THE AVERAGE SPEED IS 2.5 KM/H
Answer:
18 eggs
Step-by-step explanation:
Answer:
![c^2 = 9dp](https://tex.z-dn.net/?f=c%5E2%20%3D%209dp)
Step-by-step explanation:
Given
![dx^2 + cx + p = 0](https://tex.z-dn.net/?f=dx%5E2%20%2B%20cx%20%2B%20p%20%3D%200)
Let the roots be
and ![\beta](https://tex.z-dn.net/?f=%5Cbeta)
So:
![\alpha = 2\beta](https://tex.z-dn.net/?f=%5Calpha%20%3D%202%5Cbeta)
Required
Determine the relationship between d, c and p
![dx^2 + cx + p = 0](https://tex.z-dn.net/?f=dx%5E2%20%2B%20cx%20%2B%20p%20%3D%200)
Divide through by d
![\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%5E2%7D%7Bd%7D%20%2B%20%5Cfrac%7Bcx%7D%7Bd%7D%20%2B%20%5Cfrac%7Bp%7D%7Bd%7D%20%3D%200)
![x^2 + \frac{c}{d}x + \frac{p}{d} = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%20%5Cfrac%7Bc%7D%7Bd%7Dx%20%2B%20%5Cfrac%7Bp%7D%7Bd%7D%20%3D%200)
A quadratic equation has the form:
![x^2 - (\alpha + \beta)x + \alpha \beta = 0](https://tex.z-dn.net/?f=x%5E2%20-%20%28%5Calpha%20%2B%20%5Cbeta%29x%20%2B%20%5Calpha%20%5Cbeta%20%3D%200)
So:
![x^2 - (2\beta+ \beta)x + \beta*\beta = 0](https://tex.z-dn.net/?f=x%5E2%20-%20%282%5Cbeta%2B%20%5Cbeta%29x%20%2B%20%5Cbeta%2A%5Cbeta%20%3D%200)
![x^2 - (3\beta)x + \beta^2 = 0](https://tex.z-dn.net/?f=x%5E2%20-%20%283%5Cbeta%29x%20%2B%20%5Cbeta%5E2%20%3D%200)
So, we have:
-- (1)
and
-- (2)
Make
the subject in (1)
![\frac{c}{d} = -3\beta](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7Bd%7D%20%3D%20-3%5Cbeta)
![\beta = -\frac{c}{3d}](https://tex.z-dn.net/?f=%5Cbeta%20%3D%20-%5Cfrac%7Bc%7D%7B3d%7D)
Substitute
in (2)
![\frac{p}{d} = (-\frac{c}{3d})^2](https://tex.z-dn.net/?f=%5Cfrac%7Bp%7D%7Bd%7D%20%3D%20%28-%5Cfrac%7Bc%7D%7B3d%7D%29%5E2)
![\frac{p}{d} = \frac{c^2}{9d^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bp%7D%7Bd%7D%20%3D%20%5Cfrac%7Bc%5E2%7D%7B9d%5E2%7D)
Multiply both sides by d
![d * \frac{p}{d} = \frac{c^2}{9d^2}*d](https://tex.z-dn.net/?f=d%20%2A%20%5Cfrac%7Bp%7D%7Bd%7D%20%3D%20%5Cfrac%7Bc%5E2%7D%7B9d%5E2%7D%2Ad)
![p = \frac{c^2}{9d}](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7Bc%5E2%7D%7B9d%7D)
Cross Multiply
![9dp = c^2](https://tex.z-dn.net/?f=9dp%20%3D%20c%5E2)
or
![c^2 = 9dp](https://tex.z-dn.net/?f=c%5E2%20%3D%209dp)
Hence, the relationship between d, c and p is: ![c^2 = 9dp](https://tex.z-dn.net/?f=c%5E2%20%3D%209dp)
-13x+14=13x-12
Hope this helps!