Answer: a) [tex]\dfrac{5}{4}[/tex] b) 42
Step-by-step explanation:
Since we have given that
[tex]y=\sqrt{x}[/tex]
We need to find the
a) (a) Find dy/dt, given x = 4 and dx/dt = 5.
[tex]\dfrac{dy}{dt}=\dfrac{1}{2\sqrt{x}}\dfrac{dx}{dt}\\\\\dfrac{dy}{dt}=\dfrac{1}{2\sqrt{4}}\times 5\\\\\dfrac{dy}{dt}=\dfrac{1}{4}\times 5\\\\\dfrac{dy}{dt}=\dfrac{5}{4}[/tex]
(b) Find dx/dt, given x = 49 and dy/dt = 3.
[tex]\dfrac{dy}{dt}=\dfrac{1}{2\sqrt{x}}\dfrac{dx}{dt}\\\\3=\dfrac{1}{2\sqrt{49}}\times \dfrac{dx}{dt}\\\\3=\dfrac{1}{14}\times \dfrac{dx}{dt}\\\\\dfrac{dx}{dt}=14\times 3=42[/tex]
Hence, a) [tex]\dfrac{5}{4}[/tex] b) 42
