Answer:
The average velocity of the particle is
.
Step-by-step explanation:
In vector terms, the average velocity of a particle (
), in meters per second, at a given time change (
), in seconds:
(1)
Where
and
is the change in position for x and y axes, in meters.
![\Delta x = x(2) - x(1)](https://tex.z-dn.net/?f=%5CDelta%20x%20%3D%20x%282%29%20-%20x%281%29)
![\Delta x = (4\cdot 2 - 1)-(4\cdot 1 - 1)](https://tex.z-dn.net/?f=%5CDelta%20x%20%3D%20%284%5Ccdot%202%20-%201%29-%284%5Ccdot%201%20-%201%29)
![\Delta x = 4\,m](https://tex.z-dn.net/?f=%5CDelta%20x%20%3D%204%5C%2Cm)
![\Delta y = y(2) - y(1)](https://tex.z-dn.net/?f=%5CDelta%20y%20%3D%20y%282%29%20-%20y%281%29)
![\Delta y = 8\cdot (2)^{2}-8\cdot (1)^{2}](https://tex.z-dn.net/?f=%5CDelta%20y%20%3D%208%5Ccdot%20%282%29%5E%7B2%7D-8%5Ccdot%20%281%29%5E%7B2%7D)
![\Delta y = 24\,m](https://tex.z-dn.net/?f=%5CDelta%20y%20%3D%2024%5C%2Cm)
![\Delta t = 2\,s - 1\,s](https://tex.z-dn.net/?f=%5CDelta%20t%20%3D%202%5C%2Cs%20-%201%5C%2Cs)
![\Delta t = 1\,s](https://tex.z-dn.net/?f=%5CDelta%20t%20%3D%201%5C%2Cs)
![\vec v_{avg} = \left(\frac{4\,m}{1\,s}\right)\,\hat{i} + \left(\frac{24\,m}{1\,s} \right) \,\hat{j}](https://tex.z-dn.net/?f=%5Cvec%20v_%7Bavg%7D%20%3D%20%5Cleft%28%5Cfrac%7B4%5C%2Cm%7D%7B1%5C%2Cs%7D%5Cright%29%5C%2C%5Chat%7Bi%7D%20%2B%20%5Cleft%28%5Cfrac%7B24%5C%2Cm%7D%7B1%5C%2Cs%7D%20%5Cright%29%20%5C%2C%5Chat%7Bj%7D)
![\vec {v}_{avg} = 4\,\hat{i} +24\,\hat{j}\,\left[\frac{m}{s} \right]](https://tex.z-dn.net/?f=%5Cvec%20%7Bv%7D_%7Bavg%7D%20%3D%204%5C%2C%5Chat%7Bi%7D%20%2B24%5C%2C%5Chat%7Bj%7D%5C%2C%5Cleft%5B%5Cfrac%7Bm%7D%7Bs%7D%20%5Cright%5D)
Answer:
He will use 4.
Step-by-step explanation:
1/2 flower-1 sugar*4 = 2 flower - 4 sugar
Solve for y like the top equation:
2y = -4ax + 11
2y/2 = -4ax/2 + 11/2
y = -2ax + 11/2
The equation of the diameter which bisects the chord with slope 1/2 is
![y=-\frac{9}{8} x](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B9%7D%7B8%7D%20x)
The general form of the equation of given ellipse is
and equation of chord will be
for some m and n.
Now in order to find values of x that intercept the ellipse it must fulfill the equation as such;
![ax^2+b(mx+n)^2=c](https://tex.z-dn.net/?f=ax%5E2%2Bb%28mx%2Bn%29%5E2%3Dc)
![(a+bm^2)x^2+2bmnx+bn^2 - c=0](https://tex.z-dn.net/?f=%28a%2Bbm%5E2%29x%5E2%2B2bmnx%2Bbn%5E2%20-%20c%3D0)
<h3 /><h3>What is the definition of an ellipse?</h3>
It is a plane section curve whose sum from two fixed points will be a constant value.
Quadratic roots will give the mid value of x and value of y will be ;
![X=\frac{-b}{2a} =\frac{-bmn}{a+bm^2}](https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-b%7D%7B2a%7D%20%3D%5Cfrac%7B-bmn%7D%7Ba%2Bbm%5E2%7D)
![Y=n-\frac{bm^2n}{a+bm^2} =\frac{an}{a+bm^2}](https://tex.z-dn.net/?f=Y%3Dn-%5Cfrac%7Bbm%5E2n%7D%7Ba%2Bbm%5E2%7D%20%3D%5Cfrac%7Ban%7D%7Ba%2Bbm%5E2%7D)
Thus the final equation of required diameter will be :
![y=\frac{Y}{X} x=-\frac{a}{bm} x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7BY%7D%7BX%7D%20x%3D-%5Cfrac%7Ba%7D%7Bbm%7D%20x)
And in this case the equation of the diameter which bisects the chord with slope 1/2 is,
![y=-\frac{9}{8} x](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B9%7D%7B8%7D%20x)
Learn more from here quadratic equations,
brainly.com/question/14281133
# SPJ1