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

Answer:

• for x = 2a√t, make t the subject:

${ \tt{x = 2a \sqrt{t} }} \\ \\ { \tt{ \sqrt{t} = \frac{x}{2a} }} \\ \\ { \boxed{ \tt{t = \frac{ {x}^{2} }{4 {a}^{2} } }}}$

• then find y:

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