17.25 USE problems

Problem: 1) Appliances are connected to the power outlet, the total resistance of which is \( 60 \mathrm{Ohm} \). An electric heater is supposed to be connected to the outlet in parallel with them. Determine (in ohms) the smallest possible resistance of this electric heater, if it is known that in case of a parallel connection of two conductors with resistances \( R_{1} \) and \( R_{2} \) their total resistance is given by the formla \( R=\frac{R_{1} \cdot R_{2}}{R_{1}+R_{2}} \), and for the normal functioning of the electrical network the total resistance of it must be not less than \( 10 \mathrm{Ohm} \). 2) Find the biggest value of the function: \( y=17 x-5 \sin x+7 \) on the segment \( \left[-\frac{\pi}{2} ; 0\right] \). 3) The first pipe passes 1 liter less water per minute, than the second pipe. How many liters of water per minute passes through the second pipe, if it fills the reservoir with the volume of 624 liters 2 minutes faster, than the first pipe fills the reservoir with the volume of 650 liters?