(Solved): A kite 100ft above the ground moves horizontally at a speed of 9ft/s. At what rate (in rad/s) is ...

A kite $$100\mathrm{ft}$$ above the ground moves horizontally at a speed of $$9\mathrm{ft}/\mathrm{s}$$. At what rate (in rad/s) is the angle (in radians) between the string and the horizontal decreasing when $$200\mathrm{ft}$$ of string have been let out? $$\times \mathrm{rad}/\mathrm{s}$$ Enter a fraction, integer, or exact decimal. Do not approximate. Enhanced Feedback Please try again. Let $$?$$ be the angle between the string and the ground and $$x$$ denote the horizontal distance of the kite. Then $$x$$ is one leg of a right triangle with hypotenuse formed by the string; the other leg is facing the angle $$?$$ and has length equal to the height of the kite. You need to use a trigonometric function to relate $$?$$ and $$x$$ and then differentiate the relation with respect to $$t$$. Finally, solve for $$\frac{d?}{dt}$$ and find its value using the given values. Note that negative rate means the quantity is decreasing. If two resistors with resistances $$R_1$$ and $$R_2$$ are connected in parallel, as shown in the figure, then the total resistance $$R$$, measured in ohms $$(?)$$, is given by $$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$$. i) If $$R_1$$ and $$R_2$$ are increasing at rates of $$0.3?/\mathrm{s}$$ and $$0.2?/\mathrm{s}$$, respectively, how fast (in $$?/\mathrm{s}$$ ) is $$R$$ changing when $$R_1=100?$$ and $$R_2=110?$$ ? (Round your answer to three decimal places.) $$?/\mathrm{s}$$