Question

A particle moves along the curve $y=x^{3/2}$ in the first quadrant in such a way that its distance from the origin increases at the rate of 11 units per second. The value of when x = 3 is

• A. $4$
• B. $\frac{9}{2}$
• C. $\frac{3\sqrt{3}}{2}$
• D. none of these

Answer 1

The correct option is A $4$

Given,

$y=x^{\frac{3}{2}}$

$\frac{dy}{dx}=\left(\frac{3}{2}\right)x^{\frac{1}{2}}$

$\frac{dy}{dx}=\left(\frac{dy}{dx}\right)\left(\frac{dx}{dt}\right)$

when $x=3$

$11=1.5\times 1.732\times \frac{dx}{dt}$

$\frac{dx}{dt}=4.2340261$

$\frac{dx}{dt}=4$ Answer.