Answer:
[tex]\frac{dx}{dt}=\frac{-8}{3}\frac{ft}{s}[/tex]
Step-by-step explanation:
Be [tex]\frac{dy}{dt}=2\frac{ft}{s}[/tex] to find [tex]\frac{dx}{dt}=?, x=6ft[/tex]
[tex]x^{2} +y^{2}=10^{2};6^{2}+y^{2}=100;y^{2}=100-36=64;y=\sqrt{64}=+-8[/tex]→ y=8 for being the positive distance, deriving from t, [tex]x^{2} +y^{2}=100[/tex]→[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex]→[tex]2x\frac{dx}{dt}=-2y\frac{dy}{dt};\frac{dx}{dt}=-\frac{2y}{2x}\frac{dy}{dt}; \frac{dx}{dt}=-\frac{y}{x}\frac{dy}{dt}[/tex], if x=6 and y=8
[tex]\frac{dx}{dt}=\frac{-8}{6}2[/tex]→[tex]\frac{dx}{dt}=\frac{-8}{3}\frac{ft}{s}[/tex]
we must find the rate of change in radians over seconds, being the speed 8/3 ft / s = 2.66 ft / s the variation in degrees is determined when traveling 6 ft
