What is the area of the hexagon below?​

The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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The set containing all the colors of the marbles is given as follows:

{blue, yellow, purple, green, pink}.

A set of elements is composed by elements that respect a given characteristic, or are present in an experiment.

In this problem, we need to find the colors present in each marble, which are given as follows:

Then we have to list all these colors in a set, which are opened and closed by the brackets {}.

The color blue appears in both sets, however, it will appear only once in the set of the colors, as the elements are not repeated.

Thus, the set containing all the colors of the marbles is given by the set presented as follows:

{blue, yellow, purple, green, pink}.

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Answer:

15/ 16  

Step-by-step explanation: 3/2 x 5/8=  15/16

you flip 2/3 to 3/2 and multiply it

The integral is ln|x + cos(x)| + C, where C represents the constant of integration.

To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:

First, let's rewrite the integral in a slightly different form to simplify the process:

∫(1/(x + cos(x))) dx

We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).

Rearranging this equation, we get dx = du/(1 - sin(x)).

Substituting these values, the integral becomes:

∫(1/(u(1 - sin(x)))) du

Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:

∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C

Replacing u with its original expression, we have:

ln|x + cos(x)| + C

Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.

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Answer:

11

Step-by-step explanation:

we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7

The value of the double integration is 7776 after solving and integration. the answer is 7776.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

It is given that:

Double integration (x + y) dA

y = x²

y² = 216x

y = √216 √x

∫∫(√216 √x +  x²)

After solving:

\(\rm \int _0^{36}\int _0^6\:\left(\sqrt{216}\:\sqrt{x}\:+\:\:x²\right)dxdy\)

=7776

Thus, the value of the double integration is 7776 after solving and integration. the answer is 7776.

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Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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Answer:

Step-by-step explanation:

Next time please include the answer choices.

128x^5*y^8 is equivalent to (2^7)*x^5*y^8

The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

From the question, we have the following parameters that can be used in our computation:

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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To calculate the total surface area of a triangular prism, we need to find the area of each face and add them up.

The triangular faces have base 5cm and height 12cm, so each one has an area of:

(1/2) x 5cm x 12cm = 30cm²

There are two of these faces, so their combined area is:

2 x 30cm² = 60cm²

The rectangular faces have dimensions 5cm x 10cm and 5cm x 13cm, so their areas are:

5cm x 10cm = 50cm²

5cm x 13cm = 65cm²

Again, there are two of these faces, so their combined area is:

2 x (50cm² + 65cm²) = 230cm²

Finally, we add up the areas of all the faces to get the total surface area:

60cm² + 230cm² = 290cm²

Therefore, the total surface area of this triangular prism is 290cm².

The argument of the complex number z = 1 - i is approximately -0.785 radians.

What is the argument in complex numbers?

In complex numbers, the argument (also called the amplitude or angle) of a complex number is the angle that the complex number makes with the positive x-axis in the complex plane. It is usually expressed in radians and is denoted by arg(z).

Given a complex number z = 1 - i, the argument of z can be found using the inverse tangent function (atan). In this case, we want to find the angle θ such that tan(θ) = (imaginary part of z) / (real part of z):

θ = atan((-1) / 1) = -π/4 radians

Hence, the argument of the complex number z = 1 - i is approximately -0.785 radians.

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Answer:

BO 25556

Step-by-step explanation:

the 2875x0.80

1ft 2.092÷ answer then Times by original =

25556

Answer:

1/2

Step-by-step explanation:

Answer:

x = - \(\frac{3}{4}\) , x = 1

Step-by-step explanation:

4x² = x + 3 ← subtract x + 3 from both sides

4x² - x - 3 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 3 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

4x² - 4x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )

4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(4x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

4x + 3 = 0 ( subtract 3 from each side )

4x = - 3 ( divide both sides by 4 )

x = - \(\frac{3}{4}\)

x - 1 = 0 ( add 1 to both sides )

x = 1

solutions are x = - \(\frac{3}{4}\) , x = 1

Expressiοn which  is equivalent tο the area οf square A, in square centimeters is squared 24 squared + 45 squared

A square centimetre (cm²) is a unit οf measurement οf area. 1 square centimeter is equal tο the area οf a square with sides that measure 1 centimeter.

A square area is a measurement made up οf twο lengths. Square units οf area, such as square centimeters, are a result οf multiplying twο lengths. In the case οf square centimeters, each length is measured in centimeters, sο multiplying centimeters × centimeters results in cm². The measured area dοes nοt need tο be in the shape οf a square; any area can be calculated, οr estimated, as the area made up by sοme number οf unit squares.

Fοr example, a 4 cm × 2 cm rectangle is made up οf 8 squares with an area οf 1 cm² each. The rectangle therefοre has an area οf 8 cm²:

Given the fοllοwing :

Small square = 24cm

Medium square = 45cm

Large square =?

Frοm the diagram attached;

Since the three squares fοrms a right-angle triangle, with the leg οf the large square fοrming the hypοtenus.

Thus, the expressiοn tο calculate the area can thus be :

Hypοtenus² = οppοsite² + adjacent²

A² = 24² + 45²

Recall that the area οf a square is the square οf any οf it's side, since the sides οf a square are are equal, that is A²

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Cοmplete Questiοn:

Which expressiοn is equivalent tο the area οf square A, in square centimeters? 3 squares are pοsitiοned tο fοrm a triangle. The small square is labeled 24 centimeters, medium square is 45 centimeters, and large square is nοt labeled. One-half (24) (45) 24 (45) (24 + 45) squared 24 squared + 45 squared

Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

The length of the new room is 4 inches.

The formula for volume of a cube is given by;

V = l³

where;

V is volume

l is side length of cube

Now, we are given;

Volume of cube = 64 in³

Thus;

l³ = 64

l = ∛64

l = 4 inches

Thus, we conclude that the length of the new room is 4 inches.

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Answer:

The common ratio is 2.

Step-by-step explanation:

If a given set of elements represents a geometric, each pair of elements must the one and same ratio. That is:

\(\frac{n_{i+1}}{n_{i}} = r, \forall\,i\in \mathbb{N}\), \(n_{i}, n_{i+1}\in N\)

Where:

\(n_{i}\) - i-th element of the given set.

\(N\) - Set of elements.

If we know that \(n_{1} = 0.45\), \(n_{2} = 0.9\) and \(n_{3} = 1.8\), then common ration is:

\(\frac{n_{2}}{n_{1}} = \frac{n_{3}}{n_{2}} = 2\)

The common ratio is 2.

a) The value of k is 5.54 × 10⁻¹⁰ and the equation of the decay is N(t) = N0 * eⁿˣ.

b) It will take 1,578,843,530 years to decay to only 15 milligrams of Potassium-40.

The decay constant is the likelihood of a radioactive nucleus decaying per unit of time. It is a key characteristic of radioactive material that governs the rate of decay. The rate of material degradation increases with the value of the decay constant.

a) The decay constant is a constant value that is independent of the sample's size or age for a specific sample of radioactive material.

Given that, Potassium-40 follows an exponential decay model.

Thus,  

t(1/2) = ln(2)/k

where t(1/2) is the half-life.

Substituting the given half-life, we get:

1.25 × 10⁹ = ln(2)/k

k = ln(2)/(1.25 × 10^9) ≈ 5.54 × 10⁻¹⁰ per year

The decay equation for Potassium-40 as:

N(t) = N0 * eⁿˣ

Hence, the value of k is 5.54 × 10⁻¹⁰ and the equation of the decay is N(t) = N0 * eⁿˣ.

b) Tο find οut hοw lοng will it take the specimen tο decay tο οnly 15 milligrams οf Pοtassium-40, we have tο substitute a = 36, f(x) = 15 and  k = 5.545  ×10⁻¹⁰:

\($\begin{array}{l}{{15=36e^{-5.545\times10^{-10}t}}}\\ {{{\dfrac{15}{36}}=e^{-5.545\times10^{-10}t}}}\end{array}$\)

\($\ln{\frac{15}{36}}=-5.545\times10^{-10t}$\)

\($t={\frac{\ln15-\ln36}{-5.5285\times10^{-10}}}$\)

= 1,578,843,530

Thus, It will take 1,578,843,530 years to decay to only 15 milligrams of Potassium-40.

c) Tο find οut hοw many milligrams οf Pοtassium-40 will be left after 300 milliοn years, we have tο substitute a = 36,  t = 300,000,000 and  k = 5.545 × 10⁻¹⁰:

\($\begin{array}{l}{{f(x)=36e^{-5.545\times10^{-10}(300,000,000)}}}\\ {{=36e^{-0.16635}}}\\ {{\approx30.48}}\end{array}$\)

Abοut 30.48 grams οf Pοtassium-40, will be left after 300 milliοn years.

d) Tο find οut hοw lοng will it take Pοtassium-40 tο decay tο οne eight οf its οriginal amοunt, we have tο substitute a = 36, f(x) = 36/8 and k = 5.545 × 10⁻¹⁰:

\(${\frac{36}{8}}=36e^{-5.545\times10^{-10}t}$\)

\(${\frac{1}{8}}=e^{-5.545\times10^{-10}t}$\)

\($\ln{\frac{1}{8}}=-5.545\times10^{-10}t$\)

\($ \rm t={\frac{\ln1-\ln8}{-5.545\times10^{-10}}}$\)

= 3,750,120,003

It will take 3,750,120,003 years for a Potassium-40 to decay to one-eighth of its original amount.

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9514 1404 393

Answer:

  a. -18

  b. 87

  c. -10

  d. 26

Step-by-step explanation:

For evaluating functions with different arguments, I find a calculator to be helpful.

__

If you want to do this by hand, put the argument value where the variable is and do the arithmetic. It is helpful to know that

   \((f\circ g)(x)=f(g(x))\)

__

For example, ...

a. f(g(0)) = f(-3(0) -4) = f(-4) = 5(-4) +2 = -18

The value of line RS is 23

From the diagram shown, we have that line PS, line PQ, line QR and line RS form a square.

Note that the sides of a square are equal to each other.

The relationship is represented as;

Line PS = Line PQ = Line QR = Line RS

We have that;

Substitute the expressions

6x - 5 = 9x - 4

Now, collect like terms

6x - 9x = - 4 - 5

Subtract the like terms

-3x = -9

Make 'x' the subject of formula

-3x/-3 = -9/-3

x = 3

Then, RS = 9x - 4 = 9(3) - 4 = 27 - 2 = 23

Hence, the value is 23

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The exponential function that could be represented by the graph is given as follows:

\(y = 10^x\)

An exponential function has the definition presented as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The graph crosses the y-axis at y = 1, hence the parameter a is given as follows:

a = 1.

When x is increased by one, y is multiplied by 10, as we have that when x = 1, y = 5 and when x = 2, y = 50, hence the parameter b is given as follows:

b = 10.

Hence the function is given as follows:

\(y = 10^x\)

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The maximum and minimum points of the function are (a) (3π/2, -1) (-π/2, -1), (π/2, 3)

From the question, we have the following function that can be used in our computation:

y = –2 cos (x + π/2) + 1.

Calculating the maximum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the maximum points to be (π/2, 3)

Calculating the minimum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the minimum points to be

(3π/2, -1) (-π/2, -1)

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An example of a boundary value problem is the Sturm-Liouville problem, which entails determining the eigenvalues and eigenfunctions of a differential equation that complies with specific boundary requirements.

The general formula for the Sturm-Liouville problem's solution in x is y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the differential equation's eigenfunctions. When the differential equation and boundary conditions are solved, the eigenvalues and eigenfunctions are discovered.

For instance, if the differential equation has the following form: -y" + q(x)y = lambda* w(x)y where y is the dependent variable, y" is the second derivative of y, q(x) and w(x) are functions of x, and lambda is the eigenvalue, the boundary conditions can be of the following

form: where L is the length of the interval on which the differential equation is defined, y(0) = 0, and y(L) = 0.

The general solution in x can be expressed in the form: y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the eigenfunctions of the differential equation. The eigenvalues and eigenfunctions can be discovered by solving this differential equation and the boundary conditions.

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A fraction 3/4 is called greater than 3/4 if,

Numerator > denominator,

Otherwise it is less than 3/4 ,

\(\frac{1}{3} \times \frac{3}{4}=\frac{1}{4}\)

\($$\begin{aligned}&\frac{5}{2} \times \frac{3}{4}=\frac{15}{8} \\&\because 8 < 15 \\&\Longrightarrow \frac{5}{2}\times \frac{3}{4} < 3/4 \\&\frac{7}{7} \times \frac{3}{4}=\frac{3}{4} \\&\because 3 < 4 \\&\Longrightarrow \frac{3}{4} \times \frac{3}{4} = 1 \\& \frac{9}{7} \times \frac{3}{4}=\frac{27}{28} \\&\because 28 > 27 \\&\Longrightarrow \frac{5}{5} \times \frac{3}{4} > \frac{3}{4} \end{aligned}$$\)

A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fraction," which meaning "to break," is the source of the English term "fraction." The distribution of food and supplies as well as the lack of a metal currency were among the mathematical issues that the Egyptians utilized fractions to solve because they were the first civilization to understand fractions.

Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions were first written in India with one number above the other, but without a line. The line used to divide the numerator and the denominator was only added by Arabs.

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Answer: Around 1.33 Cups per batch

Step-by-step explanation:

4 / 3 ≈ 1.33

Answer:

1 1/3

Step-by-step explanation:

Math

The following rigid transformations are done on each figure:

We find two pictures, each with one case of rigid transformation done on a polygon. Rigid transformations are transformations done on geometric loci such that Euclidean distance at every point of the loci are conserved.

If we consider that the Euclidean distance is the radial distance with respect to the origin of the Cartesian plane, then we find the rigid transformation corresponding to each case:

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Therefore, after answering the given query, we can state that The issues with the graph shown are as follows, according to the information provided: The vertical axis does not have a 0 value.

Graphs are used by mathematicians to rationally represent or chart facts or values. Often, a graph tip will show a connection between objects in an image. A graph is a type of non-linear data structure that is made up of nodes, or polygons, and edges. affix the nodes, also referred as as vertices. This graph includes endpoints E=1, 2, 1, 3, 2, 4, and (2.5) and vertices V=1, 2, 3, 5. (3.5). (4.5). graphs of exponential growth in the form of data charts (bar plots, data tables, line charts, etc.). an equilateral triangle-shaped logarithmic graph.

The issues with the graph shown are as follows, according to the information provided:

The vertical axis does not have a 0 value.

The time frame must be mentioned.

Too much vertical axis space is allowed.

Hence, the appropriate choices are:

The vertical axis does not have a 0 value.

The time frame must be mentioned.

Too much vertical axis space is allowed.

The information given makes it unclear whether or not the fourth alternative is viable.

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Answer:

who will answer??

Step-by-step explanation:

It will take Aaron 1.38 hours to travel 18 miles downstream as per time distance calculation.

"To work out speed, divide the distance of the journey by the time it took to travel, so speed = distance divided by time. To calculate time, divide distance by speed. To get the distance, multiply speed by time.

You may see these equations simplified as s=d/t, where s is speed, d is distance, and t is time."

Given, speed of Aaron's boat is 9 miles per hour.

Speed of the river is 4 miles per hour.

Therefore, speed of Aaron's boat downstream is

= (9 + 4) miles per hour = 13 miles per hour.

Therefore, in order to travel 18 miles downstream Aaron will need

= \(\frac{18}{13}\) hours = 1.38 hours.

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Answer: 14 dollar discount

Step-by-step explanation: