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beks73 [17]
1 year ago
10

Find the absolute maximum and minimum values of the function, subject to the given constraints. k(x,y)=−x2−y2 4x 4y; 0≤x≤3, y≥0,

and x y≤6
Mathematics
1 answer:
grigory [225]1 year ago
4 0

For function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

For given question,

We have been given a function k(x, y) = -x² - y² + 4x + 4y

We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

First we find the partial derivative of function k(x, y) with respect to x.

⇒ k_x=-2x+4

Now, we find the partial derivative of function k(x, y) with respect to y.

\Rightarrow k_y=-2y+4

To find the critical point:

consider    k_x=0     and      k_y=0

⇒       -2x + 4 = 0     and    -2y + 4 = 0

⇒          x = 2            and       y = 2

This means, the critical point of function is (2, 2)

We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

Consider k(0, 0)

⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)

⇒ k(0, 0) = 0

Consider k(3, 3)

⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)

⇒ k(3, 3) = -9 - 9 + 12 + 12

⇒ k(3, 3) = -18 + 24

⇒ k(3, 3) = 6

Therefore, for function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

Learn more about the absolute maximum and absolute minimum values of the function here:

brainly.com/question/16270755

#SPJ4

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A farmers field has the dimensions 2 and 3/4 by 1 and 1/3. He needs to find the area of the field
Afina-wow [57]

Answer:

3 2/3 units²

Step-by-step explanation:

Since the field is rectangular in nature;

Area of the field = Length * Width

Given

Length = 2 3/4

Width = 1 1/3

Area of the field = 2 3/4 * 1 1/3

Area of the field = 11/4 * 4/3

Area of the field = 4/4 * 11/3

Area of the field = 1 * 11/3

Area of the field = 11/3

Area of the field = 3 2/3

Hence the area of the field is 3 2/3 units²

5 0
3 years ago
Temperature in degrees Fahrenheit is equal to 32 more than 9/5 times the temperature in degrees Celsius . One day the high tempe
bazaltina [42]

The high temperature is 35 degree celsius

<em><u>Solution:</u></em>

Given that, Temperature in degrees Fahrenheit is equal to 32 more than 9/5 times the temperature in degrees Celsius

Let "f" be the temperature in degree Fahrenheit

Let "c" be the temperature in degree celsius

Therefore,

Temperature in degrees Fahrenheit = 32 + \frac{9}{5} times the temperature in degrees Celsius

f = 32 + \frac{9}{5} \times c

One day the high temperature in Edison. Nj was 95 degrees Fahrenheit

f = 95 ; c = ?

Substitute f = 95 in above equation

95 = 32 + \frac{9c}{5}\\\\95=\frac{32 \times 5 +9c}{5}\\\\95 \times 5 = 160+9c\\\\475 = 160 + 9c\\\\9c = 475 - 160\\\\9c = 315\\\\c = 35

Thus high temperature in degrees Celsius is 35 degree celsius

5 0
3 years ago
2. Multiply and simplify: (x - 2)(2x + 3)<br> Answer
inysia [295]

Step-by-step explanation:

(x - 2)(2x + 3)

=2x²+3x-4x-6

=2x²-x-6

8 0
3 years ago
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DedPeter [7]

。☆✼★ ━━━━━━━━━━━━━━  ☾  

4x < 12

Divide both sides by 4:

x < 12/4

x < 3

That is your solution ^^

Have A Nice Day ❤    

Stay Brainly! ヅ    

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。☆✼★ ━━━━━━━━━━━━━━  ☾

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vladimir1956 [14]

It's 1/x^5

Hope it helps

8 0
3 years ago
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