Does anyone know the answer.With explanation plz.

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)

A system of equations is simply a system that contains related equations of multiply variables

It took 5 seconds for the adults to go 20 yards and catch up to the kids

Let x represents the time of the race

The kids started 15 yards ahead, and they raced at 1 yard per second.

So, the kids' equation is represented as: [tex]\mathbf{k =15 + x}[/tex]

The adults' raced at 4 yards per second.

So, the adults' equation is represented as: [tex]\mathbf{a =4x }[/tex]

When they are side by side, we have the following equivalent equation

[tex]\mathbf{4x = 15 + x}[/tex]

Subtract x from both sides

[tex]\mathbf{3x = 15}[/tex]

Divide both sides by 3

[tex]\mathbf{x = 5}[/tex]

It means that, it took the adults 5 seconds to catch up with the kids

Substitute 5 for x in any of the equations to calculate the distance travelled.

[tex]\mathbf{a =4 \times 5}[/tex]

[tex]\mathbf{a =20}[/tex]

It means that, the adults catch up with the kids at 20 yards

Read more about systems of equations at:

https://brainly.com/question/12895249

Answer:

The adults went 123 yards and caught up to the kids in 41 seconds

Step-by-step explanation:

ixl :)

Answer:

x=4

Step-by-step explanation:

11x - 2(x + 3) = 30

distribute: 11x-2x-6=30

add like terms: 9x-6=30

add 6: 9x=36

divide by 9: x=4

Answer:

x = 4

Step-by-step explanation:

11x - 2(x +3) = 30

11x -2x - 6 = 30

11x - 2x = 30 + 6

9x = 36

9x/9 = 36/9

x = 4

Answer:

yes

Step-by-step explanation:

since the format of ordered pairs is (x,y) we can plug in the values into the equation to see if they are on the line

y = -3x - 3​

-15 = -3(4)-3........plug in values

-15 = -12 - 3........multiply

-15 = -15..............subtract

-15 = -15..............this is true

Answer:

yes

Step-by-step explanation:

y = -3x-3

Substitute the point into the equation

-15 = -3(4) -3

-15 =-12-3

-15=-15

This is true so the point is on the line

Answer:

y = - x + 3

Step-by-step explanation:

Assuming you require the equation of the line

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 1 , then

y = - x + c ← is the partial equation

To find c substitute (5, - 2 ) into the partial equation

- 2 = - 5 + c ⇒ c = - 2 + 5 = 3

y = - x + 3 ← equation of line

Answer:

-7 4/5 or -7.8

Step-by-step explanation:

Product means multiplication

( - 13/8 )( 24/5)

= (-13 · 24)/(8 · 5)    negative · positive = negative

= - 312/40

=  -7  32/ 40 = -7 4/5 or 7.8

[tex]\huge\mathfrak\pink{answer} [/tex]

Answer:

i wrote answer of the question 1 to 4 but i don't know the answer to 5

Answer: 1) (3,0) 2) (4,2) 3) (5,1) not sure about 4 and 5

1) (3,7/2) 2) (1,-4) 3) (-3,2) im bad at word problems, sorry.

Step-by-step explanation: all i can say without sounding confusing is divide on both sides!! <3

Answer:The volume of the soup pot is of 226.19 cubic inches.

Step-by-step explanation:

Format of a soup pot:

A soup pot has a cylindrical format.

Cylinder volume:

The volume of a cylinder, with radius r and height g is given by:

The soup pot is 8 inches tall with a radius of 3 inches.

This means that

What is the volume of the soup pot?

The volume of the soup pot is of 226.19 cubic inches.

Answer:

W4 is our new scaled side

Step-by-step explanation:

Look at scale factor like this and it helps everytime so if it doesn’t help you there different methods.

3/2 has a larger number as a numerator so that means that the shape being scaled will get larger and if the number is smaller than denominator then the scaled figure will get smaller :3

In our case it gets bigger

do 16 divided by 2 which gives us 8 then times that by 3 to get 24

now thats how I solved this problem but if that not how you did it then you can do it your way :3

HOOE THIS HEEELPPED :DDD

Answer:

[tex]18ft[/tex]

[tex] \frac{bm}{ba} = \frac{bn}{bc} \\ \frac{4}{8} = \frac{3}{6} \\ \frac{1}{2 } = \frac{1}{2} [/tex]

Answer:

C. Q′ (−3, −4)  

D. Q′ (−4, −3)

Step-by-step explanation:

From looking at the graph it looks like the answer would be

Q= (3, -4) if the X-axis goes first

Q= (-4, 3) if the Y-axis goes first

Answer:

$63.75

Step-by-step explanation:

10% = 7.5

5% = 3.75

15% = 11.25

75.00

-11.25

63.75

Answer:

A= adult tickets, C=children tickets, S=senior tickets

A-10=C; C+10=A

4C=S

4C+6S+10A=1240, but S=4C and C=A-10

4C+24C+10C+100=1240

38C=1140

C=30 children tickets and $120

A=C+10=40 adult tickets and $400

4C=S=120 senior tickets and $720

$120+$400+$720= $1240.

Answer:

12

Step-by-step explanation:

divid half of line

Answer:

Perimeter = 60

Step-by-step explanation:

In order to find the perimeter of the given triangle, we must first determine the value of the missing side. We can use the Pythagorean Theorem to find the missing side of the given right triangle.

According to the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse (the side that is opposite of the right angle, 90°), and a and b represent the legs of the triangle. Use the formula to solve for the missing side. Rearrang the formula to isolate the variable, a:

a² + b²  =  c²

Subtract b² from both sides:

a² + b² - b² =  c² - b²

a² =  c² - b²

Next, substitute the given values into the formula:

c (hypotenuse) = 26

b (leg) = 24

a² =  c² - b²

a² =  (26)² - (24)²

a² = 676 - 576

a² = 100

[tex]\sqrt{(a)^{2}} = \sqrt{100}[/tex]

a = 10

The value of the missing side is 10.

Now, we can solve for the perimeter of the triangle:

P = a + b + c

P = 10 + 24 + 26

P = 60

Therefore, the perimeter of the given right triangle is 60.

Answer:

£59.80

Step-by-step explanation:

299 ÷ 5 = 59.80

59.80 × 5 = 299

Answer: 84%

Step-by-step explanation:

Step-by-step explanation:

cheese : pepperoni : sausage : mushroom =

10 : 7 : 5 : 8

so, in total there are 10+7+5+8 = 30 "business pieces".

to get the total number of pizzas, we need to see how many pizzas are sold per "business piece" ?

we get this from the 35 orders of pepperoni pizzas.

these 35 orders represent 7 "business pieces".

that means 1 "business piece" = 35/7 = 5 pizzas.

that means that 30 "business pieces" are 5×30 = 150

so, in total, 150 pizzas were ordered.

The required value of the given numerical expression is 118, as evaluated by including the PEMDAS rule in the expression.

Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.

The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.

The given numerical expression would be below as:

⇒ 3⋅23 + 52 − 18 ÷ 6

Using the PEMDAS rule in the above expression,

⇒ 3⋅23 + 52 − 18 ÷ 6

Apply the multiplication operation,

⇒ 69 + 52 − 18 ÷ 6

Apply the division operation,

⇒ 69 + 52 − 3

Apply the addition operation,

⇒ 121 − 3

Apply the subtraction operation to get

⇒ 118

Therefore, the evaluated value of the given expression would be 118.

Learn more about the PEMDAS rule here :

https://brainly.com/question/20876480

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Answer:

[tex](x-4)(x^2+6)[/tex]

Step-by-step explanation:

x³-4x²+6x-24 is our equation

Once we factor it we get

[tex](x-4)(x^2+6)[/tex]

Answer:

400/π

Step-by-step explanation:

Well, we know that the formula for circumference is πd. (d is the diameter) Then, we set up the equation 'πd = 400'. Now, simplifying for d, we get d = 200/π.

Answer:

400/π

Step-by-step explanation:

Answer:  F distribution. chi-square distribution. t distribution. normal distribution.

Step-by-step explanation:

Answer:

yes, yes they do

Step-by-step explanation:

i dont know what you're asking

Answer:

4.61

did that help??

Step-by-step explanation:

[tex]2 \dfrac 16 + 3 \dfrac 49 \\\\\\= 2 + \dfrac 16 + 3+ \dfrac 49\\\\\\ = 5+\dfrac{11}{18}= 5 \dfrac{11}{18}[/tex]

Answer:

Administer 14 ml, 350mg/125mg=2.8×5ml=14ml

Answer:

a) A. Arithmetic Sequence

b) A. Arithmetic Sequence

c) A. Arithmetic Sequence

d) A. Arithmetic Sequence

e) B. Not an arithmetic Sequence

Step-by-step explanation:

if there is a common difference it is arithmetic, if there not then it is not arithmetic.

a) d= 3

b)d=3

c)d=2

d)d=-4

e)not arithmetic