Question

Plz help w this math problem

y=ar^2-2at

x=2a√t

express y in terms of x and a

give your answer in the form y=x^p/ma^3-x^q/na

Answer 1

• for x = 2a√t, make t the subject:

`{ \tt{x = 2a √(t) }} \\ \\ { \tt{ √(t) = (x)/(2a) }} \\ \\ { \boxed{ \tt{t = \frac{ {x}^(2) }{4 {a}^(2) } }}}`

• then find y:

`{ \tt{y = {ar}^(2) - 2at}} \\ \\ { \tt{y = {ar}^(2) - 2a( \frac{ {x}^(2) }{4 {a}^(2) } ) }} \\ \\ { \boxed{ \tt{y = {ar}^(2) - \frac{ {x}^(2) }{2a} }}}`