![y = \dfrac{\sqrt{3 - x}}{3^{x} - 1}](https://tex.z-dn.net/?f=y+%3D+%5Cdfrac%7B%5Csqrt%7B3+-+x%7D%7D%7B3%5E%7Bx%7D+-+1%7D)
Чтобы найти область определения функции, мы должны учесть два условия (ОДЗ):
![\left \{ {\bigg{3 - x \geqslant 0 \ } \atop \bigg{3^{x} - 1 \neq 0}} \right. \ \ \ \ \ \ \ \ \ \ \ \ \ \left \{ {\bigg{x \leqslant 3 \ } \atop \bigg{3^{x} \neq 1}} \right.\\\\\left \{ {\bigg{x \leqslant 3 \ \ \ } \atop \bigg{3^{x} \neq 3^{0}}} \right. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left \{ {\bigg{x \leqslant 3} \atop \bigg{x \neq 0}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%5Cbigg%7B3+-+x+%5Cgeqslant+0+%5C+%7D+%5Catop+%5Cbigg%7B3%5E%7Bx%7D+-+1+%5Cneq+0%7D%7D+%5Cright.+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5Cleft+%5C%7B+%7B%5Cbigg%7Bx+%5Cleqslant+3+%5C+%7D+%5Catop+%5Cbigg%7B3%5E%7Bx%7D+%5Cneq+1%7D%7D+%5Cright.%5C%5C%5C%5C%5Cleft+%5C%7B+%7B%5Cbigg%7Bx+%5Cleqslant+3+%5C+%5C+%5C+%7D+%5Catop+%5Cbigg%7B3%5E%7Bx%7D+%5Cneq+3%5E%7B0%7D%7D%7D+%5Cright.+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5C+%5Cleft+%5C%7B+%7B%5Cbigg%7Bx+%5Cleqslant+3%7D+%5Catop+%5Cbigg%7Bx+%5Cneq+0%7D%7D+%5Cright.)
Итак, объединяем оба условия и получаем: ![x \in (-\infty; 0) \cup (0; \ 3]](https://tex.z-dn.net/?f=x+%5Cin+%28-%5Cinfty%3B+0%29+%5Ccup+%280%3B+%5C+3%5D)
Ответ: ![D(y): \ x \in (-\infty; 0) \cup (0; \ 3]](https://tex.z-dn.net/?f=D%28y%29%3A+%5C+x+%5Cin+%28-%5Cinfty%3B+0%29+%5Ccup+%280%3B+%5C+3%5D)
<span>sin*x+1,5sin2x-3cos*x=1.
</span>sin*x+1,5*2sin*x*cosx-3cos*x=1
sin*x+3sin*x*cosx-3cos*x=1. Погрупуємо і винесемо спільне за дужки.
(sin*x-1) + 3cosx(sinx-1)=0
(sin*x-1) (1+3cosx)=0; sin*x-1=0; sin*x=1 ; x= pi/2+2pi*n, n єZ.
1+3cosx=0; 3cosx=-1; cosx=-1/3; x=+-arccos1/3 +2*pi*n, n єZ
123+880=1003
1003+453=1456
( 990 / X ) - ( 990 / ( X - 9 )) = - 1
990 * ( X - 9 ) - 990X = - X^2 + 9X
X^2 - 9X - 8910 = 0
D = 81 + 3560 = 35721 ; √ D = 189
X1 = ( 9 + 189 ) : 2 = 99
X2 < 0
Cкорость первого 99 ( км/час )