pwease help me with math question pwease

We first compute the partial derivatives of f(x, y):

f(x, y) = 5x² + 5y² - 10x + 21

∂f/∂x = 10x - 10

∂f/∂y = 10y

The critical points of f occur where both ∂f/∂x and ∂f/∂y are equal to zero. This only happens at the point (x, y) = (1, 0). (And this point does lie inside R.)

Next, compute the Hessian matrix H(x, y) for f :

[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2 f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}10&0\\0&10\end{bmatrix}[/tex]

Since det(H(x,y)) = 100 is positive for all x and y, this means the critical point (1, 0) is a local minimum, and we have f(1, 0) = 16.

Next, we check for extrema along the boundary of R, which is comprised of a semicircle with radius 2 and the line segment connecting (-2, 0) and (2, 0).

• Parameterize the semicircular portion by

x(t) = 2 cos(t)

y(t) = 2 sin(t)

with 0 ≤ t ≤ π. Then

f(x(t), y(t)) = 20 sin²(t) + 20 cos²(t) - 20 cos(t) + 21

which is simplifies to a function of one variable t,

g(t) = 41 - 20 cos(t)

Find the extrema of g over the interval [0, π] : we have critical points when

g'(t) = 20 sin(t) = 0

which happens at t = 0 and t = π. At these points, we get local extreme values  of

•• t = 0   =>   x = 2 and y = 0   =>   f(2, 0) = 21

•• t = π   =>   x = -2 and y = 0   =>   f(-2, 0) = 61

• Over the line-segment portion, we take y = 0, so f(x, y) again reduces to a function of one variable:

f(x, 0) = 5x² - 10x + 21

Completing the square, we have

5x² - 10x + 21 = 5 (x - 1)² + 16

which has a maximum value of 16 when x = 1 (and this happens to be the critical point (1, 0) we found earlier).

So, over the region R, f(x, y) has

• an absolute maximum of 61 at the point (-2, 0), and

• an absolute minimum of 16 at (1, 0)

Answer:

Area = 100cm²

Perimeter = 48cm

Area of rectangle=Length×Breadth

[tex]\\ \sf\longmapsto Area=4y+10[/tex]

[tex]\\ \sf\longmapsto Area=2(2y+5)[/tex]

Answer:

5

Step-by-step explanation:

The answer is 60/12 becuase we can simfly both of theese mixed numbers into an improper fraction, wich will be 4/3*15/4. We do the multiplication, and we get 60/12. 60/12 can be simplifed to 5 becuase 60 divided by 12 is 5

Answer: 4928

Step-by-step explanation:

Area= LxW

88 x 56= 4928

Answer:

{ - 5, 19, 31 }

Step-by-step explanation:

Substitute the values from the domain ( input) into f(x) to obtain range (output )

f(- 3) = 2(- 3) + 1 = - 6 + 1 = - 5

f(9) = 2(9) + 1 = 18 + 1 = 19

f(15) = 2(15) + 1 = 30 + 1 = 31

range is { - 5, 19, 31 }

Answer:

C, 18.

Step-by-step explanation:

Since 24 divided by 8 is 3, which means that

8x3 = 24, then the amount of boys must be solved using the equation 6x3 which equals 18.

Answer:

a) 5.25m^2

b) 1 can

Step-by-step explanation:

a)

area of a triangle = bh/2

=(4.2 x 4.5)/2

=18.9/2

=9.45m^2

area of a rectangle = 2(l+w)

=2 x (0.6 + 1.5)

=4.2m^2

9.45-4.2 = 5.25m^2

b) 1 can, you can't have a partial can of paint

Answer:

Step-by-step explanation:

The equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)

Let l be the original length of the pool.

Since the length of the pool is increased by 3.7 m, the new length L = l + 3.7.

Also, the area of the pool A = 205.85 square meter and it is a rectangle with width, W = 11.6 meters,

So, A = LW

Substituting the values of the variables into the equation, we have

A = LW

205.85 = (l + 3.7)11.6

So, the equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)

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Answer:

Step-by-step explanation

205.85=11.6(l+3.7)

O NEGATIVE ONE-HALF ........

Answer:

answer is D

Step-by-step explanation:

the answer is 1.75

Answer:

A is correct.

C. is correct.

D. is correct.

Step-by-step explanation:

A follows the commutative property, putting two fractions in parenthesis, and follows PEMDAS to simplify the answer.

B uses other random numbers and does NOT follow the property.

C follows the commutative property too.

D. also follows the property, same as A and C.

I hope this is a multiple choice question.

Answer:

5:1

Step-by-step explanation:

5/6 won

1/6 lost

5:1=6

Answer:

5:1

Step-by-step explanation:

Total numbers of match = 6

No. of matches Peter wins = 5

Ratio of wins to lose = 5:(6-5) = 5:1

Please, don't write the answer as 1:5. Because, 5:1 and !:5 both are different so don't be confused.

Answer:

Step-by-step explanation:

(-7 - k)/(6 + 4) = -15

(-7 - k)/10 = -15

-7 -k = -150

-k = -143

k = 143

Step-by-step explanation:

If the chocolated had 16 squares.

there we're only two children was there.

60

Step-by-step explanation:

(-47)-(-107)

(-47)-1(-107)

-47+107

=60

9514 1404 393

Answer:

  a. Z: 30,000; T: 50,000

  b. Z: 37.5%; T: 62.5%

Step-by-step explanation:

a. The "ratio units" add up to 3+5 = 8, so we can find the investment amounts by multiplying the ratio by 10,000

  Z : T = 3 : 5 = 30,000 : 50,000

__

b. Zoe's investment amount is 3/8 of the total, or ...

  3/8 × 100% = 37.5%

Toria's percentage is the rest of it:

  100% -37.5% = 62.5%

  Zoe invested 37.5% of the total; Toria invested 62.5% of the total.

Answer:

Step-by-step explanation:

Given:

Simplify equation for perimeter and solve for W:

Find L:

Using a system of equations, the height of the tree would be 12.80 meters.

Equating the height and shadows of the tree and pole :

Height of pole / shadow of pole = height of tree / shadow of tree

Representing the equation thus :

Let the height of the tree = h

3/4 = h/17

Cross multiply

4h = 17 × 3

4h = 51

Divide both sides by 4

h = 51/4

h = 12.75.

Hence, the height of the tree to the nearest tenth of a meter is 12.80 meters.

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Answer:

Step-by-step explanation:

Answer:

[tex]solution 1: \ \frac{7+\sqrt{65}}{2};[/tex]

[tex]solution2: \ \frac{7-\sqrt{65} }{2}.[/tex]

Step-by-step explanation:

x²-7x-4=0;

D=[b²-4ac]=49+16=65.

[tex]\left[\begin{array}{ccc}x=\frac{7+\sqrt{65}}{2} \\x=\frac{7-\sqrt{65}}{2} \end{array}[/tex]

The value of "s" as a function of other  variables is s =  (w - rh)/c

If you earn both hourly wages and a commission at your job, your gross wages, w, can be calculated with the following equation:

cs + rh = w

We will make "s" the subject of the formula:

Subtract rh from both sides

cs + rh - rh = w - rh

cs = w - rh

Divide both sides by c

cs/c = (w - rh)/c

s =  (w - rh)/c

Hence the value of "s" as a function of other  variables is s =  (w - rh)/c

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Answer:

Step-by-step explanation:

Solve for k.

14k+3k–16k=5

17k - 16k = 5

k = 5

Answer:

this is the correct answer happy

Answer:

1. tenths = 0.3

   thousandths = 0.346

   hundred thousandths = 0.34600

   hundredths = 0.35

2. thousandths = 20.006

    hundredths = 20.01

   hundred thousandths = 20.00642

Step-by-step explanation:

Hope it helps

============================================================

Explanation:

The order of a matrix is a way of describing its size. Specifically, the order is represented in the form [tex]m \times n[/tex], where,

The rows are laid out horizontally, and the columns are vertical.

In this case, we have 5 rows and 3 columns. Therefore, the answer is 5 x 3. The order is important because a 5 x 3 matrix is different from a 3 x 5 matrix.

Answer:

subtract 22 from both sides then multiply 3 to both sides

Step-by-step explanation:

F/3+22=17

-22. -22

F/3 = -5

x3. x3

F= -15

Answer:

Mary:604

Mona:796

Step-by-step explanation:

Answer:

Ms. Mary spend $302

Ms. Mona spend $ 686

Step-by-step explanation: We know that Ms. Mary spend $192 less than Ms. Mona.

So we are to divide $988 by 2 which is 494

now both have $494 each but Ms. Mona spend 192 so we are to add 192 + 494 to get the right sum of how much money Ms. Mona have and take away 494-192 to get the right sum of how much money Ms. Mary spend.

192 + 494 = 686

494 - 192 = 302