Answer:
possible maximum and minimum values : f (1,1), f (-1,-1)
Step-by-step explanation:
Given function :
f(x,y) = x^2 + y^2
constraint = xy = 1
attached below is the detailed solution of the method of using Lagrange method of Multipliers to find the maximum and minimum values of the function
Answer:
Step-by-step explanation:
Factorize 175 and 50
175 = 5 * 5 * 7
50 = 5 * 5 * 2
![\frac{\sqrt[3]{175}}{\sqrt[3]{}50}=\sqrt[3]{\frac{175}{50}}\\\\\\ =\sqrt[3]{\frac{5*5*7}{5*5*2}}\\\\\\=\sqrt[3]{\frac{7}{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B175%7D%7D%7B%5Csqrt%5B3%5D%7B%7D50%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B175%7D%7B50%7D%7D%5C%5C%5C%5C%5C%5C%20%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B5%2A5%2A7%7D%7B5%2A5%2A2%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B7%7D%7B2%7D%7D)
Step-by-step explanation:
y = -3x² + mx + 10
dy/dx = -6x + m.
When dy/dx = 0, -6x + m = 0. => x = m/6.
We have y = -3(m/6)² + m(m/6) + 10 = 37.
=> -m²/12 + m²/6 = 27
=> -m² + 2m² = 324
=> m² = 324
=> m = 18 or m = -18.
Answer:
We have a + b as;
2 + 3 = 5
Step-by-step explanation:
Here, we want go get the value of a and b
from the second equation, we can get an expression for b
We have this as;
7a - b = 11
Thus,
b = 7a - 11
Now, from here, we can substitute the value of b into the first equation
We have this as;
5a + 4(7a - 11) = 22
5a + 28a -44 = 22
33a = 22 + 44
33a = 66
a = 66/33
a = 2
Recall;
b = 7a - 11
substituting the value of a from above;
b = 7(2) - 11
b = 14 - 11
b = 3
9 gallons of water
Divide the gallons by the number of plants.
6 ÷ 20 = 0.3
Multiply that by the number of plants you want.
0.3 x 30 = 9
