Slope Definition and 770 Threads

Homework Statement A rock is thrown from the top of a slope that makes an angle of 30 degrees with the horizontal. At what angle to the horizontal should the rock be thrown to get a maximum range? (Hint: pick the direction of the slope as a new x-axis and the normal to the slope as the new y...

Homework Statement You're using a rope to pull a sled at constant velocity across level snow,with coefficient of kinetic friction 0.050 between sled and the snow. The sled is loaded with physics books, giving a total mass of 19 {\rm kg}. Homework Equations F=\mu*n The Attempt at a Solution...

Homework Statement I just want to confirm this. A block m1=10 kg is hanging from a rope. the rope is attached by a frictionless pulley to a block m2=5 kg on a frictionless slope with a 40 degree angle from the ground. Find the tension in the rope and the acceleration of the first block...

Homework Statement A bicyclist coasts down a 7.0 degree slope at a steady speed of 5.0 m/s. Assuming a total mass of 75 kg (bicycle plus rider), what must the cyclist's power output be to pedal up the same slope at the same speed? Homework Equations P=Fvcos\theta K=\frac{1}{2}mv^2...

The coefficient of static friction between the m = 2.80 kg crate and the 35.0° incline of the figure below is 0.260. What minimum force must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? Attached is a picture. I broke down the...

Find a curve whose slope at any point (x,y) is equal to 5y, and which passes through the point (1,-2) All previous examples which i have seen of this type of question give a much more complex slope and always in terms of x. This is causing me a bit of confusion with my answer. Should I...

Homework Statement x^4 - 6x^3 + 12x^2 - 8x a) Find all points of infliction of this function b) Sketch the function and identify all convex and concave portions of the curve c) Find the equations of the slopes at each point of infliction Homework Equations x^4 - 6x^3 + 12x^2 - 8x...

if there are two diabatic expansions of gases A and B and slope of their P/V curve are in this way: slopeA> slopeB then which gas is monoatomic and which is diatomic?

Homework Statement 324,000 cubic feet of soil is to be placed in a rectangular area (constructed from hay bales) of 80 feet x 100 feet. Using a slope of 1:1 for the fill soil, how many bales high must the walls be stacked to accommodate the soil? Assume the hay bales have a height of 18"...

Homework Statement You always see slope represented as \frac{\delta y}{\delta x}. Is there any particular reason for why the change in "y" is in the numerator and the change in "x" in the denominator? Why couldn't we represent it as delta x over delta y? Homework Equations \frac{\delta...

Hello, I am trying to fit a sine function to a general curve. Convolution isn't giving me what I want, which is for every point on a general curve, displace that point by another function. I have written some code in Octave, and it's close, but not quite it. What I did was to take a general...

Homework Statement I need assistance in learning the proper way to calculate error/uncertainty in a few things for my undergrad thesis.Homework Equations 1) how to calculate the uncertainty in the slope and intercept of calibration curves (peak area vs mol of compound) I have made via excel...

Homework Statement I have a graph with the radius on the x-axis and Fc on the y axis. I had to then calculate the slope of this linear relationship. I did that, and I got 0.17. The problem is that I don't know what this represents. mass? acceleration?? Homework Equations Fc = m4π^2rf^2...

Hi, I've these values: # x y=f(x) 50 1957768251 100 3915542997 150 5873311096 500 19577709464 1000 39155455160 1500 58686574963 2000 78292255800 2500 97888617384 3000 117466340329 3500 137044056081 4000 156491263529 4500 176177759312 These values...

I'm about one week into a Calc II course, and I realized that I have no idea why finding the area under the curve (integrating) would be the inverse operation of finding slope (differentiating). I get that they are opposites, but not why that should be the case... it's not at all intuitive. Is...

Hello. I have attached an image of a free body diagram of a car traveling up a ramp at 30 degrees. I was wondering if anyone can help me determine the sumation of forces in the X and Y direction. I understand that the forces in the Y-direction must be equal to zero or else the car will not...

Homework Statement f(x)=x1/3 use the definition of f'(a) to calculate the slope of the curve at x=1 (Hint: by rationalizing the numerator. useful formula a3 -b3=(a-b)(a2+ab+b2) The Attempt at a Solution f'(x)=lim (x->1) f(x)-f(1)/x-1 =lim (x->1) x1/3-11/3/ x-1 How can I do x1/3-11/3...

If there is an an ellipse x^2/9 + y^2/16 = 1, and the slope of the tangent is dx/dy = -16x/9y, how do you find what points at which the slope of the tangent is 1? I have no idea how to answer this and I've been trying for like an hour. Can anyone help me?

Homework Statement Find the coordinates of point A and B The function is f(x) = x2 -6x +a (where "a" is a parameter) The equation tangent line to the function at point A is y = -2x +1 The equation tangent line to the function at point B y = 2x -11...

hi, we have a spline which consists of two splines,is it possible the two splines have the same curvature but different slopes?

Homework Statement http://img64.imageshack.us/img64/7782/circleb.jpg I'm supposed to find the slope equation of the tangent line to the circle at point A. A = (2, 7) The circle's formula is (x+1)2+(y+3)2 = 25 The center point of the circle is therefor (-1, 3) So the slope from the...

Homework Statement [PLAIN]http://img824.imageshack.us/img824/5387/idkz.jpg Homework Equations The Attempt at a Solution I really don't even understand where to start. I mean, the graph just seems to go continuous and so wouldn't that mean their is no maximum slope?

Homework Statement A box is trying to be pulled by a rope up a hill that is 30 degrees above the horizontal. The coefficient of friction (\mu) is 0.25. The acceleration is 1.5m/s^{2} down the hill. The mass of the box is 2.0 kg. Find the force of tension in the rope.Homework Equations Fg = mg...

I'm given that a particle launched at 30 degrees, and 40m/s from the horizontal axis travels a certain distance d up a constant slope of 1/5. I need to determine how far up that slope the particle goes. I got a velocity vector the obvious way: \vec{v}=(40cos(30},40sin(30)-9.8t) Then...

inverse best fit slope...expected vs calculated Given a set of data (X,Y) pairs, we can get the best fit line using many techniques. Assume the correlation is not perfect. We can use the least squares method to get the best fit line slope and intercept. So we have Y = mX + b In other...

1. Homework Statement A cylindrical hoop rests on a rough uniform incline. It is released and rolls without slipping through a vertical distance h0. It then continues up a perfectly smooth incline. What height does it reach? 2. Homework Equations GPE=mgh Rotational Ke =0.5Iw2...

f uniformly continuous --> finite slope towards infinity Homework Statement Given f:R \rightarrow R uniformly continuous. Show that \limsup_{x\rightarrow \infty} \displaystyle|f(x)|/x<\infty i.e. \exists C \in R: \, |f(x)|\leq C|x| as x \rightarrow \pm \infty. Homework Equations The...

Homework Statement Imagine a block with mass m being pulled up a frictionless incline with upward angle theta by a rope with tension force T. The mass is pulled until another point of rest at a point distance d away from the original point (with d measured on the incline) and h measured on the...

A 170 g block is launched by compressing a spring of constant k=200N/m a distance of 15 cm. The spring is mounted horizontally, and the surface directly under it is frictionless. But beyond the equilibrium position of the spring end, the surface has coefficient of friction mu = 0.27. This...

Homework Statement A 2.10 multiplied by 103 kg car starts from rest at the top of a 4.7 m long driveway that is sloped at 20° with the horizontal. If an average friction force of 4.0 multiplied by 103 N impedes the motion, find the speed of the car at the bottom of the driveway. Homework...

Help with box on sled slope problem! I've attempted this question and have re done the question about 3 times, getting the same answer. A rope attached to a 20kg wood sled pulls the sled up a 20 degree snow covered hill. A 10kg wood box rides on top of the sled. If the tension in the rope...

1. An elastic spring has modulus of elasticity \lambda and natural length l0. This spring is placed on the slope of a hill with an angle \alpha to the horizontal such that one end of the spring is fixed at the foot of the hill and the other end can move freely along the slope. A body of mass m...

Homework Statement The graph below shows the potential (V) applied to, and the current I(mA) drawn by, an electrical circuit. Use the max and min slope method to determine the: a) equation of line of best fit of the graph below (answer must be and equation relating to V and I). Your answers...

What is the minimum and maximum slope method and how do i use this to determine the line of best fit and uncertainties in the data? I can't find information on google or my textbook about this method which is odd.

Question: Determine the equation the line passing through (-1,4) with undefined(infinite) slope. I put "y=-1" This was because if it was constant there would be a undefined slope? Altough, it was obviously wrong. Help please? [Wrong section if possible get moved to homework]

Homework Statement An object of mass 3kg is sliding down a slope with a friction coefficient of 0.2. The distance over which it slides down before it hits the ground is 7m. Write down an expression for work peformed on the object over the seven metres as a function of the angle X that the...

Homework Statement Would constant velocity down a slope be achieved by a cart, by having the frictional force equal to that of Wsinθ (Where W is the weight force and θ is the angle between the slope and the horizontal). Homework Equations/The Attempt at a Solution For example if θ...

Hi, (Firstly, This is not a perpetual motion discussion. Nor am I suggesting anything of the sort. I'm just wondering where the energy losses enough to stall the system creep in.) ok, I was having a discussion at lunchtime which I didn't have an answer to , so I'll post it here: A...

Homework Statement A Book (initially at rest) slides down an inclined plane, when it is at the bottom of the slope, its speed is 2.5 m/s. What is its speed half way and a third way down the slope. V1 = 0 t1 = 0 V2 = 2.5 m/s Homework Equations a = \Deltav / \Delta t v = \Deltad...

Homework Statement Hi Guys, Its great to be on this forum, some of the posts here have been really useful for me . Anyway, I am trying to calculate the lift curve slopes of an aircraft wing, tail and fin. (3D wing) The only data I have are the various quarter chord sweep angles, Aspect...

Homework Statement Linearize the equation y = Ae^{-\frac{b}{2m}t}, so that lny is the x variable and t is the y-variable. What happens to the slope and the intercept if you increase b? The Attempt at a Solution Taking ln of both sides, I get the equation t = -\frac{2m}{b} \ln y +...

Hello, I'm trying to figure out a method of calculating the work done by friction on an object sliding down a surface with a variable slope, assuming an equation can be determined to fit the line along which the object travels and we have a known coefficient of friction for the surface...

Homework Statement Determine the slope of the tangent at x = 0 for the function f(x) = \frac{cosx}{1-x}?Homework Equations Product rule: F'(x) = f'(x)g(x)+f(x)g'(x) Chain rule: f'(x) = nx^n-1·(x)' The Attempt at a Solution So first I rewrite the equation to get rid of the fraction: f(x) =...

A skier is traveling at a constant speed of 4 m/s on a ski slope. The kinetic coefficient of frictionbetween her skis and the slope is 0.2. Find the angle of the slope. attempt: sin feda = f/w but i have no weight f=mgsinfeda and N=mg cos feda all of this ends up being mu=tan feda but...

I am working on a project in which we get the derivative of a sawtooth waveform as our output. I am having trouble deciding how I should go about finding the average slope of that waveform. We used a Fourier transform to construct the wave so I have the amplitude and phase relationships of 4...

Homework Statement Find the slope of the curve for the given value of x. y=x3-8x; x=1 a. the slope is -3. b. the slope is 1. c. the slope is -5. d. the slope is 3. Homework Equations Would it be... Vav= s(t)-s(a)/t-a? The Attempt at a Solution I know this is a really simple problem, but I...

Hello all, We know that for some well-behaved, smooth/continuous, twice differentiable function of x, f[x] there exists at each point a slope (f ' [x]) and a radius of curvature \rho [x]=\frac{\left(1+f'[x]^2\right)^{\frac{3}{2}}}{f\text{''}[x]} It also seems intuitive to think that at...

Homework Statement Slope of: y=.00002715x^2-.04934171x+44.18240907 Homework Equations d/dx The Attempt at a Solution d/dx[.00002715x^2-.04934171x+44.18240907] = .0000543x-.04934171 This is the derivative (slope) of the function though it's looking for a numerical value. It is...

Hi there, If there are 2 bicycle riders who use exactly the same type of bicycle, start at the same spot but one rider is 100kg and another rider is 50kg.. would the heavier rider coming down the slope faster than the lighter rider? basically, I just want to know if the weight would affects...

Homework Statement Find the slope of the tangent line to the curve: 2(x^2 + y^2)^2 = 25(x^2 - y^2) at the point (-3, -1) Homework Equations Implicit differentiation The Attempt at a Solution 2(x^2 + y^2)^2 = 25(x^2 - y^2) 1. 4(x^2 + y^2)(2x + 2y(dy/dx)) = 25(2x -...