Обе функции сложные, поэтому будем находить производную сложной функции
![y= \sqrt{15-7x} \\ y'=( \sqrt{15-7x} )'= \frac{(15-7x)'}{2 \sqrt{ 15-7x} } =- \frac{3.5}{ \sqrt{ 15-7x } } \\ \\ \\ y= \sqrt{42+0.5x} \\ y'=(\sqrt{42+0.5x})'= \frac{(42+0.5x)'}{2 \sqrt{42+0.5x} }= \frac{0.5}{2 \sqrt{42+0.5x} } = \frac{1}{4 \sqrt{42+0.5x} }](https://tex.z-dn.net/?f=y%3D+%5Csqrt%7B15-7x%7D++%5C%5C+y%27%3D%28+%5Csqrt%7B15-7x%7D+%29%27%3D+%5Cfrac%7B%2815-7x%29%27%7D%7B2+%5Csqrt%7B+15-7x%7D+%7D+%3D-+%5Cfrac%7B3.5%7D%7B+%5Csqrt%7B+15-7x+%7D+%7D++%5C%5C++%5C%5C++%5C%5C+y%3D+%5Csqrt%7B42%2B0.5x%7D++%5C%5C+y%27%3D%28%5Csqrt%7B42%2B0.5x%7D%29%27%3D+%5Cfrac%7B%2842%2B0.5x%29%27%7D%7B2+%5Csqrt%7B42%2B0.5x%7D+%7D%3D+%5Cfrac%7B0.5%7D%7B2+%5Csqrt%7B42%2B0.5x%7D+%7D++%3D+%5Cfrac%7B1%7D%7B4+%5Csqrt%7B42%2B0.5x%7D+%7D+)
√x² -x -2 <2x +6⇔ | x | -x -2 <2x +6.
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a) { x < 0 ; -x -x -2 < 2x +6 ⇔{ x < 0 ; x > -2 . x ∈ (-2 ; 0) .
b) { x ≥ 0 ; x -x -2 < 2x +6 ⇔{ x ≥ 0 ; x > - 4 . x ∈ [0 ; ∞).
x ∈ (-2 ; 0) ∪ [0 ; ∞)⇒ x ∈ ( -2 ; ∞).
<span>ответ : x ∈ ( -2 ; ∞).
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√( x² -x -2) < 2x +6
</span>a) 2x +6 ≤ 0 ⇔ x ≤ -3 ⇒нет решения .
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b) { x > -3 ; 0 < x² -x -2 < (2x+6)² ⇔ { x > -3 ; 0 < (x +1)(x-2) < 4x²+24x+36
x² -x -2 >0 ⇔ (x +1)(x-2) >0 ⇒ x ∈ (-∞ ; -1) ∪ ( 2 ;∞) ;
x² -x -2 < 4x²+24x+36⇔3x² +25x +38 >0 ⇔3(x+19/3)(x+2) >0 <span>⇒
</span>x ∈ (-∞ ;-19 / 3 )∪ (-2 ; ∞<span>)) .
</span>{ x ∈ ( -3 ;∞) ; x ∈ (-∞ ; -1) ∪ ( 2 ;∞) ;x ∈ (-∞ ;-19 / 3 )∪ (-2 ; ∞) ⇒ <span> x</span>∈ (-2 ; -1) U (2 ; <span>∞).</span><span>
ответ : x</span>∈ (-2 ; -1) U (2 ; ∞).
4.5/1.5=3 кг хлеба из кг муки
3*70000=210000 = 210 т хлеба.
отв:210т хлеба
![1+tg ^{2} \alpha = \frac{1}{Cos ^{2} \alpha }\\\\Cos ^{2} \alpha = \frac{1}{1+tg ^{2} \alpha } = \frac{1}{1+( \frac{5}{12}) ^{2} } = \frac{1}{1+ \frac{25}{144} } = \frac{1}{ \frac{169}{144} }= \frac{144}{169}](https://tex.z-dn.net/?f=1%2Btg+%5E%7B2%7D++%5Calpha+%3D+%5Cfrac%7B1%7D%7BCos+%5E%7B2%7D+%5Calpha++%7D%5C%5C%5C%5CCos+%5E%7B2%7D+%5Calpha+%3D+%5Cfrac%7B1%7D%7B1%2Btg+%5E%7B2%7D+%5Calpha++%7D+%3D+%5Cfrac%7B1%7D%7B1%2B%28+%5Cfrac%7B5%7D%7B12%7D%29+%5E%7B2%7D++%7D+%3D+%5Cfrac%7B1%7D%7B1%2B+%5Cfrac%7B25%7D%7B144%7D+%7D+%3D+%5Cfrac%7B1%7D%7B+%5Cfrac%7B169%7D%7B144%7D+%7D%3D+%5Cfrac%7B144%7D%7B169%7D++++)
α - угол третьей четверти, значит Sinα < 0
![Sin \alpha =- \sqrt{1-Cos ^{2} \alpha }=- \sqrt{1- \frac{144}{169} } =- \sqrt{ \frac{25}{169} } =- \frac{5}{13}](https://tex.z-dn.net/?f=Sin+%5Calpha+%3D-+%5Csqrt%7B1-Cos+%5E%7B2%7D+%5Calpha++%7D%3D-+%5Csqrt%7B1-+%5Cfrac%7B144%7D%7B169%7D+%7D+%3D-+%5Csqrt%7B+%5Cfrac%7B25%7D%7B169%7D+%7D+%3D-+%5Cfrac%7B5%7D%7B13%7D++)