Hey, I'm new to the boards, and I figured I'd ask you knowledgeable people about my problem. Thankyou!
Directions: Eliminate the parameter to find a cartesian equation in terms of x of the following curve.
x(t)= 6ln(5t) , y(t)= √t
Thanks!
Hey, I'm new to the boards, and I figured I'd ask you knowledgeable people about my problem. Thankyou!
Directions: Eliminate the parameter to find a cartesian equation in terms of x of the following curve.
x(t)= 6ln(5t) , y(t)= √t
Thanks!
Hello Inexcess
Welcome to Math Help Forum!You have:
$\displaystyle x = 6\ln (5t)$
$\displaystyle \Rightarrow \ln(5t) = \frac{x}{6}$
$\displaystyle \Rightarrow 5t = e^{\frac{x}{6}}$
$\displaystyle \Rightarrow t = \tfrac15e^{\frac{x}{6}}$
$\displaystyle \Rightarrow \sqrt{t} = \sqrt{\tfrac15e^{\frac{x}{6}}}$
which can be written as
$\displaystyle \sqrt{t}= \tfrac{1}{\sqrt5}e^{\frac{x}{12}}$
But $\displaystyle y = \sqrt{t}$
So a Cartesian equation is
$\displaystyle y =\tfrac{1}{\sqrt5}e^{\frac{x}{12}}$
Grandad