Work out the size of angle A

The length of the second arc is 8 feet.

The rope is swinging in such a way that the length of the arc is decreasing geometrically.

If the first arc is 18 feet long and the third arc is 8 feet long,

The length of the second arc :

In order to find the second arc length, we need to use the formula of the geometric sequence.

We have to understand what is given and what is required.

Given : First arc = 18 feet

Third arc = 8 feet.

To Find : Length of the second arc.

The formula of the geometric sequence is :

[tex]a_n[/tex] = [tex]a_1[/tex] × rn − 1

where, r = Common ratio [tex]a_1[/tex] = First term [tex]a_n[/tex] = [tex]n^{th}[/tex] term

Here, the length of the first arc is [tex]a_1[/tex] = 18.

The length of the third arc is [tex]a_3[/tex] = 8.

We have to find the length of the second arc, which is [tex]a_2[/tex]

Using the formula of the geometric sequence, we can find the [tex]a_1[/tex]: r= [tex]a_3[/tex] / [tex]a_2[/tex]

We know that [tex]a_1[/tex]= 18 and [tex]a_3[/tex]= 8

Substitute the values: r= 8 / [tex]a_2[/tex]

Now, we can rewrite the formula of the geometric sequence: an=[tex]a_1[/tex]×rn−1an= [tex]a_1[/tex] x r(n-1)

The length of the first arc is [tex]a_1[/tex] = 18 feet.

Substituting the value of r, we get:

8 / [tex]a_2[/tex] = r18 x r(n-1) = [tex]a_2[/tex]

We are given that the length of the third arc is 8 feet,

thus : 8 = 18 x r(3-1)8

= 18 x [tex]r_2[/tex][tex]r_2[/tex]

= 8 / 18[tex]r_2[/tex]

= 4 / 9r

= √(4/9)

Using this value of r, we can find the length of the second arc :

[tex]a_2[/tex] = 18 x (4/9) (2-1) [tex]a_2[/tex]

= 18 x (4/9)[tex]a_2[/tex]

= 8

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Option D, which has 92° and 66° curves, is the correct choice. The total of these angles is 158°, which is needed for the final two angles.

The triangle with edges in the ratio $3:4:5 is therefore "yes" a right-angled triangle. Note: We can only apply Pythagoras' Theorem to right-angled triangles; it cannot be applied to any other triangles.

Let's add the given angle measures: 52° + 70° + 44° + 36° = 202°. This means that the sum of the measures of the remaining two angles in the two triangles is:

360° - 202° = 158°

As a result, since both options A and B have one angle that is higher than 90 degrees, we can rule them out.

Option C has angles of 88° and 68°, which add up to 156°.

Since the highest sum of two acute angles is 180°, the other two angles would have to have a sum of 204°, which is not feasible.

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The Solutions to 12m ² - 4mn-5n² are:

m = n/3 or m = -5n/3

To solve the quadratic equation 12m² - 4mn - 5n² = 0, we can use the quadratic formula:

m = (-b ± √(b^2 - 4ac)) / 2a

where a = 12, b = -4n, and c = -5n².

Substituting these values into the formula, we get:

m = (-(-4n) ± √((-4n)^2 - 4(12)(-5n²))) / 2(12)

Simplifying:

m = (4n ± √(16n² + 240n²)) / 24

m = (4n ± √(256n²)) / 24

m = (4n ± 16n) / 24

So the solutions are:

m = n/3 or m = -5n/3

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The length of one of the ropes is approximately 10.77 feet when rounded to the nearest foot.  

Let's call the distance between the poles "d" and the height of the poles "h". We can use the Pythagorean theorem to find the length of the ropes:

If we draw a diagram, we can see that the four ropes form the hypotenuses of four right triangles. Each right triangle has a base of d/2 and a height of h - (banner height)/2.

Therefore, we have:

[tex]x^2[/tex] = [tex](d/2)^2[/tex] + [tex](h - (banner height)/2)^2[/tex]

Substituting the given values, we get:

[tex]x^{2}[/tex] = [tex](20/2)^2[/tex]+ [tex](16 - (8/2))/2)^2[/tex]

[tex]x^{2}[/tex]= 100 + [tex](8/2)^2[/tex]

[tex]x^{2}[/tex] = 100 + 16

[tex]x^{2}[/tex] = 116

Taking the square root of both sides, we get:

x = [tex]\sqrt{116}[/tex]

x ≈ 10.77

Therefore, the length of one of the ropes is approximately 10.77 feet when rounded to the nearest foot.  

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The average rate of change of the function f(x) over the interval [-2, -9] is -6.

To determine the average rate of change of the function f(x) over the interval [-2, -9], we need to find the slope of the secant line that connects the points (-2, f(-2)) and (-9, f(-9)).

We first find the values of f(-2) and f(-9):

f(-2) = (-2)² + 5(-2) + 14 = 4 - 10 + 14 = 8

f(-9) = (-9)² + 5(-9) + 14 = 81 - 45 + 14 = 50

So, the two points are (-2, 8) and (-9, 50).

The slope of the secant line between these two points is:

slope = (f(-9) - f(-2)) / (-9 - (-2)) = (50 - 8) / (-9 + 2) = 42 / -7 = -6

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Answer:

2.1

Step-by-step explanation:all side lengths are the same (duh) use 4 and 3 (4 bc there is 4 sides). 4 as the diagonal support

4²=16

3²=9

16-9=7 then use square root for 7 the square root of 7 is 2.6457513111 or 2.1

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{p})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{p}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{7}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -5 }\implies \cfrac{4-p}{1}=-5 \\\\\\ 4-p=-5\implies 4=-5+p\implies 9=p[/tex]

To determine the approximate length of the underground pipeline needed from the lake to the water level in Apache Durham Park, we would know the distance between the lake and park, as well as the specific path that the pipeline would take from the lake to the park.

Length is a physical or conceptual measurement of the extent of something from one end to the other.

It refers to the distance between two points or the size of an object or entity in the direction of its longest dimension. In mathematics and geometry, length is a fundamental concept used to describe the size and shape of geometric figures and objects.

It is measured in units such as meters, feet, inches, or centimeters

Assuming that we have this information, we can use the distance between the two points as the approximate length of the pipeline. To calculate this distance, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) represents the coordinates of the lake and (x2, y2) represents the coordinates of Apache Durham Park.

Once we have the distance between the two points, we can round it to the nearest meter to get the approximate length of the pipeline needed.

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We would know the distance between the lake and park, as well as the precise route that the pipeline would travel from the lake to the park, if we knew the approximate length of the underground pipeline required from the lake to the water level in Apache Durham Park.

A gauge of length is one that shows how far something extends from one end to the other.

It describes the separation of two points or the size of an item or entity measured along its longest axis. Length is a basic notion in mathematics and geometry that is used to describe the size and shape of geometric figures and objects.

Its dimensions are expressed in terms of meters, feet, inches, or millimeters.

Assuming we have this knowledge, we can use the distance between the two locations to estimate the pipeline's length. We can use the following algorithm to determine this distance:

[tex]d=\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2} }[/tex]

where [tex](x_{1},y_{1} )[/tex] stands for the lake's coordinates and [tex](x_{2} ,y_{2} )[/tex] for Apache Durham Park's coordinates.

Once we know how far apart the two locations are, we can round it to the closest meter to determine how long the pipeline should be roughly.

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The complete question is as follows:

Answer:20.25

Step-by-step explanation:

the relationship between the diameter of the pizza and its cost per square inch is non-proportional.

The relationship between the diameter of the pizza and its cost per square inch is non-proportional.

If the relationship were proportional, then the cost per square inch of the pizza would remain constant as the diameter changes. However, in this case, we see that as the diameter of the pizza increases, the cost per square inch decreases. This is because the area of a circle increases more rapidly than its diameter, so the cost must be spread out over a larger area, resulting in a lower cost per square inch.

Therefore, the relationship between the diameter of the pizza and its cost per square inch is non-proportional.

the complete question is :

would relationship between the dilation factor k and the resulting volume of a solid best be described as proportional or non proportional? justify your answer

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Step-by-step explanation:

La première baisse de prix est de 30%, ce qui signifie que le prix du vêtement est maintenant de 70% de son prix initial :

Prix après la première baisse = 100€ - (30% x 100€) = 70€

Ensuite, le prix est réduit à nouveau de 20%. Cela signifie que le prix final est de 80% du prix après la première baisse :

Prix après la deuxième baisse = 70€ - (20% x 70€) = 56€

Le pourcentage de réduction totale correspond donc à la différence entre le prix initial et le prix final, exprimé en pourcentage du prix initial :

Pourcentage de réduction totale = ((100€ - 56€) / 100€) x 100% = 44%

Le vêtement a donc subi une réduction de 44% au total après les deux baisses successives de prix.

Answer:

yes

Step-by-step explanation:

I remember doing this but I don’t seem to remember sorry

Answer:

220-8pi

Step-by-step explanation:

Using strategy 1 (in your head), divide 60m by 10m to get 6, then multiply that number by one to get 6cm. the length on drawing is 6cm

Procedure 2 (proportions)

Create a proportion first.

We know that 1 cm equals 10 metres, so we place them on a fraction (the operation is unaffected by the denominator or numerator). However, we don't know how many cm equal 10m, so we make that into a variable, in this case x.

1cm x cm

——— ———

100m 60m

Go diagonally to where the variables have already been put in to solve a proportion. You are unable to calculate 60 metres and x centimetres because you are unsure of x. Yet you can travel 60m. Start by multiplying 1 by 30 to reach the number 60. The result of multiplying 60 by 10m is x. This will equal 6.

Thus, your response is 6.

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(a) The distance that the tip of the hour hand covers in twelve hours is 28.29 cm.

(b)The distance that the tip of the minute hand covers in one hour is 34.57 cm.

(c) The tip of the minute hand covers a longer distance than the tip of the hour hand by 6.28 cm.

(a) To find the distance that the tip of the hour hand covers in twelve hours, we need to calculate the circumference of the circle that the tip of the hour hand traces in twelve hours. The circumference is given by:

C = 2πr

where r is the length of the hour hand

C = 2 x 22/7 x 4.5

C = 28.29 cm

(b) Also, the distance that the tip of the minute hand covers in one hour is:

C = 2 x 22/7 x 5.5

C = 34.57 cm

(c) We can see that the distance covered by the minute hand in one hour (34.57 cm) is greater than the distance covered by the hour hand in twelve hours (28.29 cm).

difference = 34.57 cm - 28.29 cm = 6.28 cm

Thus, the tip of the minute hand covers a longer distance than the tip of the hour hand by 6.28 cm.

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Answer:

Step-by-step explanation:

As a result, the difference is 837 grammes between the cones' respective masses.

Describe density.

Mass per unit volume is measured using density. It is described as a substance's mass per unit volume. The following is the density formula:

Mass / Volume equals density.

So, The formula m = V, where m is the mass, is the density, and V is the volume, can be used to determine each cone's mass.

The formula below can be used to determine each cone's mass:

- The mass of a steel cone weighs 1298.21 grams or 7.75 grams per cubic centimeter.

- The granite cone weighs 460.76 grams, or 2.75 grams per cubic centimeter.

- Mass of steel cone = 7.75 g/cm³ × 167.55 cm³ = 1298.21 grams

- Mass of granite cone = 2.75 g/cm³ × 167.55 cm³ = 460.76 grams

for difference of masses = 1298.2 grams - 460.76  grams = 837 grams

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Answer:

If the shopkeeper sold the radio for 336 rs and gained a 5% profit, then the cost price (c.p.) of the radio can be calculated as follows:

Let x be the cost price of the radio. Since the shopkeeper gained a 5% profit, we can write the equation: x + 0.05x = 336 Solving for x, we get: x(1 + 0.05) = 336 x = 336/1.05 x = 320

So, the cost price (c.p.) of the radio is 320 rs.

Step-by-step explanation:

The cheaper price for the 12 orchid is the 8.60 pounds for 4 orchid.

The cheaper price for the 12 orchid can be calculated as follows;

Therefore, for the first Orchid:

4 orchid = 8.60 pounds

12 orchid = ?

cross multiply

cost for 12 orchid = 8.60 × 12 / 4

cost for 12 orchid = 103.2 / 4

cost for 12 orchid = 25.8 pounds

For the second orchid:

5.40 pounds for each.

Now, 1 / 3 off,

Therefore,

1 / 3 ×5.40 = 1.8

Therefore,

5.40 - 1.8 = 3.6 pounds for each

Therefore,

12 orchid = 12 × 3.6 = 43.2 pounds

Therefore, the cheaper price is 8.60 pounds for 4 orchid.

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Answer:

Commutative property of addition

Step-by-step explanation:

The property being used in this equation is the commutative property of addition. This property states that when two numbers are added, the order in which they are added does not change the sum. So, in this case, we can rearrange the terms 5/6 and 7/12 and still get the same result.

Based on the table provided, the statement that is true is of all the cats adopted, about 66% were adopted in a month or less.

To calculate a percentage, you need to divide a part by the whole and then multiply the result by 100. The formula for calculating a percentage is:

Percentage = (Part / Whole) x 100

Alternatively, if you have the percentage and the whole, you can use the following formula to find the part:

Part = (Percentage / 100) x Whole

Based on this, let's prove the true statement:

Total of animals: 58 cats

Total of cats adopted in a month or less: 38

Percentage = 38/ 58 x 100 = 65.5% which can be rounded as 66%

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The expression of the function using the specified formats are presented as follows;

Please find attached the required graph of the function f(x) = -2·(x - 4)² + 1 created with MS Excel

The table of values for the function can be presented as follows;

[tex]\begin{tabular}{|c|c|c|} \cline{1-2}x& f(x) \\ \cline{1-2}1 & -17\\ \cline{1-2} 2 & -7 \\ \cline{1-2} 3 & -1 \\ \cline{1-2} 4 & 1 \\ \cline{1-2} 5 & -1\\\cline{1-2} 6 & -7 \\ \cline{1-2} 7 & -17 \\ \cline{1-2}\end{tabular}[/tex]

The mapping diagram can be presented as follows;

x [tex]{}[/tex]  f(x)

1 → -17

2 → -7

3 → -1

4 → 1

5 → -1

6 → -7

7 → -17

The function expressed using set notation can be presented as follows;

f(x) = {-17, -7, -1, 1, -1, -7, -17} where x ∈ {1, 2, 3, 4, 5, 6, 7}

A function is a rule that assigns a unique value for the output for each input value.

The specified function is; f(x) = -2·(x - 4)² + 1

Please find attached the graph of the parabola, created with MS Excel, which is a parabola that opens downwards, with a vertex of (4, 1)

The table of values can be presented as follows;

 x  |  f(x)

-----|------

 1  |  -17

 2  |   -7

 3  |   -1

 4  |    1

 5  |   -1

 6  |   -7

 7  |  -17

Mapping diagram:

A mapping diagram is a diagram that illustrates how an element of a set is paired with elements in another set.

The mapping diagram for the function can be made to show how the x-values are mapped to the f(x) values as follows;

1  →  -17

2  →   -7

3  →   -1

4  →    1

5  →   -1

6  →   -7

7  →  -17

Set notation;

The function, f(x) = -2·(x - 4)² + 1 can be expressed using set notation for the interval 1 ≤ x ≤ 7, which is the set of integers between 1 and 7, inclusive, which is presented as follows;

Set of x-values; {1, 2, 3, 4, 5, 6, 7}

Set of f(x) values is therefore; {-17, -7, -1, 1, -1, -7, -17}

Therefore, we get f(x) = -2·(x - 4)² + 1 expressed using set notation can be presented as follows;

f(x) = {-17, -7, -1, 1, -1, -7, -17}, where, x ∈ {1, 2, 3, 4, 5, 6, 7}

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196 children's tickets and 328 adult tickets were sold.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: One night a theater sold 524 movie tickets. An adult's ticket costs $6.50 and a child's ticket cost $3.50. In all, $2881 was taken in.

Let the amount of the child's ticket be x

Let the amount of adults tickets be y

If the total number of tickets sold is 524 movie tickets, then;

x + y  = 524

x = 524 - y...(1)

If an adult ticket cost $6.50 and a child’s ticket cost $3.5 with a total of $2881 in all, then;

3.5x +  6.5 y = 2881

35x + 65y = 28810 ...(2)

Substitute equation 1 into 2:

35x + 65y = 2881

35(542-y) + 65y = 28810

18970 - 35y + 65y = 28810

30y = 9840

y = 328

Put the value of y in equation (1) and we get

x = 524 - 328

x = 196

Hence,  196 children's tickets and 328 adult tickets were sold.

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The cone and cylinder above have the same radius and height and the volume of the cone is 171 cubic inches.

Volume of a three-dimensional shape is the space occupied by the shape.

Given that,

Radius and height of the cylinder and the cone are same.

Let r and h be the radius and height of each of the cylinder and the cone.

Volume of the Cone = 1/3 π r² h

Volume of the cone = We have, volume of the cylinder is 57 cubic inches.

1/3 π r² h = 57

Multiplying both sides by 3,

π r² h = 57 × 3

π r² h = 171 cubic inches π r² h

Hence the volume of the cone is 171 cubic inches

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The number of horizontal square of D over the number of vertical

squares  = 3 : 2

What is square in math?

A planar shape with four equal sides and four right (90°) angles is referred to as a square in geometry. An equilateral rectangle is a specific sort of square, while a parallelogram is a special kind of square (an equilateral and equiangular one). All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees apart from each other or at right angles. The square's diagonals are also equal and split at an angle of 90 degrees.

the number of horizontal squares of A, B , and C over the number of vertical square = 2 : 3

  the number of horizontal square of D over the number of vertical

squares  = 3 : 2

                       6 : 4 = 3 : 2

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Answer:22.1%

Step-by-step explanation:

The volume of the sphere is increasing at a rate of 209,439.51 mm³/s when the diameter is 100 mm

The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 100 mm? (Round your answer to two decimal places).Formula to calculate the volume of a sphere = (4/3) × π × r³where r = radius of the sphere, π = pi = 3.14, d = diameter of the sphere. The diameter of the sphere, d = 100 mm.So, the radius of the sphere, r = d/2 = 100/2 = 50 mm.

Now, we need to find the rate of change of the volume of the sphere when the radius of the sphere is increasing at a rate of 4 mm/s.We know that the volume of the sphere is given by V = (4/3) × π × r³.We have to differentiate the above formula with respect to time (t).dV/dt = d/dt [(4/3) × π × r³]dV/dt = (4/3) × π × 3r² × dr/dt, substitute r = 50 mm and dr/dt = 4 mm/s in the above equation to find dV/dt.dV/dt = (4/3) × π × 3(50)² × 4dV/dt = 209,439.51 mm³/sTherefore, the volume of the sphere is increasing at a rate of 209,439.51 mm³/s .

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Step-by-step explanation:

12 lemons   / 4 people      *     30 people =   90 lemons

1 liter/ 12 lemons   *  90 lemons =  7.5 liters of water

These are the polynomial equations:

A = x^ (1/4) - ∛x + 4√x - 8x + 16

B = 3x² - 5x⁴ + 2x - 12

C = x³ - 7x² + 9x - 5x⁴ - 20

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

These are the non-polynomial equations:

E = 4/x⁴ + 3/x³ - 2/x² - 1

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

Polynomials are mathematical expressions that only use addition, subtraction, multiplication, and non-negative exponentiation of the variables, along with coefficients (constants that multiply with the variables), coefficients, and constants.

Some of the elements of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides.

Let the polynomial equations be represented by the following letters: A, B, C, D, E, and F.

In the equation, we can solve for other values to obtain:

Moreover, a polynomial equation is not an algebraic equation that has a negative exponent or an exponent that is fractional. Thus, negative exponent expressions are not polynomials.

A = x^ (1/4) - ∛x + 4√x - 8x + 16

This polynomial exists.

B = 3x² - 5x⁴ + 2x - 12

This polynomial exists.

C = x³ - 7x² + 9x - 5x⁴ - 20

This polynomial exists.

D = x⁵ - 5x⁴ + 4x³ - 3x² + 2x - 1

It is a polynomial.

E = 4/x⁴ + 3/x³ - 2/x² - 1

It is not a polynomial.

F = x⁻⁵ - 5x⁻⁴ + 4x⁻³ - 3x⁻² + 2x⁻¹ - 1

A polynomial is not what it is.

The polynomials are thus resolved.

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