 0.5m sag in the middle, when is it fixed at two point, both at the same hight. From the research I have done...

Hello, I am looking for the area between \[f(x)=x\cdot ln^{2}(x)-x\] and the x-axis. I have a solution in hand, it suggests that the area is: \[\int_{\frac{1}{e}}^{e}(x-x\cdot ln^{2}(x))dx\approx 1.95\] I have a problem with this solution, I don't understand where the area between 0 and...

Problem statement F(x)= x^2-3x P=(1,f(1)) Revelant equation Lim f(a+h)-f(a)/ (h) As h approaches 0 Attempt at a solution Now this is where I get stuck.. Because usually you have a h that cancels out and then you have something in the form of (h+a) that can be used to determine the slope...

Hi, I'm trying to plot the the ionisation curve of an ionisation chamber against the theoretical curve outlined by Boag and Wilson in their paper - http://ab-div-bdi-bl-blm.web.cern.ch/ab-div-bdi-bl-blm/Beam_loss_detectors/Literature/saturation_spacecharge/saturation_Boag_1952.pdf I can't...

I have to find the area of the loop of the curve $$a^4 y^2=x^4(a^2-x^2).$$ I have confusion regarding the shape of the graph the limits of integration.

Homework Statement A curve with a 140m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s, what is the minimum coefficient of static friction between tires and road needed to prevent skidding? Homework Equations F_fr =...

Here's the problem I was given: Find the area of the surface generated by revolving the curve $$x=\frac{e^y + e^{-y} }{2}$$ from 0 $$\leq$$ y $$\leq$$ ln(2) about the y-axis. I tried the normal route first... g(y) = x = $$\frac{1}{2} (e^y + e^{-y})$$ g'(y) = dx/dy = $$\frac{1}{2} (e^y -...

Homework Statement Find the area of the surface generated by revolving the curve x=\frac{e^y + e^{-y} }{2} from 0 \leq y \leq ln(2) about the y-axis. The Attempt at a Solution I tried the normal route first... g(y) = x = \frac{1}{2} (e^y + e^{-y}) g'(y) = dx/dy = \frac{1}{2}...

So I have this question: After screen-shotting it I realized I added instead of subtracting, so my answer to the first part is about 4.7...is that right? The second part I'm not sure at all how to find the equation for the derivative of the curve.. when I don't have the equations for h(x)...

Searching through Wikipedia (http://en.wikipedia.org/wiki/File:Resonance.PNG), I found this graph about resonance. I do notice from the graph that as the driving frequency gets closer to the natural frequency of the system, the peaks of the curves (i.e. the amplitudes) of the curves increase...

Homework Statement For the 1st one you wouldn't really need MATLAB I guess to find the area under the curve, it is 0 and so is its energy. For the 2nd one I got A=1.73 and so E=2.99.Homework Equations area under curve = evaluate integral from t=t1 to t=t2. in this case t=-2 to t=5 since they...

I am thinking about how to find the volume rotate around its function.Let f be a function of x in the interval [a,b] . The function could be any curve. And the curve is rotation around itself. Would there exist a volume of the curve? And how to find the volumeThank you CBARKER1

Homework Statement The problem involves a calibration curve which was created and where % T vs concentration was favored for use over the usual Absorbance vs concentration and a question of why would this be used in favor over the latter relationship curve was presented. other details...

Hello. I have a program that, given a value for (x), needs to find the corresponding y-value along a cubic Bezier curve. So long as the Bezier does not switch direction in (x), there is always one, and only one, value of (y) for every value of (x). In solving for (y), I discovered that...

I will state the specifics to this problem if necessary. I need to find the parametric equations for the the tan line at point, P(x1,y1,z1) on the curve formed from paraboloid intersection with ellipsoid. The parametric equations for the level surfaces that make up paraboloid and ellipsoid...

Hello MHB, I have the following conjecture which I cannot seem to settle either way: Let $f:[0,1]\to\mathbb R^2$ be a differentiable function such that $f(0)=(0,0)$. Then there exists a continuous function $g:[0,1]\to\mathbb R^2$ such that: 1) $g(0)=(0,0)$ 2) $g([0,1])\cap f([0,1])=\{(0,0)\}$...

Hello! I am having an issue with something that should be extremely simple. Essentially, all I am trying to do is plot the blackbody curve at 2000K in terms of the wavelength. The formula I am using can be seen here.. (Don't feel like typing it)...

Hi, I have an involute gear and measured co-ordinates of two arbitrarily chosen points (on the involute portion) of a tooth. Can I find out the base circle with this information? Thanks.

Find the work done by the Force Field F to make a displacement on the curve C. F= <-y^2 , x> C: semicircle x^2 + y^2 = 1 , y<=0 , from (-1,0) to (1,0)since y<=0 , then it's the semi circle under the x-axis. and according to the solution I have: Work=integral[sin t - sin t cos^2 t +(1+cos...

If I start with the standard FRW cosmology equations, $${\eqalign{ 3\dot a^2/a^2&=8\pi\rho-3k/a^2\cr 3\ddot a/a&=-4\pi\left(\rho+3P\right),}}$$ and set [/tex]\rho=P=0[/itex] (or $T^{\mu\nu}=0$), I have $${\eqalign{ 3\dot a^2/a^2&=-3k/a^2\cr 3\ddot a/a&=0.}}$$ The second equation gives $$\ddot...

There are a lot of contents regarding finding vertical, horizontal and oblique asymptotes for the so called 'rational' functions online. All of these curves are given in the form y=f(x)=(g(x))/(h(x)). But as far as my search results go, there are none regarding general algebraic...

The question was too long to post in the title so I just wrote down the first part. I hope this is alright. Here is the question that I am doing right now: This is the graphical representation (thanks to Desmos Graphing Calculator): So I have substituted the points in the equation to get...

Homework Statement Using Stokes law, calculate the work done along a curve ##\Gamma ## which is defined as edge of a spherical triangle in first octant of a sphere ##x^2+y^2+z^2=R^2##. Vector field is ##\vec{F}=(z^2,x^2,y^2)##.Homework Equations Stokes law: ##\int _{\partial \Sigma...

Homework Statement Find a parameterization of a curve which we get from ##x^2+y^2+z^2=4## and ##x^2+y^2=2x##.Homework Equations The Attempt at a Solution I hope this doesn the job, I am just not sure, so if anybody could check my result I would be really happy. I started with ##x=1+\cos...

Homework Statement Find the length of the curve y = x^3/a^2 + a^2/12x between a and a/2 Homework Equations Length L = integrate (1+ dy/dx)^2)^0.5 The Attempt at a Solution I got to integrate (9x^4/a^2 + 1/2 + a^4/144x^4)^0.5 but I can't simplify it

Given the parametric equations, find an equation of the tangent line at the given point on the curve. Homework Statement Find an equation of the tangent line at each given point on the curve: x = 2cotΘ and y=2sin^{2}θ at point (\frac{-2}{\sqrt{3}},\frac{3}{2}) Homework...

To quote Goursat: Would somebody mind developing some intuition for this statement, along with an example or four (if not an intuitive proof), that would help motivate me to pick up classical books on analytical geometry & encourage me to wade through hundreds of pages to get to results like...

Homework Statement Given the parametric equations:x= t^{5}- 4t^{3} and y= t^{2}A)Determine whether or not the curve described by the parametric equations crosses itself at some point. B)If so, find the (x,y) coordinate point where the curve crosses itself. Where would I begin? How...

In order for an equation to be a function, it has to pass the vertical line test. A circle is not a function because it does not pass the vertical line test. A curve containing a loop does not pass the vertical line test and to me that means it is not a function. However, if I am given...

Homework Statement A car rounds a banked curve as discussed in Example 6.4 and shown in Figure 6.5.The radius of curvature of the road is R,the banking angle is θ,and the coefficient of static friction is μs. Determine the range of speeds the car can have without slipping up or down the...

How can I get the equation of the plotted curve (see attachment) without using the trend line? I've already fitted the random red points using the log-Pearson Type III Distribution (and the result is the blue curve) so I don't need to fit them anymore using any trend lines available in excel...

Homework Statement A vector field ##\vec{F}(x,y,z)=(e^y+z^2cosx,xe^y,2zsinx)## is given and a curve ##\Gamma## with parametrization ##\vec{r(t)}=(sin(3t),cost(5+sin(10t)),sint(5+sin(10t)))##. Calculate the work done along the curve ##\Gamma## for ##t\in \left [ 0,2\pi \right ]##Homework...

Homework Statement Homework Equations The Attempt at a Solution Hello, Comparing these two problems, 9.6 says to calculate the elastic curve for portion BC. However, in the solution they include the contribution from P which is not contained in portion BC in the representative cut to calculate...

Here is the question: I have posted a link there to this thread so the OP can view my work.

My problem: I don't know how to begin with this problem.

I am confused with solving for horizontal asymptotes. I know you are supposed to find limits to positive and negative infinity. I am able to solve for positive infinity but how are you supposed to do it for negative infinity, since you are not actually plugging in a particular value. This...

I have a program that generates a bunch of power curve functions and would like to know what the 'average' function between all of them would be. Here is my data set so far: 4.638013x^0.076682586 4.834884x^0.034875062 4.0432342x^0.13476002 3.8535004x^0.12178477 How do I do this...

Homework Statement My apologies in advance for the messiness of the equations; the computers available to us do not correctly process the LaTex code. I am tasked with estimating the area under the curve f(x)=x2+1 on the interval [0,2] using 16 partitions. Online calculators and my...

Hello guys, I'm really stuck on this problem. Could anyone provide help? f(x) = x^2 - 1 Obtain: (i) domain (ii) intercepts (iii) symmetry (iv) asymptotes (v) intervals of increase/decrease (vi) local maxima and minima (vii) concavity and points of inflection Use these values to...

Find region between these 3 curves. 2y=4sqrt(x) y=5 2y+2x=6 Not sure how to find limits or actually setup the intigration.. is it just (left-mid-right?) But no idea for limits..