Answer:
An alternative definition for the acceleration ax that can be written in terms of
and
is 
Step-by-step explanation:
We know that :

Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of
and 
So, We will use chain rule over here :
![a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}](https://tex.z-dn.net/?f=a_x%3D%5Cfrac%7Bdv_x%7D%7Bdt%7D%5C%5Ca_x%3D%5Cfrac%7Bdv_x%7D%7Bdt%7D%20%5Ctimes%20%5Cfrac%7Bdx%7D%7Bdx%7D%5C%5Ca_x%3D%5Cfrac%7Bdv_x%7D%7Bdx%7D%20%5Ctimes%20%5Cfrac%7Bdx%7D%7Bdt%7D%5C%5Ca_x%3D%5Cfrac%7Bdv_x%7D%7Bdx%7D%20%5Ctimes%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%20%5B%5Cfrac%7Bdx%7D%7Bdt%7D%3Dv_x%5D%5C%5Ca_x%3D%5Cfrac%7Bdv_x%7D%7Bdx%7D%20%5Ctimes%20v_x%5C%5Ca_x%3Dv_x%5Cfrac%7Bdv_x%7D%7Bdx%7D)
Hence an alternative definition for the acceleration ax that can be written in terms of
and
is 
From the problem, the vertex = (0, 0) and the focus = (0, 3)
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12
Source:
http://www.1728.org/quadr4.htm
Celia bought a bag of 12 goldfish for $3, Cost of 1 goldfish is $0.25 .
<u>Step-by-step explanation:</u>
The goldfish is a freshwater fish in the family Cyprinidae of order Cypriniformes. It is one of the most commonly kept aquarium fish. A relatively small member of the carp family, the goldfish is native to East Asia.
Here we have , Celia bought a bag of 12 goldfish for $3 . We need to find the cost of 1 goldfish . Let's find out:
Celia have a bag of 12 goldfish which cost her $3 . So , cost of 1 goldfish is equivalent to
⇒ 
⇒ 
⇒ 
⇒ 
Therefore, Celia bought a bag of 12 goldfish for $3 , Cost of 1 goldfish is $0.25 .