Slope Definition and 787 Threads

What is the difference between slope w.r.t origin and slope at a point on the curve and when are they used ?

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...

Homework Statement identifying the slope of the line?[/B] Homework Equations y2-y1/x2-x1 The Attempt at a Solution i chose two points on the line, the first point is (8,-3) and the second point is (-6,4). Are these points accurate? i used the slope equation to solve for the slope of the line...

Homework Statement Write the equation 4x – 7y – 14 = 0 in the form y = mx + b. Homework Equations "Y= mx + b" and "standard form". The Attempt at a Solution4x – 7y – 14 = 0 (add 14 to both sides of the equation) 4x – 7y = 14 (subtract 4x from both sides of the equation) -7y = -4x + 14...

Hi Community, I have this following tutorial question and I am stuck. I understand how to take the derivative and find the tangent line at certain value for x Which would say if x=2 and the derivative of \frac{1}{x} equals \frac{-1}{x^{2}} then the slope would be y=\frac{-1}{4}x I am unsure...

Homework Statement A child starts from rest and slides on a sled first slope down over a distance of 25 m . Then, the child slides further over a horizontal plane. The angle of inclination is 35 ° and the kinetic coefficient of friction between the sled and the snow is 0.100. The mass of the...

Homework Statement A skier on a slope inclined at 4.7 degrees to the horizontal pushes on ski poles and starts down the slope. The initial speed is 2.7 m/s. The coefficient of kinetic friction between skis and snow is 0.11. Determine how far the skier will slide before coming to rest. Answer...

Homework Statement Find the angle of inclination of a line when the slope, m, is equal to -1/2 Homework Equations m = rise/run = tan(φ) φ=angle of inclination The Attempt at a Solution I thought the answer would simply be using arctan on the slope, but my answer gives me -26.565051 degrees...

Homework Statement Find the slope of the tangent line to the give polar curve at the point specified by the value of theta R = 1/θ, θ=π Homework Equations ##\frac{(dr/dθ)sinθ + rcosθ}{(dr/dθ)cosθ - rsinθ}##The Attempt at a Solution The derivative of r is -1/θ2 Then plugging things into the...

Homework Statement A block of mass is held in equilibrium on an incline of angle 30 degrees by the horizontal force 500N. Determine the blocks's weight, ignore friction. Homework Equations F = MA Normal Force y = Fg*sin(theta) Normal Force x = Fg*cos(theta) The Attempt at a Solution I'm...

Hi, Im on a sking trip with 6 od my friends and they all say thathat a heavier skieer caches up on speed on slope faster than lighter one, (no matter the volume od the ski person). I am saying that mass od the skier does not matter, but the won't listem to me. Am I wrong and crazy? IF I am...

Homework Statement "A 68 kg crate is dragged across a floor by pulling on a rope attached to the crate and inclined 15° above the horizontal. (a) If the coefficient of static friction is 0.50, what minimum force magnitude is required from the rope to start the crate moving? (b) If μk = 0.35...

Box is sliding down the slope with angle 30 , and v_0=0. Because coefficient of friction is $$\mu=0.1x$$ where x is distance covered, the box will stop before reaching the end of a slope. Find the time needed for a box to stop. I get $$F_1=G \sin \alpha , F_{fr} = \mu \cdot G \cos \alpha$$...

Homework Statement No official problem, just a study guide fill-in-the-blanks with an extended simplification blank. Basically, no values were given, and it is a standard block on a standard slope with a north-east applied force pushing down on the block (not parallel to horizontal or vertical...

Homework Statement The points P (2,-1) and Q (3,-4) lie on the parabola y = -x2+2x-1 a) Find the slope of the secant line PQ. b) Find the slope of the tangent line to the parabola to the parabola at P. c) Find the equation of the tangent line at P. Homework EquationsThe Attempt at a Solution I...

Homework Statement A small object with mass m sits on a ramp with mass M which itself sits on the ground (ignore friction between the ramp and the ground). Given the coefficient of static friction μ , compute the minimum horizontal force F that when pushing on M will just barely start the...

Homework Statement If m=5.0kg, φ=30◦ and μs =0.87, what is the minimum force needed to make the box slide down the slope? [/B] Homework Equations force of status friction is less than or equal to the normal force multiplied by the coefficient of static friction F,normal=mgcosφ The image...

Hi All, I am trying to understand better the tests used to determine the existence of a linear relation between two variables X,Y. AFAIK, one way of testing the strength of any linear relationship is by computing ##r^2##, where ##r## is the correlation coefficient; this measures the extend to...

Homework Statement "A block is projected up a frictionless inclined plane with initial speed v0 = 3.50 m/s. The angle of incline is θ = 32.0°. (a) How far up the plane does the block go? (b) How long does it take to get there? (c) What is its speed when it gets back to the bottom?" Homework...

Homework Statement A car attempts to accelerate up a hill at an angle θ to the horizontal. The coefficient of static friction between the tires and the hill is µ > tan θ. What is the maximum acceleration the car can achieve (in the direction upwards along the hill)? Neglect the rotational...

Homework Statement A skier of mass 70 kg is pulled up a slope by a motor-drive cable. a. How much work is required to pull him 60 m up a 30° slope (assumed frictionless) at a constant speed of 2 m/s? b. What power must a motor have to perform this task? Help would be greatly appreciated...

I don't get how to solve this problem in the simplest form... I would appreciate your help thanks! I have had some attempts at the question but the question is supposed to be non-calculator-use, so the method should rather be simple, and I couldn't come up with any sort of neat way to solve the...

We have a slope, which has a M mass and a particle with m mass. There are no friction forces between the slope and the ground nor with the particle. The question is, how can i set up the differential equations to get t time. The slope has an h height and an angle of alpha with the ground...

1. Homework Statement A block, of mass M1, on the rough slope shown is attached to another mass M2 by a light, inextensible string which passes over a frictionless pulley as shown in the diagram (the coefficient of friction between the block and the slope is u ). The block is released from...

Homework Statement when the object is moving , why the theta is larger than the theta(s) when the object is started moving ? I was told that when the object is moving , the Fk will become smaller than Fs , right ? so, IMO , the theta should be larger than the theta(s) , am i right ...

Hello, I am trying to find the magnitude of the resistance force of an object moving down a slope. The question I was given says: A skateboarder heads down a gentle slope (Θ=5°) at a constant speed of 5m/s. Calculate the magnitude of the resistance force. Using the equation mgSinΘ - ma = R, (g...

Consider a object of 5 kilos which is fixed with 4 rolling tyres (like in a trolly) which is in a slanting position of 30 degree angle. My question:How to find the force required to move the object upwards the slope along with rolling resistance considered? I tried the force using the F push...

Hello, Could somebody help me finding the relation between the horizontal force, the weight acting vertically, and the slopes Angle (same for both) that correspond to static equilibrium of the blue ball ? In a first step, I'd like to study this problem without considering friction at all. And...

Homework Statement What would the slope of a position vs time squared graph represent?Homework Equations X=my^2+bThe Attempt at a Solution I thought the slope of this graph would be velocity due to the fact that the normal position vs time graph slopes are velocity. However, I was told that the...

A tractor pulls a 5000kg asked up a hill at a constant velocity. If the hill had a constant grade of 30° with respect to the horizontal and there is a 10,000 N frictional force between the sled and the ground, what is the minimum force the tractor must exert on the sled? I think I'm supposed...

1. Homework Statement I was wondering if my phi angle was in the right position from the picture. Also, it is correct that my normal force FN is perpendicular to the surface?Homework Equations Newton's second law fk=ukFN[/B]The Attempt at a Solution Refer to picture[/B]

Homework Statement A girl of mass mg = 52 kg is pulling a sled up a slippery slope. The coefficient of friction between the girl's boots and the slope is µs = 0.157; the friction between the sled and the slope is negligible. The girl can pull the sled up the slope with a ≤ a max = 0.015 m/s2...

Hello, I need some help with describing the dependency with some nonlinear First ODEs. The question: "Using DField, [a java program to graph first-ODEs], draw the direction field for the DE. Based on the direction field, e the determine behavior of y as t approaches infinity. If this behavior...

Homework Statement A hill is described with the following function: f(x,y) = 3/(1+x2 +y2) Where f(x,y) is the height. Find the points where the hill is steepest! Homework Equations ∇f(x,y) = d/dx(f(x,y))i + d/dy(f(x,y))j The Attempt at a Solution d/dx(f(x,y)) = -6x/(1+x2+y2)2 d/dy(f(x,y)) =...

I know that slope in 2D = $$\frac{\Delta{y}}{\Delta{x}}$$. But what about 3D slope? I mean for every line in 3D there are 3 2D slopes. Those are: $$\frac{\Delta{y}}{\Delta{x}}$$ $$\frac{\Delta{y}}{\Delta {z}}$$ and $$\frac{\Delta{z}}{\Delta{x}}$$ But how do you combine those 3 slopes to form...

we know that in the cartesian plane, slope between two perpendicular lines is -1. but what about the x and y axis? if we find the slope between them it is not equal to -1. why is the slope between two perpendicular lines on the cartesian plane is -1 but the axes themselves do not behave such?

Sorry for the very confusing title, I couldn't think of a different way to better explain my question shortly. Also please bare with me, I find this very hard to explain. So I'm trying to find the slope between two points when one point is moving in a set direction with a set speed. Confused...

Hello, today our teacher told us that on tomorrow's test there is going to be a problem where you drop a mass on a slope which connects into a loop. The point of the problem is to calculate exactly how tall the slope must be for the mass to complete exactly one course through the loop...

An object starts at a height of 5m. The initial incline is 63.4 deg. After moving 2m in the x direction, the incline decreases to 7.125 deg and the motion continues for an additional 8m in the x direction. What is the total time for the object to complete the path?Homework Equations The initial...

Homework Statement Hello. The resistance of a wire increases when the temperature increases. How would this cause the shape of the graph to change? Explain why. The graph shown is a straight line graph with the line traveling at 45 degrees path. The x-axis is VOLTS. The y-axis is CURRENT...

Homework Statement Hi all, I'm trying to calculate a parameter of polymers known as the fragility index. I've attached an image of this curve, which can be either strong of fragile depending on the material. The image also contains the definition for calculating this. However, I don't...

This is no homework; but I cannot work it out so I assume one of my assumption is off... no matter how much I looked at it I can't get to the textbook answer. I tried searching (Google is my friend); I got to Prof. Burge's wonderful lectures slides (Arizona.edu) but he follows a different path...

I want to be able to calculate the change in velocity of a fluid flowing down a slope using the drag equation as the source of friction. However the drag equation uses velocity squared which is constantly changing as the fluid accelerates/decelerates. How do I integrate the drag equation into...

Homework Statement A loaded penguin sled weighing 75 N rests on a plane inclined at angle θ = 21° to the horizontal (see the figure). Between the sled and the plane, the coefficient of static friction is 0.30, and the coefficient of kinetic friction is 0.18. (a) What is the minimum magnitude of...

Homework Statement A girl, with the mass m, slides down an icy slope at the time t1=τ. The slope is inclined at 30° below horizontal. The coefficient of kinetic friction between the girl and icy slope is μk. The girl notices that she can slide down the slope significantly faster if she sits on...

Homework Statement a particle on a slope with angle theta with no friction. v(0) = 0, x(0) = 0, with coordinates i down the slope and j normal to it. I am confused about why with the constant velocity forumla I get a different answer to my attempted method.. I can't see what's wrong..I need to...

I have attached an image of a function that I fit to a scatter plot, and I would like to know if there is a term for the point on the function at which the slope transitions from being less than -1 to greater than -1. I have highlighted this point approximately in yellow...

Hi guys, I have a few tries at this but I keep coming up wrong, so can anyone show me how to convert these two standard form equations into slope intercept form? 2x - 11y = 2, -6x + 3y = 9. Greatly appreciate any help offered :) Thank you!

Homework Statement Find the points on the curve xy^2+x^2y=16 when the tangent line is horizontal The attempt at a solution I found the derivative of the curve -(y(2x+y))/(x(x+2y)) then I found what values of y make the derivative equal 0 y=0,-2x Then I went to plug into the original curve to...

okay so as usual I am stumped ( I am not sure if I dislike math, or simply those who proclaim to be teachers of it. Spouting off steps is not the same thing as teaching ) Anyway, I have a problem that requires me to determine the equation of the line described: Through (6,-4), perpendicular to...