FizeauV

2021-09-28

Consider the parametric equations $x=\sqrt{t-2}\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}y=\frac{1}{2}t+1,t\ge 2$ . What is implied about the domain of the resulting rectangular equation?

tabuordg

Skilled2021-09-29Added 99 answers

Step 1

Consider the given parametric equation as

$x=\sqrt{t-2}\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}y=\frac{1}{2}t+1$

Step 2

Now find the value of t

$x=\sqrt{t-2}$

${x}^{2}=t-2$

$t={x}^{2}+2$

Substitute the value of t in the$y=\frac{1}{2}t+1$

$y=\frac{1}{2}({x}^{2}+2)+1$

Now find the domain as

${x}^{2}+2\ge 2$

${x}^{2}\ge 0$

$x\ge 0$

Function is defined for all real numbers$[0,\mathrm{\infty})$ .

Consider the given parametric equation as

Step 2

Now find the value of t

Substitute the value of t in the

Now find the domain as

Function is defined for all real numbers

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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