What is calculas of variations?
​

The volume of a cone with diameter 11.5 inches and a height of 15 inches is  519 in³.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreases to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, A cone with a radius of 11.5 inches and a height of 15 inches.

Now, The diameter is 11.5 inches, hence radius is 11.5/2 = 5.75 inches.

We know the volume of a cone is (1/3)πr²h.

∴  The volume of a cone is = (1/3)×π×(5.75)²×15 inch³.

= 519 in³.

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We might add 10 pounds of mixed nuts which include 20% peanuts by solving the governing equations.

An equation is a claim that shows the equality of two mathematical expressions.

For instance, the equal sign separates the two equations that make up the equation 3x + 5 = 14: 3x + 5 and 14.

So, we need a total of x pounds of mixed nuts.

Peanuts weigh 0.70 pounds in this combo.

Three pounds of peanuts are used to create the 20% mixture, or 0.20*15.

The equation we got: 0.70 x + 3 = 0.40(x + 15)

Now, solve as follows:

0.70 x + 3 = 0.40(x + 15)

0.70 x + 3 = 0.40(x + 15)

0.70x + 3 = 0.40x + 6

0.70x - 0.40x = 6 - 3

0.30x = 3

x = 10 pounds

Therefore, we might add 10 pounds of mixed nuts which include 20% peanuts by solving the governing equations.

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The linear function g(x) = 3 · x + 6 has the following features:

Domain: - ∞ < x < + ∞

Range: - ∞ < y < + ∞

x-Intercept: (- 2, 0)

In this problem we must determine the domain, the range and the x-intercept of a linear function, that is, a polynomial of the form y = m · x + b, where m is the slope and b is the x-intercept. We must find the information by understanding the following features:

If we know that the function is g(x) = 3 · x + 6, then its domain and range are - ∞ < x < ∞ and - ∞ < y < ∞ and its x-intercept is:

0 = 3 · x + 6

- 3 · x = 6

x = - 2

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Step-by-step explanation:

The given function is g(x) = 3x + 6.

Domain: The domain of a function is the set of all possible input values (x) for which the function is defined. Since the function is a linear equation, it is defined for all real values of x. Therefore, the domain of the function is: Domain: -∞ < x < ∞ Range: The range of a function is the set of all possible output values (y) that the function can produce. The slope of the given function is positive (3), so the function increases without bound as x increases.

Therefore, the range of the function is: Range: -∞ < y < ∞ x-intercept: The x-intercept of a function is the point at which the graph of the function intersects the x-axis. To find the x-intercept, we set y = 0 and solve for x. 0 = 3x + 6 -6 = 3x -2 = x Therefore, the x-intercept is (-2, 0).

So, the correct option is: Domain: -∞ < x < ∞; Range: -∞ < y < ∞; x-intercept (-2, 0).

Answer:

Step-by-step explanation:

You want the formula that represents (p, a) = (3.50, 250) and (2.50, 350) as a linear function. Then you want the value of 'a' for p = 1.50.

We can see from the ordered pairs that 'a' goes up by 100 when p goes down by 1.00. The slope is ...

  m = ∆a/∆p = 100/(-1) = -100

The y-intercept (b) can be found by solving the slope-intercept equation for b:

  y = mx +b

  b = y - mx

For (x, y) = (3.50, 250), the value of 'b' is ...

  b = 250 -(-100)(3.50) = 600

The slope-intercept equation for 'a' in terms of p is ...

  a = -100p +600

The value of 'a' for p = 1.50 is ...

  a = -100(1.50) +600

  a = 450

They will sell 450 items if the price per item is $1.50.

Translate the graph [tex]5[/tex] units right, reflect over the [tex]x[/tex]-axis, and then perform a vertical stretch with a factor of [tex]3[/tex].

The graph of the system of equations is shown below, and the solution is: (6, 1).

When a system of equations are plotted on a graph, the lines of the two equations in the system will intersect at a point. The coordinates of that point represents the solution of the system of equations.

In the graph shown below in the attachment, the red line represents the line 3x - y = 17, which has a slope of 3 and intercepts the y-axis at -17.

The green line represents the equation, x + 4y = 10, which has a slope of -1/4 and a y-intercept of 2.5.

Both lines intersect at point (6, 1).

Therefore, the solution is (6, 1)

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The maximun value (63) is located at point (1, 2).

Check attached image 1.

The purple coloured area represents the resulting area of possible answers that meet all the requirements established by the restrictions within the cartesian plane.

In this step, we need to look for extreme values, these are normally found on the edges and corner of the area drawn by all the restrictions.

Check attached image 2 to see the extreme values.

Point A is located at: (-3, -2)

Point B is located at: (-3, -4)

Point C is located at: (3, -4)

Point D is located at: (1, 2)

Given function: [tex]P=10x+6y+41[/tex]

Since we are tryong to obtain the point where there is a maximun value for function "P", we need to evaluate all the extreme points and choose the one that makes the function return the maximum value out of all 4 points.

Evaluating the points:

[tex]P(-3, -2)=10(-3)+6(-2)+41=-1\\ \\P(-3, -4)=10(-3)+6(-4)+41=-13\\ \\P(3, -4)=10(3)+6(-4)+41=47\\ \\P(1, 2)=10(1)+6(2)+41=63[/tex]

The maximun value (63) is located at point (1, 2).

There's a different method called "Simplex" that can also be used to solve these type of optimization problems. It's more complicated but can be useful when working with more than 2 variables.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0

The equation of the line passing through (-1, 2) and (1, -8). Then the equation of the line will be

y + 8 = [(-8 - 2) / (1 + 1)] (x - 1)

y + 8 = -5x + 5

y = - 5x - 3

The equation that best represents a line perpendicular will be y = - 5x - 3.

Answer:

2/7 ​≈0.285714286

Step-by-step explanation: 3/7−1/7

Since 3/7​ and 1/7​ have the same denominator, subtract them by subtracting their numerators.

3−1​ over 7

Subtract 1 from 3 to get 2.

2/7

the Factor

so 2/7 ≈0.285714286

Hello,

I hope you and your family are doing well!

To find the mean of a set of numbers, you need to add up all of the numbers and divide the sum by the total number of numbers in the set.

In this case, the mean would be calculated as follows:

(678 + 592 + 652 + 800 + 502 + 396 + 502 + 301) / 8 = 515.25

So the mean of this data set is 515.25.

The mean is a measure of the central tendency of a data set and can be used to represent the entire set of numbers by giving a single value that is representative of the set as a whole. It is also known as the average.

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Happy Holidays!

You will need 51.2 lbs of the cheaper candy and 4 lbs of the expensive candy.

A equation is supposed to be straight condition in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight conditions in two factors

Let x be number of pounds of cheaper candy and y represent that of expensive candy.

Then, x + y = 55.2----(1)

And

2x + 8.9y = 55.2(2.5) = 138

2x + 8.9y = 138---------(2)

On solving above two equation, we get

x = 51.2

y = 4

Thus, cheaper candy are of 51.2 ib and expensive are of 4 ib

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Answer: x=3

Step-by-step explanation:

When you plug in each number only 3 is the right answer.

A. 8(-4)-4=2(2(-4)+4)

-36=8 False

B. 8(12)-4=2(2(12)+4)

92=56 False

C. 8(0)-4=2(2(0)+4)

-4=8 False

D. 8(3)-4=2(2(3)+4)

20=20 True

Answer:

A

Step-by-step explanation:

There is no difference between -0 and +0.

So the ans is -3.29 itself.

Answer:V = 550 ft^3

Step-by-step explanation:

The volume of a cylinder is

V = pi r^2 h

We know the radius is 2.5 and the height is 28

V = 3.14 * (2.5)^2 * 28

V =549.5 ft^3

Rounding to the nearest whole number

V = 550 ft^3

Answer:

Step-by-step explanation:

It will lie in quadrant 3

Step-by-step explanation:

Here, we want to know where the resulting image will lie after the rotation

After the rotation, it is expected that the resulting image will lie in quadrant 3

First 90 to quadrant 1

second 90 to quadrant 2

Third 90 to quadrant 3

Answer:

B is the correct answer

Step-by-step explanation:

i think:)

Answer:

z = -8

Step-by-step explanation:

6(z-1) + 14 = -40

6z - 6 + 14 = -40   Distribute the 6

6z + 8 = -40   Combine Like Terms

6z = -48   Subtract 8 on Both Sides

z = -8   Divide by 6 on Both Sides

a. The coordinates of vertex B is (-3, -4)

b. The coordinates of vertex A' is (3,8)

What do you mean by rotation 180° about the origin?

The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).

Solution:

a. Current coordinate of vertex B is (3, 4).

  After rotating it 180° it becomes B (-3 , -4)

b. After translation the coordinates of vertex A is (5-2,4+4)

Coordinates of vertex A is (3,8)

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If ΔA B C is rotated 180° about the origin, the coordinates of B' (-3, -4)

b. The coordinates of vertex A' is (3,8)

What do you mean by rotation 180° about the origin?

The rotation of 180° of any coordinate or vertex about the origin means that the coordinates are rotated to the negative axis that is (x, y) >>>>(-x,-y) or (-x,-y) >>>>(x, y).

Solution:

a. Current coordinate of vertex B is (3, 4).

 After rotating it 180° it becomes B (-3 , -4)

b. After translation the coordinates of vertex A is (5-2,4+4)

Coordinates of vertex A is (3,8)

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The value of x would be 11° and the value of y would be 6.

What are congruent triangles?

Two triangles are congruent if all of their sides are the same - so side, side, side. We also know they are congruent if we have a side and then an angle between the sides and then another side that is congruent-- so side, angle, side.

ΔRWS ≅ ΔTUV

As both triangles are congruent then we can say that

∠S ≅ ∠V

so ∠S = 29°

Now in ΔRWS,

By using the sum of all angles of the triangle property, we can write

∠R +∠W + ∠S = 180°

(8x - 27)° + 90° + 29° = 180°

8x = 180° - 92°

8x  = 88°

x = 88/8

x = 11°

Now Side RS ≅ Side TV

         3y + 7 = 25

         3y = 25 - 7

         3y = 18

            y = 18/3

            y = 6

Hence, the value of x would be 11° and the value of y would be 6.

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Answer:

[tex]\textsf{A)} \quad -\dfrac{9}{5}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given sum:

[tex]\displaystyle \sum^{\infty}_{n=1} -3\left(\dfrac{3}{8}\right)^n[/tex]

Therefore, the first term in the series is:

[tex]a_1=-3\left(\dfrac{3}{8}\right)^1=-\dfrac{9}{8}[/tex]

The common ratio, r, is:

[tex]r=\dfrac{3}{8}[/tex]

Substitute the first term, a, and common ratio, r, into the formula:

[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{1-\frac{3}{8}}[/tex]

[tex]\implies S_{\infty}=\dfrac{-\frac{9}{8}}{\frac{5}{8}}[/tex]

[tex]\implies S_{\infty}=-\dfrac{9}{5}[/tex]

Therefore, the sum of the given series is:

Answer:P(3 men) =

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know the values of x and y in the given figure.

The left-side triangle has angles marked as congruent. Hence it is an equilateral triangle, which also has congruent sides.

  8y = 40

  y = 40/8 = 5

The angle at the middle of the longest line is supplementary to the adjacent angle in the equilateral triangle, hence is 120°.

The marked side length of 40 and the equilateral triangle side length of 40 mean the triangle on the right is an isosceles triangle with an a.pex angle of 120°. Its congruent base angles (x°) must be (180° -120°)/2 = 30°.

  x° = 30°

The values of x and y are 30 and 5, respectively.

The rate of change of the width of the rectangle at that instant is 3.8 inches/sec.

Rectangulus, a combination of the Latin words rectus (as an adjective, right, appropriate), and angulus, is where we get the word rectangle (angle).

A crossed rectangle is a crossed quadrilateral made up of two opposing sides and the two diagonals of a rectangle. It is a specific case of an antiparallelogram with angles that are not all equal and right angles, even though opposite angles are. Other geometries, including spherical, elliptic, and hyperbolic,  with opposite sides of equal length and equal angles that are not right angles.

We have,

W=width of the rectangle

H=height of the rectangle

A=Area of the rectangle

We know that,

A=W×H

A=20, W=4

20=4×H

H=5 inches

dA/dt=7 (inches)²/sec

dH/dt= -3 inches/sec

dA/dt=W.(dH/dt)+H×dW/dt

dA/dt=4(-3)+5(dW/dt)

7=-12+5(dW/dt)

dW/dt=19/5

dW/dt=3.8 inches/sec

Therefore, the rate of change of the width of the rectangle at that instant is 3.8 inches/sec.

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The system of linear inequalities is graphed is y≥3x-2; x+2y ≤4. Hence option b is the correct.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The graph consists of two inequalities.

Since the graph lines are solid, thus the inequality sign either "less than or equal" or "greater than or equal".

First find the equation of line.

One line passes through the points (0,2) and (4,0).

The equation of line that passes through the point (a,0) and (0,b) is

x/a + y/b = 1

The equation of the line is x/4 + y/2 =1

(x + 2y)/4 = 1

x + 2y = 4

The equation of the inequality will be either x + 2y ≤ 4 or x + 2y ≥ 4.

Putting x =0  and y = 0 in x + 2y ≤ 4

0 + 0 ≤ 4

0≤ 4 (true)

In the graph (0,0) includes in the shaded region. Therefore the inequality is  x + 2y ≤ 4.

The second line passes through the points (0,-2) and (3,7).

If a line passes through the points (x₁, y₁) and (x₂, y₂), then the equation of line is y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).

The equation of the line is

y - 7 = (7 + 2)/(3 - 0)(x - 3)

y - 7 = 3x -9

y = 3x - 2

The equation of the inequality will be either y ≥ 3x-2 and  y ≤ 3x-2:

Putting x =0  and y = 0 in y ≥ 3x-2

0 ≥ 0-2

0 ≥ -2 true

In the graph (0,0) includes in the shaded region. Therefore the inequality is y ≥ 3x-2.

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Answer:

Step-by-step explanation:

angle A = 63.7°, B= 26.3°, D= 49° , then angle C = 221

Two shapes that are the same size and the same shape are congruent.Congruent shapes are shapes that are exactly the same.

The corresponding sides are the same and the corresponding angles are the same.

This means the corresponding angles of the two shapes are equal.

With this, angle A = 63.7°, angle B= 26.3° , angle D =49°

The sum of angles in a quadrilateral is 360°

therefore angle C = 360-(63.7+49+26.3)

C = 360-139

C = 221°

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Answer:

Area = 28.27 in²

Step-by-step explanation:

Now we have to,

→ find the area of the circle.

Formula we use,

→ π × r²

Now the required area will be,

→ π × r²

→ 3.14 × 3²

→ 3.14 × 9

→ 28.27 in²

Hence, the area is 28.27 in².

The Greatest Number of orders were in the month = September

The Numbers of orders increased in month = August to September

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

According to the given information

From graph

We got to know

In may , orders = 3150

In June , orders = 3050

In July , orders = 2900

In August , orders = 3200

In September , orders = 3250

a) The Greatest Number of orders were in the month = September

b) The Numbers of orders increased in month = August to September

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To find a book it is necessary to write the name "a vacation trip" in the search engine and add the word PDF to obtain better results.

To download a book from the Internet it is necessary to review various pages since some do not contain the complete book and others may have some type of virus that can damage the device.

In the same way, there are some platforms or applications that require a subscription payment to be able to access the content in an unlimited way.

¡Hope this helped!