In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called the eliminant.The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently on a computer. It is a basic tool of computer algebra, and is a built-in function of most computer algebra systems. It is used, among others, for cylindrical algebraic decomposition, integration of rational functions and drawing of curves defined by a bivariate polynomial equation.
The resultant of n homogeneous polynomials in n variables (also called multivariate resultant, or Macaulay's resultant for distinguishing it from the usual resultant) is a generalization, introduced by Macaulay, of the usual resultant. It is, with Gröbner bases, one of the main tools of effective elimination theory (elimination theory on computers).
Homework Statement
Starting at the origin of coordinates, the following displacements are made in the xy-plane (that is, the displacements are coplanar): 60 mm in the +y-direction, 30 mm in the Ñx-direction, 40 mm at 150°, and 50 mm at 240°. Find the resultant displacement both graphically...
In a lab that my class was doing, we had to hit two tuning forks (of different frequencies) at the same time. One tuning fork had a frequency of 340 and the other had a frequency of 320Hz. I am aware that due to the Principle of Linear Superposition, when two sound waves are combined, the...
Homework Statement
I attached the question as a picture to this threadHomework Equations
M=FdThe Attempt at a Solution
I was taught that the moment produced by two equal but opposite forces is the magnitude of one force multiplied by the distance between the two forces.
I used Pythagoras to...
The question is: The 150lb. force shown is the resultant of two forces, one of which is shown. Determine the other force.
I cannot figure out how to get the other force. I tried using the parallelogram method and method of components, but have been way off on the answers. The answers on the...
Homework Statement
Q: Make a scale drawing showing both the forces produced by the cables and the resultant force. Estimate the angle carefully or measure it with a protractor.
Supplement:
A person with an injured jaw has a brace below his chin. The brace is held in place by two cables...
Hello All,
Please guide me to calculate the resultant of the following two 3D vectors.
vec1 =(-0.3960i,4.6660j,15.2610k)
vec2 =(-4.1230i,-13.2200j,17.9170k)
Thanks
Suneyna
Two coherent waveforms (could be pulses or wavetrains), that intersect at an angle, as in the picture below.
Assume that we are able to make the waveforms in phase and superposed at the point of intersection, such that they constructively interfere.
In what direction does the...
Homework Statement
Given two vectors(d and e) in the form of (x,y,z), and given the angle between the vectors, how do you find the resultant vector (a)
Homework Equations
Cosine equation
The Attempt at a Solution
I know that we can use cosine law some how?
Here's the question:
A bird drops a seed, which falls with a steady vertical terminal velocity of 4.8 m/s. A
slight breeze blows the seed toward the west at 1.2 m/s.
(a) What is the magnitude of the resultant velocity of the seed?
(b) What is the direction (in degrees west of the...
Homework Statement
A person walks 20m [N20(degrees)E], then 120m [N50(degrees)W], then 150m[W], and finally 30m [S75(degrees)E]. Find the person's final displacement.
Homework Equations
Is my solution correct? The textbook answers are 230m[N23(degrees)W]
What did I do incorrect...
hi,
let's take something simple, for example:
(a>b) && ((b>c) && c>d) || (d > c)
Intuitively, it's easy to work out given the values of a, b, c and d and just evaluating the brackets in order of precedence.
i.e.
Is b > c?? then is c > d
Then in addition to the above answer being...
Homework Statement
Two forces P and Q are applied as shown to the corners A and B of a square plate. Determine their magnitudes P and Q and the angle (weird B) knowing that their resultant R has a magnitude R = 120 N and a line of action passing through O and forming an angle of 30 degeres...
Homework Statement
A car travels 20.0 km due north and then 35.0 km in a direction 60.0° west of north. Using a graph, find the magnitude and direction of a single vector that gives the net effect of the car's trip. This vector is called the car's resultant displacement.
I am...
Hello, can someone please explain why (B.y) for the y-component is negative for the sin30. thanks .
question is below.
[PLAIN]http://img710.imageshack.us/img710/6150/resulant.jpg
A force Farrowbold1 of magnitude 5.30 units acts on an object at the origin in a direction θ = 51.0° above the positive x-axis. (See the figure below.) A second force Farrowbold2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude...
Homework Statement
A packing crate rests on a horizontal surface. It is acted on by three horizontal forces: 1000N to the left, 300N to the right, and friction. The weight of the crate is 500N. If the 1000N force is removed, the resultant force acting on the block is
A) zero
B) 300 N to...
I have a pretty simple question: What is the purpose of a resultant velocity in 2D motion? Is it used for anything besides finding the vertical and horizontal components?
For example, I was given this problem:
Sharron dives off a spring board into the pool 3m below with a velocity of 8...
Homework Statement
I need to calculate the resultant resistance between points A and B
The |-| parts are short curcuited ideal DC power supplies (illustration only)
This is the circuit:
Homework Equations
R_P = \frac{1}{\frac{1}{R1}+\frac{1}{R3}+\frac{1}{Rn}}
R_S = R_1 + R_2 +...
Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in the figure. (985N @ 31 Degrees Quad 1, 788 N 32 degrees Quad 2, and 411N 53 degrees quad 3.
How do I find the direction of the resultant of...
Hello. Let's say that I am in a frame in which I see a rocket traveling at v. This rocket then fires a projectile forward with velocity u in its rest frame.
I can find u' easily enough using the Einstein velocity addition formula. However, I recall seeing a version of the formula that uses...
Homework Statement
Three vectors are shown in the figure (A = 68.0 ; qB = 54.0°). Their magnitudes are given in arbitrary units. What is the magnitude of the resultant vector?
Homework Equations
here's the image that goes with it
The Attempt at a Solution
well i figure the angle...
hi
I have multiple torques acting at different points on a rigid body
I want to find the resultant force and torque (about the body CM)
I think I can see how to "convert" an off-center torque to a torque + translation using the parallel axis theorem - but am wondering if there is a...
I am working with some wind speed data and need to work out the standard deviation of the magnitude of the horizontal wind. Unfortunately the only information I have is the standard deviation for the streamwise and cross-stream components of the wind (which are orthogonal). Is it possible to...
Homework Statement
Points: 3)
A vector X is added to vector Y = 12i -16j. The resultant vector lies along the positive x-axis and has the same magnitude as X. What is the magnitude of X?
a. 20.7
b. 16.7
c. 11.3
d. 4.7
Homework Statement
Compute the magnitude and location of the resultant of the parabolic loading shown in the figure below. The slope of the parabola is zero at the origin.
See figure: http://imageshack.us/photo/my-images/819/prob6.jpg/
Homework Equations
The Attempt at a...
Hi guys, please help me with this problem. thanks
A 75 kg sky-diver in free fall is subjected to a crosswind exerting a force of 60 Newton and to a vertical air resistance force of 100 Newton. Describe the resultant force acting on the skydiver.
I used the formula to calculate the resultant...
Homework Statement
Two waves of the same frequency have amplitudes 1.02 and 2.27. They interfere at a point where their phase difference is 59.5°. What is the resultant amplitude?
Homework Equations
Resultant Amp = (Amp1 + Amp2)cos(theta/2)
The Attempt at a Solution
Okay this...
Resultant Force: Something I am messing up on in calculation - ?
Homework Statement
Hey all,
This is a resultant force word problem. I will just post the my answer and the problems answer. I have no idea why there is a different answer here.
Correct: R^2=1500^2+2300^2 - 2 x 1500 x...
1. Find the magnitude of resultant of OA, OB and OC ( there is an arrow sign upwards of OA, OB and OC showing these are vectors.)
(Sorry but i am not good at making computer drawings.)The Attempt at a Solution
I tried to find the resultant of OA and OC and then the angle of resultant with OA...
How would I go about calculating the resultant forces / torques on a system if it's previously spinning at a constant angular velocity, but then an external torque is applied to it?
I would like to use this for some very basic analysis of a custom gear box used in a robotic joint. We attach...
Homework Statement
A rowboat starts across river. If the average speed of the boat is 5.39 m/s and the river is flowing at a speed of 2.91 m/s, what is the resultant speed and resultant angle of the boat?
i know this is super basic but i havn't done this type of problem since the...
Homework Statement
Two wave generators S1 and S2 produce water-waves of wavelength 4m. They are placed 4m apart in a water tank and a detector P is placed on the water surface 3 m from S1. (90 degree to S1S2, S2 to P is 5m)
When operted alone, S1 and S2 produce waves with intensity I and...
Homework Statement
you have a vector in the positive "x" direction with a magnitude of 450' and a vector in the positive "y" direction with a magnitude of 250' determin the magnitude and direction of the resultant
Homework Equations
The Attempt at a Solution
I solved it =...
Two forces, 489 N at 11
◦
and 444 N at 25
◦
are
applied to a car in an effort to accelerate it What is the magnitude of the resultant of
these two forces?
Answer in units of N.
1. A tank with vertical walls, 2m wide and 2m long and 2.5m high, is filled with 4800 litres of water (density 1000 kg/m3) and 3200 litres of light oil (density 900 kg/m3). Calculate the magnitude and location of the resultant force on each of the vertical walls of the tank.
2. By doing some...
I've got a question concerning the resultant force due to hydrostatic pressure. I understand how to calculate an object with uniform dimensions as depth (and pressure) increase. But I got thrown a serious curve ball on a Statics test.
The situation was such:
A downward facing isosceles...
When find the resultant force on a plane surface under uniform pressure why do we use ybar, the distance to the centroid when the resultant force acts through the centre of pressure?
Shouldn't we use the distance to the centre of pressure?
Figure 1a shows a system of forces is pulled an object on different directions.
1a) Determine the magnitude and direction of the resultant force for the system of forces shown.
1b) Explain the changes of magnitude and direction of resultant force for the system of forces based on the...
Homework Statement
Two sinusoidal waves have the same angular frequency, the same amplitude ym, and travel in the same direction in the same medium. If they differ in phase by 50 degrees, the amplitude of the resultant wave is?
Homework Equations
The Attempt at a Solution
How do...
Homework Statement
Let's say that there are 2 speakers, A and B. They are equidistant from location Q and differ in distance from Location P. Speaker A is closer to Location P than Speaker B is to Location P. Both speakers emit sound waves and are in phase with each other.
The problem asks...
Homework Statement
A force of 5N acts along the vector (-4,-3,-1)
A force of 2N acts along the vector (-3,-6,5)
A force of 4N acts along the vector (-9,-1,8)
find the resultant force vector.
Homework Equations
The Attempt at a Solution
i tried to multiply the vectors by the...
Homework Statement
An object has two ropes attached. One is on the x-axis (positive) with a 60 lb force. One is 120* (Quadrant II) from the first rope with a 30 lb force. I have to find the resultant force and angle using the component vector method of addition NOT the parallelogram method...
1. Homework Statement
a beaker contains 200mL of ethyl alcohol at 22 C degrees. what is the minumum amount of energy that must be removed to produce solid ethyl alcohol..
the melting/freezing pt is -114 C degrees
Latent heat fusion = 1.09x10^5
density is 790kg/m^3
specific heat capacity...
Homework Statement
An orienteer runs 5km east, 4 km south and 1km west. If she completed the course in exactly 1 hour, calculate her displacement from the start.
Homework Equations
There were questions before it I've already answered but I am not sure if I can do this question through...
Homework Statement
a square of sides 10cm has four charges at each corner starting clockwise from top right they are 5,10,6 and 3nC. Determine the resultant electric field including magnitude and direction at the centre of the square. Owww and the medium is air. Finally what is the force on...
Homework Statement
An airplane is traveling with airspeed of 225 mph at a bearing of 205 degrees. A 60 mph is blowing with a bearing of 100 degrees. What is the resultant ground speed and direction of the plane?
Homework Equations
x = u cos(degrees)
y = v sin(degrees)
However, I think the...
In school, we've been using the parallelogram method to calculate the resultant force of 2 forces.
I've noticed the teacher using his calculator to give the answer, so I think there must be a formula to calculate Resultant force.
Can someone tell me the formula please ?