let's not forget that when a relation is "even" f(-x) = f(x), or namely any negative of "x" yields the same result as any positive one.
if this relation is "even" and has (3 , 3), where x = 3, then if we were to plug f(-3) we should get a result or y-value of the same 3, giving us a point of (-3 , 3).
Answer:
- The values of x and y that minimize the function, subject to the given constraint are 6 and 8 respectively.
- The minimum value of the function = -44
Step-by-step explanation:
The Lagrange multiploer method finds the optimum value of a multivariable function subjected to a given constraint
It replaces the function with a Lagrange equivalent which is
L(x, y) = F(x, y) - λ C(x, y)
where λ Is the lagrange multiplier which can be a function of x and y
F(x, y) = x² - 10x + y² - 14y + 28
C(x, y) = x + y - 14
L(x, y) = x² - 10x + y² - 14y + 28 - λ (x + y - 14)
We now take the partial derivatives of the Lagrange function with respect to x, y and λ respecrively. Then solving to obtain values of x, y and λ that correspond to the minimum of the function. Since the first partial derivatives are all equal to 0 at minimum point.
(∂L/∂x) = 2x - 10 - λ = 0 (eqn 1)
(∂L/∂y) = 2y - 14 - λ = 0 (eqn 2)
(∂L/∂λ) = x + y - 14 = 0 (eqn 3)
Equating eqn 1 and 2
2x - 10 - λ = 2y - 14 - λ
2x - 10 = 2y - 14
2y = 2x - 10 + 14
2y = 2x + 4
y = x + 2 (eqn *)
Substitute eqn ^ into eqn 3
x + y - 14 = 0
x + x + 2 - 14 = 0
2x - 12 = 0
2x = 12
x = 6
y = x + 2 = 6 + 2 = 8
2x - 10 - λ = 0
12 - 10 - λ = 0
λ = 2
The values of x and y that minimize the function are 6 and 8 respectively.
F(x, y) = x² - 10x + y² - 14y + 28
At minimum point, x = 6, y = 8
F(x, y) = 6² - 10(6) + 8² - 14(8) + 28 = 36 - 60 + 64 - 112 + 28 = -44
Hope this Helps!!!
x + x + 6 - 7 + x
2x+2+x
3- X + 2x - 4 + 2x
X-1
X+1
Answer:
a and c
Step-by-step explanation:
Answer:
A- x + x + 6 – 7 + x
C- 3 – x + 2x – 4 + 2x
Step-by-step explanation:
EDG2021
Rebecca tried to solve the problem but made a mistake in her calculations. You must analyze Rebecca's work, identify the error, and then correctly solve the problem. Then, create a model to justify your thinking.
Rebecca's Math Calculations
Step 1: 14×312
Step 2: 141×72
Step 3: 982=49
Solution: In September, 49 inches of rain fell.
Be sure to –
Identify the error that the student made
Answer the question prompt
Create a pictorial model that represents the problem situation and justifies your identification of the error and its solution
Explain how the model justifies the identified error and how to correct it
Answer:
4 inches
Step-by-step explanation:
Given that :
Amount of Rainfall in October = 14 inches
Amount of Rainfall in October = 3 1/2 times more than Rainfall during September
How much rain fell.during September :
The problem is a division problem ;
Since the amount of Rainfall in October is greater, then obtaining the amount of Rainfall in September requires dividing The amount of Rainfall in October by the number of times it is more than the September rainfall;
If multiplication is applied, then tbe value obtained will be greater than 14 inches. Which makes no sense since, the Rainfall in October is much greater than that in September.
14 inches ÷ 3 1/2
14 ÷ 7/2
14 * 2 / 7
= 28 / 7
= 4 inches
Hence, the amount of Rainfall in September is 4 inches
Answer:
46
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
good luck :)
Answer:
(32, 31) (33,30) (34, 29) (35, 28) (36,27) (37, 26)
Step-by-step explanation:
The pairs of whole numbers that add to 63 and have a difference less than 10 are (27, 36), (28, 35), (29, 34), (30, 33), and (31, 32).
This problem is based in the domain of basic algebra. Essentially, you are being asked to find pairs of whole numbers that, added together, equal 63, with the condition that the difference between these two numbers is less than 10.
Starting from the number 32 (as any larger number plus any number greater than 0 would exceed 63), you can begin to list pairs, subtracting one number from the total of 63 while simultaneously adding that same amount to the other half of the pair. This will ensure that the sum always equals 63.
Here are the pairs satisfying the given conditions: (27, 36), (28, 35), (29, 34), (30, 33), (31, 32). For these pairs, the difference between the two numbers in each pair is less than 10.
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9514 1404 393
Answer:
(a) k = –2.5
Step-by-step explanation:
When the function f(x) is transformed to f(x -h) +k, the graph is translated h units right and k units up.
If the absolute value function has its original vertex of (0, 0) moved to (1, -2.5), then (h, k) = (1, -2.5).
The value of k is -2.5.
_____
Additional comment
The above answer applies to the given problem statement. The question asked in the comment has a vertex of (0, 2.5), so (h, k) = (0, 2.5) for that question.
If you're going to copy the answer, make sure it is the answer to the question you're looking at.
In an absolute value function expressed as f(x) = |x – h| + k, the value of k corresponds to the y-coordinate of the function's vertex. In this case, as the vertex is at the point (1, -2.5), the value of k is -2.5.
The student's question relates to the concepts of Two-Dimensional (x-y). Graphing and the graphing of the absolute value function. It is vital to remember that the vertex of an absolute value graph in the form f(x) = |x – h| + k corresponds to the point (h, k) on the Cartesian coordinate plane. The student states that the vertex is at the point (1, -2.5), so based on our function analysis, the value of k, which represents the y-coordinate of the vertex, is -2.5. Therefore, the correct answer is k = -2.5.
For more about Absolute Value Graph here:
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