60 это 100%
57,90 это x
составляем пропорцию:
100*57,90=60x
x=5790:60
x=96,5%
100-96,5= 3,5% скидка для покупателей
Проверяем:
60:100%*3,5%= 2,1
60-2,1= 57,9 рублей= 57 рублей 90 копеек
Производную ищем, как производную произведения.
![f'(x)=( (x-1)* \sqrt{x+1} )'=( (x-1)* (x+1)^{ \frac{1}{2} } )'= \\ =(x-1)' *(x+1)^{ \frac{1}{2} } +(x-1)*((x+1)^{ \frac{1}{2} } )'= \\ =1*(x+1)^{ \frac{1}{2} } +(x-1)*\frac{1}{2}*(x+1)^{ -\frac{1}{2} } = \\ =(x+1)^{ \frac{1}{2} } +\frac{1}{2} *(x-1)* \frac{1}{(x+1)^{ \frac{1}{2} }} = \sqrt{x+1} + \frac{x-1 }{ 2\sqrt{x+1}}](https://tex.z-dn.net/?f=f%27%28x%29%3D%28+%28x-1%29%2A+%5Csqrt%7Bx%2B1%7D++%29%27%3D%28+%28x-1%29%2A+%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%29%27%3D+%5C%5C+%3D%28x-1%29%27+%2A%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%2B%28x-1%29%2A%28%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%29%27%3D++%5C%5C+%3D1%2A%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%2B%28x-1%29%2A%5Cfrac%7B1%7D%7B2%7D%2A%28x%2B1%29%5E%7B+-%5Cfrac%7B1%7D%7B2%7D+%7D+%3D++%5C%5C+%3D%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%2B%5Cfrac%7B1%7D%7B2%7D+%2A%28x-1%29%2A+%5Cfrac%7B1%7D%7B%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D%7D+%3D+%5Csqrt%7Bx%2B1%7D+%2B+%5Cfrac%7Bx-1+%7D%7B+2%5Csqrt%7Bx%2B1%7D%7D+)
Подставляем x = 3
![\sqrt{x+1} + \frac{x-1 }{ 2\sqrt{x+1}} = \sqrt{3+1} + \frac{3-1}{2 \sqrt{3+1} } =2+ \frac{1}{2} =2,5](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B1%7D+%2B+%5Cfrac%7Bx-1+%7D%7B+2%5Csqrt%7Bx%2B1%7D%7D+%3D+%5Csqrt%7B3%2B1%7D+%2B+%5Cfrac%7B3-1%7D%7B2+%5Csqrt%7B3%2B1%7D+%7D+%3D2%2B+%5Cfrac%7B1%7D%7B2%7D+%3D2%2C5)
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Готово!!Удачи)))
2x<π/3+πn
x<π/6+πn/2
x∈(-π/2+πn;π/6+πn/)
sin(x/2-π/4)+√2/2<0
sin(x/2-π/4)<-√2/2
5π/4+2πn<sin(x/2-π/4)<7π/4+2πn
5π/4-π/4+2πn<sinx/2<7π/4-π/4+2πn
π+2πn<sinx/2<3π/2+2πn
2π+4πn<sinx<3π+4πn
<span>1) ac2-ad+c3-cd-bc2+bd= = (ac2 – ad) + (c3 –
bc2) + (bd – cd) = a·(c2 – d) + c2·(c – b) + d·(b – c) = a·(c2 – d) +
c2·(c – b) – d·(c – b) = a·(c2 – d) + c2·(c – b) – d·(c – b) = a·(c2 –
d) + (c – b)·(c2 – d) = (c2 – d)·(a + c – b)</span>
<span>2) mx2+my2-nx2-ny2+n-m= x2 ( m - n ) + y2 ( m - n ) - ( m - n ) = ( m-n ) (x2 + y2 - 1 ) </span>
<span>3) am2+cm2-an+an2-cn+cn2= m2 (a + c ) + n2 ( a + c ) - n ( a + c ) = ( a+ c) ( m2 + n2 - n) </span>
<span>4) <span> xy2-ny2-mx+mn+m2x-m2n= y2 ( x - n ) + m2 ( x - n) - m ( x - n ) = ( x-n) ( y2 + m2 - m ) </span></span>
<span>5) a2b+a+ab2+b+2ab+2=ab ( a + b + 2 ) + ( a+ b+ 2 ) = 2 ( a+ b + 2 ) </span>
6) x2-xy+x-xy2+y3-y2= x ( x – y + 1) – y 2 ( x – y + 1)=( x – y + 1)( x – y 2 ).