Question

Suppose y=3t+5 and x=21t^2. Write a function of f(x) that determines y in terms of x. (Assume that t≥0)

Answer 1

Answer:

$y=\sqrt{\dfrac{3}{7}x}+5$

Step-by-step explanation:

Suppose $y=3t+5$ and $x=21t^2.$

Express t from the first equation:

$3t=y-5\\ \\t=\dfrac{y-5}{3}$

Substitute it into the second equation:

$x=21\left(\dfrac{y-5}{3}\right)^2\\ \\x=21\cdot\dfrac{(y-5)^2}{9}\\ \\(y-5)^2=\dfrac{9}{21}x\\ \\y-5=\pm \sqrt{\dfrac{3}{7}x}$

Since $t\ge 0,$ then $y-5\ge 0,$ so

$y-5=\sqrt{\dfrac{3}{7}x}\\ \\y=\sqrt{\dfrac{3}{7}x}+5$