670-120=300+250 ,120+430= 250+300, 360+430=970-180, 540-360=180 я считаю что так верно
поверхност задана в явном виде
![z(x,y)=\sqrt{4+x^2+y^2};](https://tex.z-dn.net/?f=z%28x%2Cy%29%3D%5Csqrt%7B4%2Bx%5E2%2By%5E2%7D%3B)
Частные производные равны
![z'_x=\frac{1}{2\sqrt{4+x^2+y^2}}*(2x)=\frac{x}{\sqrt{4+x^2+y^2}};\\\\z'_y=\frac{y}{\sqrt{4+x^2+y^2}}](https://tex.z-dn.net/?f=z%27_x%3D%5Cfrac%7B1%7D%7B2%5Csqrt%7B4%2Bx%5E2%2By%5E2%7D%7D%2A%282x%29%3D%5Cfrac%7Bx%7D%7B%5Csqrt%7B4%2Bx%5E2%2By%5E2%7D%7D%3B%5C%5C%5C%5Cz%27_y%3D%5Cfrac%7By%7D%7B%5Csqrt%7B4%2Bx%5E2%2By%5E2%7D%7D)
Значение частных производнхых в данной точке равны
![z'_x|(3;6;7)=\frac{3}{\sqrt{4+3^2+6^2}}=\frac{3}{\sqrt{4+9+36}}=\frac{3}{7};\\\\z'_y|(3;6;7)=\frac{6}{7}](https://tex.z-dn.net/?f=z%27_x%7C%283%3B6%3B7%29%3D%5Cfrac%7B3%7D%7B%5Csqrt%7B4%2B3%5E2%2B6%5E2%7D%7D%3D%5Cfrac%7B3%7D%7B%5Csqrt%7B4%2B9%2B36%7D%7D%3D%5Cfrac%7B3%7D%7B7%7D%3B%5C%5C%5C%5Cz%27_y%7C%283%3B6%3B7%29%3D%5Cfrac%7B6%7D%7B7%7D)
Уравнение касательной
![z'_x |(x_o;y_o;z_o)*(x-x_o)+z'_y |(x_o;y_o;z_o)*(y-y_o)=z-z_0;\\\\ \frac{3}{7}*(x-3)+\frac{6}{7}*(y-6)=z-7;\\\\ 3(x-3)+6(y-6)=7(z-7);\\\\ 3x-9+6y-36-7z+49=0;\\\\ 3+-6y-7z+4=0;](https://tex.z-dn.net/?f=z%27_x%20%7C%28x_o%3By_o%3Bz_o%29%2A%28x-x_o%29%2Bz%27_y%20%7C%28x_o%3By_o%3Bz_o%29%2A%28y-y_o%29%3Dz-z_0%3B%5C%5C%5C%5C%20%5Cfrac%7B3%7D%7B7%7D%2A%28x-3%29%2B%5Cfrac%7B6%7D%7B7%7D%2A%28y-6%29%3Dz-7%3B%5C%5C%5C%5C%203%28x-3%29%2B6%28y-6%29%3D7%28z-7%29%3B%5C%5C%5C%5C%203x-9%2B6y-36-7z%2B49%3D0%3B%5C%5C%5C%5C%203%2B-6y-7z%2B4%3D0%3B)
Координаты нормали
![(-\frac{z'_x|(x_o;y_o;z_o)}{\sqrt{(z'_x|(x_o;y_o;z_o))^2+(z'_y|(x_o;y_o;z_o))^2+1}};-\frac{z'_y|(x_o;y_o;z_o)}{\sqrt{(z'_x|(x_o;y_o;z_o))^2+(z'_y|(x_o;y_o;z_o))^2+1}};1)=\\\\](https://tex.z-dn.net/?f=%28-%5Cfrac%7Bz%27_x%7C%28x_o%3By_o%3Bz_o%29%7D%7B%5Csqrt%7B%28z%27_x%7C%28x_o%3By_o%3Bz_o%29%29%5E2%2B%28z%27_y%7C%28x_o%3By_o%3Bz_o%29%29%5E2%2B1%7D%7D%3B-%5Cfrac%7Bz%27_y%7C%28x_o%3By_o%3Bz_o%29%7D%7B%5Csqrt%7B%28z%27_x%7C%28x_o%3By_o%3Bz_o%29%29%5E2%2B%28z%27_y%7C%28x_o%3By_o%3Bz_o%29%29%5E2%2B1%7D%7D%3B1%29%3D%5C%5C%5C%5C%20)
![(-\frac{\frac{3}{7}}{\sqrt{(\frac{3}{7})^2+(\frac{6}{7})^2+1}};-\frac{\frac{3}{7}}{\sqrt{(\frac{6}{7})^2+(\frac{6}{7})^2+1}};1}=\\\\ (-\frac{3}{\sqrt{46}};-\frac{6}{\sqrt{46}};1)](https://tex.z-dn.net/?f=%28-%5Cfrac%7B%5Cfrac%7B3%7D%7B7%7D%7D%7B%5Csqrt%7B%28%5Cfrac%7B3%7D%7B7%7D%29%5E2%2B%28%5Cfrac%7B6%7D%7B7%7D%29%5E2%2B1%7D%7D%3B-%5Cfrac%7B%5Cfrac%7B3%7D%7B7%7D%7D%7B%5Csqrt%7B%28%5Cfrac%7B6%7D%7B7%7D%29%5E2%2B%28%5Cfrac%7B6%7D%7B7%7D%29%5E2%2B1%7D%7D%3B1%7D%3D%5C%5C%5C%5C%20%28-%5Cfrac%7B3%7D%7B%5Csqrt%7B46%7D%7D%3B-%5Cfrac%7B6%7D%7B%5Csqrt%7B46%7D%7D%3B1%29)
Уравнение нормали
![\frac{x-x_0}{l}=\frac{y-y_o}{m}=\frac{z-z_0}{n};\\\\ \frac{x-3}{-\frac{3}{\sqrt{46}}}=\frac{y-5}{-\frac{6}{\sqrt{46}}}=\frac{z-7}{1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-x_0%7D%7Bl%7D%3D%5Cfrac%7By-y_o%7D%7Bm%7D%3D%5Cfrac%7Bz-z_0%7D%7Bn%7D%3B%5C%5C%5C%5C%20%5Cfrac%7Bx-3%7D%7B-%5Cfrac%7B3%7D%7B%5Csqrt%7B46%7D%7D%7D%3D%5Cfrac%7By-5%7D%7B-%5Cfrac%7B6%7D%7B%5Csqrt%7B46%7D%7D%7D%3D%5Cfrac%7Bz-7%7D%7B1%7D)
1 грядка-10 кобачков
2 грядка 8 кобачков
потом фигурная скобка всего разложили поровну
10+8=18 кобачков собрали всего
18:2= 9 кобачков положили в одну корзину
Было - 20 тр.
Отправили - 9 тр. + 9 тр.
Ремонт - ? тр.