solve the following question​

Answer:

HURRYYYY PLEASE HELP ME T-T

Step-by-step explanation:

https://brainly.com/question/19692618

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 :

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

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:

x^8/3

Step-by-step explanation:

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

Read more on perimeter of a rectangle here: brainly.com/question/26787666

#SPJ1

904.32 is the volume.

Volume of sphere

= (4/3)πr³

= (4/3) × 3.14 × (6cm)³

= (4/3) × 3.14 × 6cm × 6cm × 6cm

= 4 × 3.14 × 2cm × 6cm × 6cm

= 904.32 cm³

Answer:

IT IS EASY FORMULAE OF SPHERE IS 4/3πr³ so,

Step-by-step explanation:

                                                    put the value,

                                              =   4/3 * 3.14 *  6³

                                              =  1.333 * 3.14 * 216

                                              =  4.18562 * 216

                                               =  904.09 cm³ ans

Answer:

Pete -> Dan -> Ed -> Leo -> Ilya

Step-by-step explanation:

Quite tricky, but here it is.

If Pete stood in the middle, let's call it position 3.

He would be between Dan and Leo. Let's say Dan is at position 2, and Leo is at position 4. I got that from arithmetic, numbers before and after 3. In this scenario, we don't know we're both Ed and Ilya are.

Now, another says if Pete were to stand at the end, say position 5, he would be next to Ilya, say position 4. In this scenario, we don't know where Ed, Leo and Dan are, but we know for certainty they are ahead of Ilya since Ilya is 4th.

Last scenario, if Pete is standing in front of his friends, then who is where?

From the first scenario, we know that Dan is second, ahead of Leo.

From the second, we know that Ilya is just behind, so, Dan and Leo are ahead of him, yeah? That means we've established them in this order.

Dan -> Leo -> Ilya

And that leaves us with where Ed is.....

Going by the second scenario, we can adjudge that Ilya is the last person and thus, Ed is before him. If Pete stands in front with Dan at second, Leo at fourth and Ilya at fifth, that leaves us with the 3rd position for Ed.

So, we have

Pete -> Dan -> Ed -> Leo -> Ilya

Answer:

7/5

Step-by-step explanation:

just divide

Answer:

The cookie recipe can be made 7 1/2 times.

Step-by-step explanation:

To solve this you need to change 11 1/4  and 1 1/2 into improper fractions so you can get 45/4 and 3/2. Now you have to flip 3/2 so its 2/3, and you can cross cancel so since the 3 in 2/3 can go into the 45 in 45/4 fifteen times, 45/4 becomes 15/4 and 2/3 becomes 2/1. You can multiply across now, so if you multiply 15 and 2, you get 30, and if you multiply 4 and 1 you get 4, so now you have 30/4. To change 30/4 into a mixed number, you have to divide 30 by 4. Since 4 can go into 30 seven times, your whole number is 7, and since 28 + 2 = 30, your numerator is 2, while the denominator is 4. Also, 2/4 can be simplified to 1/2, so your final result is 7 1/2.

I hope this helps you :D

Answer: 112 people.

Step-by-step explanation:

Answer:

You would need 112.5 people to eat all the stacks of pancakes.

Step-by-step explanation:

45 times 5 = 225

and then 225 divided by 2 is 112.5

Hope this helps!

Good question lol

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

For more such question Algebraic  expression visit:

https://brainly.com/question/2164351

#SPJ8

Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

0.75

Step-by-step explanation:

0.47 + 0.28 = 0.75

Answer:.75 or;3/4

Step-by-step explanation: .47 +.28=.75

The height of the ladder on the building is 19.77 feet

Represent the height of the ladder on the building with h

So, the given parameters are:

Angle, x = 64 degrees

Length of ladder, l = 22 feet

The height of the ladder on the building is calculated using

sin(x) = h/l

Substitute the known values in the above equation

sin(64) = h/22

Multiply both sides by 22

h = 22 * sin(64)

Evaluate the product

h = 19.77

Hence, the height of the ladder on the building is 19.77 feet

Read more about elevation angles at

https://brainly.com/question/19594654

#SPJ1

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

for such more questions on  weight

https://brainly.com/question/29892643

#SPJ8

Answer:

Step-by-step explanation:

Maria had a test with 20 questions

if 17 are correct,

20 questions................................100%

17 questions................................?%

she was 85% right

Answer:

5 ft

Step-by-step explanation:

30/6 = 5

20/4 = 5

25/x = 5

25/5 = 5

x = 5

Answer:

5 feet

Step-by-step explanation:

the triangles are scaled by the factor of 5

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

For more such questions on polynomial, click on:

https://brainly.com/question/1600696

#SPJ8

Answer:

Step-by-step explanation:

a)

b)

5 + 4 × 2 + 6 - 2 × 2 - 1 as it is the result is:

We'll add the parentheses considering we need to increase the result by 5:

Step-by-step explanation:

\(\frac{8}{5}\)÷6\(\frac{3}{4}\)

First, simplify the 6\(\frac{3}{4}\) to an improper fraction, which is:

\(\frac{27}{4}\)

Next rewrite the equation using the improper fraction:

\(\frac{8}{5}\)÷\(\frac{27}{4}\)

Now, in order to divide the fraction, we will need to flip the second fraction over, and then multiply the two fractions together. A great way to remember this is the phrase Copy Dot Flip - Copy the first fraction, put a dot for multiplication, and flip the second fraction.

\(\frac{8}{5}\)·\(\frac{4}{27}\)

Finally, multiply together and simplify/reduce if needed:

The final answer is \(\frac{32}{135}\) and no simplification or reduction is needed

The ways to elect the candidates from the total is 462

From the question, we have

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 11 and r = 6

Substitute the known values in the above equation

Total = ¹¹C₆

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 11!/5!6!

Evaluate

Total = 462

Hence, the number of ways is 462

Read more about combination at

brainly.com/question/11732255

#SPJ1

The square root of 9 by long division method will give an answer of 3.

1: Group the digits of 9 into pairs from right to left. Since 9 is a single-digit number, we can consider it as a pair by itself.

2: Find the largest number whose square is less than or equal to the leftmost pair. In this case, the largest number whose square is less than or equal to 9 is 3.

3: Write 3 as the divisor on the left, and the quotient on the top right.

3 √ 9 |  0

4: Multiply the divisor (3) by the quotient (3), and write the result under the 9.

3 √ 9 |  0

      - 9

5: Subtract the result (9) from the leftmost pair (9), and write the difference (0) below the line.

3 √ 9 |  0

      - 9

       0

6: Bring down the next pair (0) to the right of the difference.

3 √ 9 |  0

      - 9

       0

     -----

7: Double the quotient (3) and write a blank space to the right.

3 √ 9 |  0

      - 9

       0

     -----

       0

      ?

8: Find a digit to fill in the blank space, such that when the new divisor (37) is multiplied by the digit, the result is less than or equal to the current dividend (0). In this case, the largest digit we can use is 0.

9: Write the digit (0) as the new quotient, and write the product of the new divisor (37) and the new quotient (0) below the line.

3 √ 9 |  0

      - 9

       0

     -----

       0

      0

10: Subtract the product (0) from the current dividend (0), and write the difference (0) below the line.

3 √ 9 |  0

      - 9

       0

     -----

       0

      0

      - 0

11: Since there are no more pairs to bring down, we have reached the end of the division. The square root of 9 is 3.

√9 = 3.

Learn more on finding square roots by long division methods here https://brainly.in/question/52760816

#SPJ1

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Answer:

a

Step-by-step explanation:

a

Answer: I think the 3rd one is silver, so that one.

Step-by-step explanation:

5 or the best conductors are as follows: Silver, gold, Copper, aluminum, Mercury

A ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

The steps for constructing a copy of an angle:

Step 1: Draw the angle.

Step 2: Place the center of the protractor on the vertex of the angle.

Step 3: Line up the baseline of the protractor with one of the angle's rays.

Step 4: Read the degree measure where the other ray crosses the protractor.

Step 5: Draw a ray from the vertex of the angle to the right.

Step 6: Use a ruler to mark the same distance on the ray that was just drawn.

Step 7: Draw a ray from the vertex through the point just marked on the ray.

This is the copy of the angle's second ray.

Step 8: Use a compass to draw an arc centered at the vertex of the original angle that passes through one of the angle's rays.

Step 9: Without adjusting the compass, draw another arc that intersects the previous arc at a point.

Step 10: Draw a ray from the vertex through the point where the two arcs intersect.

This is the copy of the original angle.

Using a compass, draw an arc centered on the vertex of the original angle passing through one of the angle rays. Place the tip of the

compass on the vertex of the original angle and draw an arc that intersects one of the angle rays.

Draws another arc that intersects the previous arc at a point without adjusting the compass.

Draw a second arc that intersects the first arc at another point, keeping the compass latitude.

Using a ruler or ruler, draw a ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

For more related questions on original angle.:

https://brainly.com/question/27243531

#SPJ8

Answer:

First choice

Step-by-step explanation:

The difference quotient in general is  \(\frac{g(x+h)-g(x)}{h}\). To get an expression for  \(g(x+h)\), replace  x  with x + h.

For this question,

\(\frac{4^{x+h}-4^x}{h}=\frac{4^x\cdot4^h-4^x}{h}\)

Factor  \(4^x\) out of the numerator.

\(\frac{4^x(4^h-1)}{h}\)

Answer:

The answer is A the first option

Step-by-step explanation:

Just took the unit review and got a 100

The size of angle ACB to the nearest degree is 88 degree.

Construction Steps:

Create a line segment BC with the property AC = 4 cm.

Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.

Join AB and AC now. Consequently, the necessary triangle is ABC.

With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.

Cut an arc of 3 cm from point B.

Embrace BC and AC

Triangle with  angle ABC is necessary.

< ACB = 88 degree

To learn more about angle  refer to:

https://brainly.com/question/25716982

#SPJ1

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

Learn more on Pythagorean theorem here;

https://brainly.com/question/343682

#SPJ1

Answer:

7/20

Step-by-step explanation:

You would do one whole tank minus how much she used on Saturday and minus how much of the tank she used on Sunday.

1-(1/4)-(2/5)=7/20

The rule applied to obtain each vertex of the triangle DEF after the transformations is given as follows:

(x,y) -> 1/3(x - 3, y + 5).

The original coordinates of triangle DEF have the following format:

(x,y).

The dilation by a scale factor of 1/3 means that each of the coordinates is multiplied by 1/3, hence:

(x,y) -> 1/3(x,y).

The translation along the vector <-3,5> means that the x-coordinate is subtracted by 3 while 5 is added to the y-coordinate, hence:

(x,y) -> 1/3(x - 3, y + 5).

More can be learned about transformations at https://brainly.com/question/29209050

#SPJ1

F(x) is one-to-one, and it is invertible.

The inverse of f(x) is f^-1(x) = (x + 8)^(1/4)/∛3.

We need to check if it is a one-to-one function.

A function is one-to-one if every element in the domain is paired with a unique element in the range.

To check if f(x) is one-to-one, we can use the horizontal line test. If no horizontal line intersects the graph of the function more than once, then the function is one-to-one.

Taking the derivative of f(x), we get:

f'(x) = 12x^3

Since f'(x) is always positive, f(x) is a strictly increasing function. This means that no two different inputs x1 and x2 can produce the same output f(x1) = f(x2).

Therefore, f(x) is one-to-one, and it is invertible.

To find the inverse of f(x), we can follow these steps:

Step 1: Replace f(x) with y:

y = 3x^4 - 8

Step 2: Solve for x in terms of y:

y + 8 = 3x^4

x^4 = (y + 8)/3

x = (y + 8)^(1/4)/∛3

Step 3: Replace x with f^-1(x):

f^-1(x) = (x + 8)^(1/4)/∛3

Therefore, the inverse of f(x) is f^-1(x) = (x + 8)^(1/4)/∛3.

Learn more about function here : brainly.com/question/10439235

#SPJ1

The statement refers to the way that symbols are represented in sequences, a common practice in formal language theory, by employing a notation that makes symbols a part of the sequence.

In formal language theory, a language is often defined as a set of strings over an alphabet. By representing any alphabetic sequence of symbols as a single string using the notation outlined in the statement, we are able to recognise the language that comprises that sequence as a collection of strings. A subset of the language having all possible strings over the alphabet (a, b, and c) is the set of strings abc, which may be used to represent the language including the sequence (a, b, and c). So, this notation offers an easy approach to discuss languages and the sequences that make up such languages.

Hence, the statement relates the symbols and sequences.

Learn more about sequence here:

https://brainly.com/question/21961097

#SPJ1