P=2(a+b)=62
S=a•b=210
a+b=31
a=31-b
(31-b)•b=210
31b-b^2-210=0
b^2-31b+210=0
D=31^2-4•210=961-940=121>0
b1=(31+√121)/2=(31+11)/2=42/2=21
b2=(31-11)/2=20/2=10
a1=31-b1=10
a2=31-b2=31-10=21
ответ 10;21
Участок показан на рисунке.
Прямоугольник имеет размеры a x b, полукруг R = a/2.
Площадь участка S = a*b + pi*R^2/2 = 2R*b + pi*R^2/2 = 12,5
Выразим отсюда
![b = \frac{25 - pi*R^2}{4R}](https://tex.z-dn.net/?f=b+%3D++%5Cfrac%7B25+-+pi%2AR%5E2%7D%7B4R%7D)
Периметр
![P = a + 2b + piR = R(2+pi) + \frac{25 - piR^2}{2R}= \frac{4R^2+2piR^2+25-piR^2}{2R}](https://tex.z-dn.net/?f=P+%3D+a+%2B+2b+%2B+piR+%3D+R%282%2Bpi%29+%2B++%5Cfrac%7B25+-+piR%5E2%7D%7B2R%7D%3D+%5Cfrac%7B4R%5E2%2B2piR%5E2%2B25-piR%5E2%7D%7B2R%7D+)
![P= \frac{4R^2+piR^2+25}{2R}](https://tex.z-dn.net/?f=P%3D+%5Cfrac%7B4R%5E2%2BpiR%5E2%2B25%7D%7B2R%7D+)
Нам нужно P => min. Решаем через производную
![P'= \frac{(8R+2piR)*2R-(4R^2+piR^2+25)*2}{4R^2} = \frac{8R^2+2piR^2-4R^2-piR^2-25}{2R^2} =0](https://tex.z-dn.net/?f=P%27%3D+%5Cfrac%7B%288R%2B2piR%29%2A2R-%284R%5E2%2BpiR%5E2%2B25%29%2A2%7D%7B4R%5E2%7D+%3D+%5Cfrac%7B8R%5E2%2B2piR%5E2-4R%5E2-piR%5E2-25%7D%7B2R%5E2%7D+%3D0)
Если дробь равна 0, то числитель равен 0, а знаменатель нет.
4R^2 + pi*R^2 - 25 = 0
R^2 = 25/(4+pi)
R = 5/√(4+pi)
a = 2R
![b = \frac{25 - piR^2}{4R}= \frac{25-pi*25/(4+pi)}{4*5/ \sqrt{4+pi} } = \frac{5(4+pi)-5pi}{4+pi}: \frac{4}{ \sqrt{4+pi} } =](https://tex.z-dn.net/?f=b+%3D+%5Cfrac%7B25+-+piR%5E2%7D%7B4R%7D%3D+%5Cfrac%7B25-pi%2A25%2F%284%2Bpi%29%7D%7B4%2A5%2F+%5Csqrt%7B4%2Bpi%7D+%7D+%3D+%5Cfrac%7B5%284%2Bpi%29-5pi%7D%7B4%2Bpi%7D%3A+%5Cfrac%7B4%7D%7B+%5Csqrt%7B4%2Bpi%7D+%7D++%3D+)
![=\frac{20}{4+pi}* \frac{ \sqrt{4+pi} }{4} = \frac{5}{ \sqrt{4+pi} } =R](https://tex.z-dn.net/?f=%3D%5Cfrac%7B20%7D%7B4%2Bpi%7D%2A+%5Cfrac%7B+%5Csqrt%7B4%2Bpi%7D+%7D%7B4%7D++%3D+%5Cfrac%7B5%7D%7B+%5Csqrt%7B4%2Bpi%7D+%7D+%3DR)
Ответ: радиус R = 5/√(4+pi); a = 2R; b = R
36+4+95=135/3=45
Вот так))
Задание: <span>Найдите значение выражения.
2,1*3,5:4,9=1,51) 3,5:2,1=7,35
2) 7,35:4,9=1,5
</span>
или
1) 2,1*3,5=
![\frac{21}{10}* \frac{35}{10} = \frac{21*35}{10*10} = \frac{21*7}{2*10} = \frac{147}{20}](https://tex.z-dn.net/?f=+%5Cfrac%7B21%7D%7B10%7D%2A+%5Cfrac%7B35%7D%7B10%7D+%3D++%5Cfrac%7B21%2A35%7D%7B10%2A10%7D+%3D++%5Cfrac%7B21%2A7%7D%7B2%2A10%7D+%3D++%5Cfrac%7B147%7D%7B20%7D+)
2)
![\frac{147}{20} : \frac{49}{10} = \frac{147*10}{20*49} = \frac{3*1}{2*1} = \frac{3}{2}](https://tex.z-dn.net/?f=+%5Cfrac%7B147%7D%7B20%7D+%3A++%5Cfrac%7B49%7D%7B10%7D+%3D++%5Cfrac%7B147%2A10%7D%7B20%2A49%7D+%3D++%5Cfrac%7B3%2A1%7D%7B2%2A1%7D+%3D++%5Cfrac%7B3%7D%7B2%7D+)
=1,5
X(3+2x+4xˇ2)-2xˇ2(2x+1)=9
3x+2xˇ2+4xˇ3-4xˇ3-2xˇ2 =9
3x=9
x=3