Answer:
the minimum is located in x = -5/3 , y= -5/3
Step-by-step explanation:
for the function
f(x,y)=2x + 2y
we define the function g(x)=9x² - 9xy + 9y² - 25 ( for g(x)=0 we get the constrain)
then using Lagrange multipliers f(x) is maximum when
fx-λgx(x)=0 → 2 - λ (9*2x - 9*y)=0 →
fy-λgy(x)=0 → 2 - λ (9*2y - 9*x)=0
g(x) =0 → 9x² - 9xy + 9y² - 25 = 0
subtracting the second equation to the first we get:
2 - λ (9*2y - 9*x) - (2 - λ (9*2x - 9*y))=0
- 18*y + 9*x + 18*x - 9*y = 0
27*y = 27 x → x=y
thus
9x² - 9xy + 9y² - 25 = 0
9x² - 9x² + 9x² - 25 = 0
9x² = 25
x = ±5/3
thus
y = ±5/3
for x=5/3 and y=5/3 → f(x)= 20/3 (maximum) , while for x = -5/3 , y= -5/3 → f(x)= -20/3 (minimum)
finally evaluating the function in the boundary , we know because of the symmetry of f and g with respect to x and y that the maximum and minimum are located in x=y
thus the minimum is located in x = -5/3 , y= -5/3
Answer:
the solution is (-1/2, 6).
Step-by-step explanation:
Next time, please share the instructions.
Start by carrying out the indicated multiplication:
2x + 2y = 23 - 2y
Consolidate l ike terms: combine 2y and -2y: result: +4y on the left side:
2x + 4y = 23
Let's solve this system using elimination by substitution. Multiply 2x + 4y = 23 by -3 to obtain a -6x term:
-3(2x + 4y = 23) = -6x - 12y = -69. Now combine this result with the second equation:
-6x - 12y = -69
6x + 5y = 20 + 7
-------------------------
- 7y = -42
Dividing both sides by -7, we get y = 6. Subbing 6 for y in the 2nd equation, we get:
6x = 27 -5(6), or
6x = 27 - 30 = -3
Then x = -3/6, or x = -1/2
and the solution is (-1/2, 6).
Answer:
f(- 2) = 23
Step-by-step explanation:
substitute x = - 2 into f(x) and evaluate
f(- 2) = 3(- 2)² - (- 2) + 7 = 12 + 4 + 7 = 23
Answer:
16.8
Step-by-step explanation:
equation: x - 3.9 = 12.9
add 3.9 to 12.9
answer is 16.8
Answer:
Step-by-step explanation:8/3 = T (2.2 + 3*2.2) = 4*2.2 T
T = 2/6.6 Hr = 1/3.3 hr
so how long did the bird fly? t+T
4/6.6 + 2/6.6 = 6/6.6 hours
and how far did it go?
6.6 + 6/6.6*6.6 = 2*6.6 = 13.2km
