Curve Definition and 1000 Threads

I had a question on a quiz that I missed... I am unsure how they got this answer. If someone could explain it would be great! Write the integral that gives the length of the curve. y=f(x)=\int_{0}^{4.5x} \sin{t} dt It was multiple-choice(multiple-guess;)). \text{Choice A }...

Homework Statement Find the tangent equations to the curve y^2= x-1/x+1 at the points with x=2 Homework Equations y=mx+b dy/dx The Attempt at a Solution I tried to solve in order to y: y=sqrt((x-1)/(x+1)) Then I derived to obtain the slope, but this is the part that I don't know if it is...

Homework Statement Hi. I have a table where there is an absorbance for a 0.00 concentration (blank). I now that I have to substract that value to to each of the other absorbances that I have, but my question is... Do I have to graph (concentration 0.00, absorbance 0.00) in the calibration...

r2 = 4cos(2θ) First I graph it. Then I set up the integral. _____π (1 / 2)∫ 4cos(2θ) dθ _____0 ________π = [sin(2θ)] ________0 I thought the limits ought to be π and 0, but that comes out to zero. I pick other limits and they come out to 0. My graph matches the one in the back of the book. I...

Homework Statement Compute ∫f ds for f(x,y)= √(1+9xy), y=x^3 for 0≤x≤1 Homework Equations ∫f ds= ∫f(c(t))||c'(t)|| ||c'(t)|| is the magnitude of ∇c'(t) The Attempt at a Solution So, with this equation y=x^3 ... I got the that c(t)= <t,t^3> c'(t)=<1,3t^2> I know that from the equation...

Homework Statement Find the length of the curve: r(t) = e-2t i + e-2t*sin(t) j + e-2t*cos(t) k, 0 ≤ t ≤ 2π Homework Equations L = [SIZE="5"]∫\stackrel{b}{a} |r'(t)| The Attempt at a Solution I tried factoring out e-2t and got: e-2t (i + sin(t) j + cos(t) k) This is where...

Hello Forum, If a bike is negotiation a curve, the static friction force will supply the centripetal force F_c. If we go too fast and the friction is not enough we skid along the tangent. There are two forces: the weight W=mg pointing down, the normal (contact) force N pointing up and...

I'm trying to find the area of some shape with a straight line for the bottom, two curves on the sides and a straight top. Let's say I can only use calculus-like math. I can turn it on it's side and put it on a graph, but now there's now formula for the curved lines. What do I do? Do I split it...

Homework Statement In Austin, Texas there is a Taco Cannon (modified T-shirt cannon) that will be spreading the joy of taco'ey goodness to festival goers. The only information I have is that it can fire 200 feet (60.96 meters). My physics professor allows us extra credit for applying...

Homework Statement Find $$\int_{C} \frac{ds}{(2y^2+1)^{3/2}}$$ where $$C$$ is the parabola $$ z^2=x^2+y^2 , x+z=1$$ Homework Equations The Attempt at a Solution I tried to parametrize the C , s.t$$ x=t, z=1-t, y=\sqrt{2t-1}$$ , but it seems to become a mess, and I don't know the...

Hi folks, could someone please take a look at this for me: Here are the givens: $$\text{ Find the volume when this curve is rotated about the y-axis }$$ $$y=-4lnx\ \text{ where } 0\le y \le 2$$ I have set my working out in a geogebra file, taken a screenshot and attached same below. Would...

I attached the graph, provided in the problem, as a document. This is the wording of the problem: A 5000-kg freight car rolls along rails with negligible friction. The car is brought to rest by a combination of two coiled springs as illustrated in the figure below. Both springs are described by...

Homework Statement Use implicit differentiation to find y' if (x-y)/(x+y)=(x/y)+1. Now show that there are, in fact, no points on that curve, so the derivative you calculated is meaningless. Homework Equations The Attempt at a Solution I managed to get it into the form: dy/dx =...

Find the area under curve $y=243x^5$ and between y=1 and y=32 Here is my working out: 1. transpose to make x the subject $$x=\frac{y^{1/5}}{3}$$ 2. integrate in y $$\int^{32}_1 \frac{y^{1/5}}{3}\cdot dy=(\frac{5\cdot 32^{6/5}}{18})-(\frac{5}{18})=17.5$$ Which is discrepant with given...

I have a set of data points \{\{x_1, y_1\}, \{x_2, y_2\} ... \} each with an uncertainty \{\{dx_1, dy_1,\}, \{dx_2, dy_2\} ...\}. Is there any way of fitting a nonlinear model to the data that incorporates the uncertainties on both x and y? I know that you can use the Weights command to...

Just a simple question of what the ideal torque/engine speed graph would like? Also, could anyone direct me to a good website or book that would help me understand the following things better: tyre slip/traction control gear ratios and how they affect acceleration

Measure of the "Sharpness of a curve" I have a set of curves that belong to the family of curves y=\frac{c}{x^m}, where m and c are parameters. The attached picture (save.png) shows three such curves for different values of m and c. Now these curves have different 'sharpenss' of curvature (to...

Homework Statement A 1000kg car travels around a frictionless banked curve having a radius of 80m. If the banking is 20 degrees to the horizontal, at which specific speed must the car travel to maintain a constant radius? Homework Equations Fc = mv^2/r Fg(perp.) = mgcos(20) The...

Would you feel more centrifugal force going around a small radius curve or a large radius curve going at constant speed? Why?

I am trying to use Mathematica to fit a curve to these data points ListPlot[{{2*Pi/(1 - 0^2/16), 5 (3 - Log[2])}, {2*Pi/(1 - .05^2/16), 10 (3 - Log[2])}, {2*Pi/(1 - .1^2/16), 15 (3 - Log[2])}, {2*Pi/(1 - .15^2/16), 20 (3 - Log[2])}, {2*Pi/(1 - .2^2/16), 25 (3 - Log[2])}...

Evaluate the line integral, where C is the given curve. \int_{c} xy\:ds, when C: x=t^{2}, \ y=2t\ , \ 0\leq t\leq4 To solve this I should use the formula \int^{b}_{a} f(x(t),y(t))\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}}dt This gives me \int^{4}_{0}...

If the wheels and tires of a car are rolling without slipping or sliding when turning, the bottom of the tire is rest against the road at each instant, so the force of friction is the static friction. Essentially if you are moving around a banked curve and the car is not skidding, then friction...

I know if you have two bads the slope is negative and is curved, and the closer to 0 the better. But what if you have two bads where one is worse? I.e. good a and b are both bads, but you want 5 of good b for every 1 of good a?

Hello, I make the calculation of the curve rotation. Casertano(1982г.) [SIZE="3"]V^{2}=-8GR \int_{0}^{\infty}{r} \int_{0}^{\infty}{ [\frac {\partial p(r,z)} {\partial r}] \frac {K(p)-E(p)} {\sqrt{R r p}}}dzdr [SIZE="2"]p = x - \sqrt{x^{2}-1} x=(R^{2}+u^{2}+z^{2})/(2Rr) Density...

Hey guys, I recently did a compression lab with different materials (wood and pvc pipe) and I have to plot the stress/strain curves given the data collected, as well as find yield strength (0.2% offset), ultimate compressive strength, and modulus of elasticity. I've already calculated...

Homework Statement You have a dye, Sybr GreenI which binds only to double stranded DNA (not single stranded). Once bound, it fluoresces strongly and can be used to monitor DNA melting (transition from double stranded to single stranded). (i) on the axes provided draw the DNA melt curve...

[b]1. For what value of α is the area enclosed by r=∅, ∅=0, and ∅=α equal to 1? [b]2. x=rcos(∅) y=rsin(∅) [b]3. x=∅cos(0) x=∅cos(α) y=∅sin(∅) y=∅cos(α) Don't know what to do after this

Hi How can I calculate the area of the shaded region in picture attached? Please suggest.

Hello, My problem is as follows: The lab I am working on requires the construction of a calibration curve from the measured absorbance of samples of known phenol concentration to intrapolate the phenol concentration of two unknown samples. I have constructed the calibration curve and...

I have a curve defined by following parametric equation: \begin{equation} \gamma(\theta) = 1 + 0.5 \times \cos (N \theta) (\cos(\theta),\sin(\theta)), 0 \leq \theta \leq 2 \pi \ \end{equation} I need to calculate the length of the curve between say θ = 0 to θ = 1.0...

Hi, I have a curve defined by following parametric equation \begin{equation} \gamma(\theta) = 1 + 0.5 \times \cos (N \theta) (\cos(\theta),\sin(\theta)), 0 \leq \theta \leq 2 \pi \ \end{equation} where N is an integer. x and y coordinate of any point on the curve are simply...

If we divide the polar curve into infinitely thin sectors, the arc length of a single sector can be approximated by ds = \frac{dθ}{2π}2πr = rdθ. So why can't we model the arc length of the curve as \int^{β}_{α} rdθ It turns out that the correct formula is actually...

How dones one "flip" the graph of a parametric curve? Define the parametric curve C by x = f(t) and y = g(t) . This curve can be plotted on the Cartesian plane. Let's say we "flipped" this curve over the x-axis, that is, we reflected every point on this curve about the x-axis so that the...

Homework Statement r=5^theta theta goes from 0 to 2Pi Homework Equations Length= integral between a and b of sqrt(r^2+(dr/dtheta)^2)dtheta The Attempt at a Solution r^2=25^theta or 5^(2theta) dr/dtheta=5^theta (ln 5) (dr/dtheta)^2=25^theta+10^theta (ln 5)+...

Homework Statement (a) In Example 1.18, assume that a is less than b (so that k is less than 1) and find y as a function of x. How far does the rabbit run before the dog catches him? (b) Assume now that a=b, and find y as a function of x. How close does the dog come to the rabbit? Homework...

Homework Statement For the function z=f(x,y)=4x^2-y^2+1 I need to set z to a constant c so that the level curve created by the intersection of f(x,y) with the plane z=c is two intersecting lines. I know that the cross section of the function with x fixed is a parabola opening down and the...

Let F : \mathbb{R}^2 \rightarrow \mathbb{R}^2 be the map given by F(x, y) := (x^3 - xy, y^3 - xy). What are some singular points? Well, I know that for an algebraic curve, a point p_0 = (x_0, y_0) is a singular point if F_x(x_0, y_0) = 0 and F_y(x_0, y_0) = 0. However, this curve is not...

Let's say we have a function f(x,y,z)=k which is a level surface for a function of 3 variables. Now say at some point P we want to find the derivative in the direction of some vector, u. (the change in z in the direction of u at point P). We can easily find this direction derivative using...

Hi there, The function $f(x)= e^x+k$ has a tangent to the curve at $x=a$ and going through the origin. Find $k$ in terms of $a$

Homework Statement For my physics EEI, I have developed the formula: g-forces=√(391.88-337.12 cosθ)/9.8 I need to linearise the graph into the form y=mx+c. I'm not sure where just the angle is the independent or cos of the angle. Homework Equations y=k√(x) can be graphed as y vs...

Homework Statement Homework Equations None The Attempt at a Solution I was able to find a vertical asymptote at x=-3/8 by setting the denominator to 0 and using the quadratic formula to find the roots. However, I am unsure of how to find the horizontal asymptotes, and I am not...

Hello, As wind speed rises, the power output of wind turbine also rises. However, after it reaches a certain value (rated power), it levels off, i.e., it doesn't increase any further. According to my teacher, there is a limit to the power generation capability of the generator and hence...

This is confusing me more than it should. A curve in space is given by x^i(t) and is parameterized by t. What is the tangent vector along the curve at a point t= t_0 on the curve?

How would you go about calculating the velocity of a rollercoaster once it reaches the bottom, specifically, something like this: http://www.joyrides.com/sfmm/photos/superman1.jpg It's not hard to calculate the velocity it accumulates during the vertical part but how do you deal with the...

Can someone help me. Why does my power required curve doesn't have the region of reverse command? It goes up from vmin to 230mph. It never goes down. Thats not normal for the power required curve. Attached is the region of reverse command that a power required curve should possess...

Hi, I have a pretty simple question but I'm not certain I know how to phrase it properly. I will try. When we are integrating using cartesian coordinates to find the area under a curve, area under the x-axis is negative and area above the x-axis is positive. This makes sense when I...

I've been playing around with a computer modelling software(maya) and I come across a definition 'isoparametric curve'.Kinda recollect something in the same line during multivariable cal class,but I'm not sure what this means mathematically. Help!

Homework Statement A particle starts at rest, then accelerates at a constant rate of 1 meter per second squared.Homework EquationsPerhaps a(t) = t The Attempt at a SolutionI have a series of calculus-related questions based on this statement, but first, I just want to know if the equation above...

Homework Statement A 1200kg car rounds a dry curve (μ= .6)with a radius of 67 m banked at an angle of 12°. If the car is traveling @ 95 km/hr (26.4 m/s), will a friction force be required? If so how much and in what direction? Homework Equations Fn = mg cos 12° ƩFn sin 12° = m (v^2/r)...

When a car turns too fast, it skids away from the center and I don't understand how that's possible in terms of forces. Background idea: The confusion came about when I was approaching a question where the net force of a car on a curve was towards the center of the curve as static friction. The...