what is arc length calculus formula?

The big idea in math are abstraction and infinity.

Mathematics is a vast and fascinating subject that involves exploring the concepts of numbers, shapes, patterns, and more. Within this subject, there are several big ideas that serve as the foundation for various mathematical theories and principles. One of the most prominent big ideas in math is that of abstraction.

Abstraction is a concept that allows mathematicians to generalize ideas and create models that can be applied to a wide range of situations. It involves taking a complex problem and breaking it down into smaller, more manageable components that can be easily analyzed and understood. This process often involves using symbols and equations to represent real-world situations and finding patterns and relationships between them.

Another big idea in math is that of infinity. This idea involves exploring the concept of endlessness and how it applies to different mathematical concepts. Infinity plays a critical role in calculus, where it is used to describe the behavior of functions as they approach limits and infinity.

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Answer: look at the image for the answer and the explanation

Step-by-step explanation:

Answer: 16 degrees

Step-by-step explanation:

Answer:

2 feet.

Step-by-step explanation:

Since the volume of cube A is 64, we can divide the edge (4) by two because cube B can only hold half as much liquid.

Thus, the edge of cube b is 2 feet.

Hope it helped!

The converted values of the volume fluid ounce to gallons is given by :

128 oz  = 1 gallons.

Relation to convert fluid ounce to gallons in standard form is given by :

1 fluid ounce = 0.0078125 gallons

Now multiply both the side by 128 to get the required relation ,

⇒ ( 128 × 1 ) fluid ounce = ( 128 × 0.0078125 ) gallons

⇒ 128 fluid ounce = 1 gallons

Therefore, using the standard relation of fluid ounce to gallons the value of 128 oz is equal to 1 gallons .

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Answer:44.5

Step-by-step explanation:

To solve this problem, we can use the tangent function, which relates the angle of elevation to the length of the opposite side (the shadow) and the adjacent side (the height of the building).Let x be the length of the shadow.

Then, we have:tan(59°) = 52/xTo solve for x, we can cross-multiply and simplify:x = 52 / tan(59°)

x ≈ 44.5 feet (rounded to the nearest tenth)Therefore, the length of the shadow cast by the building is approximately 44.5 feet.

This is a linear equation with a slope of 2 and a y-intercept of -2. There is exactly one solution for y for every value of x.

In mathematics, an equation is a statement that two expressions are equal. It usually contains one or more variables, which are unknown quantities that can take on different values. Equations are used to represent relationships between quantities, and they can be used to solve problems by finding the values of the variables that make the equation true.

An equation typically consists of two sides, separated by an equal sign. Each side can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. For example, the equation:

2x + 3 = 7

contains the variable x, as well as constants 2, 3, and 7, and mathematical operations of addition and multiplication.

Equations can be solved by applying algebraic techniques to isolate the variable on one side of the equation. For example, to solve the above equation for x, we can first subtract 3 from both sides to get:

2x = 4

Then, we can divide both sides by 2 to get:

x = 2

This is the solution to the equation, which means that x must be equal to 2 in order to make the equation true.

Equations are used in many areas of mathematics, including algebra, calculus, geometry, and trigonometry. They are also used in physics, engineering, and other sciences to model physical phenomena and solve problems related to them.

To solve for y, we need to isolate y on one side of the equation.

y + 2 = 2x

Subtract 2 from both sides:

y + 2 - 2 = 2x - 2

Simplify:

y = 2x - 2

Therefore, the solution for y is y = 2x - 2.

This is a linear equation with a slope of 2 and a y-intercept of -2. There is exactly one solution for y for every value of x.

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Population growth is usually an exponential equation. By forming and solving an exponential equation the population in 2009 will be 11,373,300.08

The exponential equation for population growth is,

P = P₀ ( 1+r)ⁿ

P₀ is the initial population, r is the rate and n is the time.

Here r = 1.5% = 1.5/100 = 0.015

n is 10 years and P₀ is 9800000

Substituting the values in equation,

P = 9800000 ( 1+0.015)¹⁰

     = 9800000 × 1.160 = 11,373,300.08

So with the growth rate of 1.5% over 10 years, the population will grow and reach 11,373,300.08.

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Answer: 57.153 kilograms

Step-by-step explanation:

126 lbs is equal to 57.15 kg.

To convert pounds (lbs) to kilograms (kg).

you can use the conversion factor of 1 lb = 0.453592 kg.

To convert 126 lbs to kg:

multiply the weight in pounds by the conversion factor:

126 lbs×0.453592 kg/lb

= 57.152712 kg

Therefore, 126 lbs is equal to approximately 57.15 kg.

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The area of the triangle is 120 square centimeters.

A = 120 cm².

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

The area of the triangle = 1/2 x base x height.

Given:

The height h of the triangle is 8cm greater than its corresponding base.

That means

the height = 20 + 8 = 20 cm.

The area of the triangle,

= 1/2 x base x height

= 1/2 x 12 x 20

= 120 square centimeters.

Therefore, the area is 120 square centimeters.

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Answer:

5, 10 20, etc.

Step-by-step explanation:

You can skip count like you do in multiplying.

The vertex form of the quadratic equation is:

h(t) = -42*(x - 3)² + 378

And the maximum height is 378 ft.

We know that the height of the projectile is defined by the quadratic equation:

h(t) = -42t² + 252t

Remember that for any quadratic equation:

y = a*x² + b*x + c

The vertex is at:

x = -b/2a

So in this case, the vertex is at:

t = -252/(2*-42)

t = 3

So the maximum height of the projectile is:

h(3) = -42*3² + 252*3 = 378

And thus, the vertex is (3, 378), then the vertex form is:

h(t) = -42*(x - 3)² + 378

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The value of the average normal distribution with a 95% degree of confidence is Z 1.96 as 95% of the area under the standard normal distribution curve should fall between -Z and Z, hence Z should be selected to reflect this.

In statistics, the standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1. The region beneath the curve between any two values represents the chance of seeing a value inside a given range.

At a 95% confidence level, the value of Z should be chosen so that 95% of the area under the standard normal distribution curve is between -Z and Z. Using a calculator or a generic table of the normal distribution, we may determine Z = 1.96 with a 95% confidence interval. In 95% of the situations, the values of the classic normal distribution lie between +/- 1.96 standard deviations from the mean.

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Answer: 20.8

Step-by-step explanation: .

Around 98.4 feet are equal to 30 metres.

The common formula 1 metre (m) = 3.28 feet (ft) will be used to convert measurements from metres to feet. Here, the conversion value is 3.28. To convert 10 metres to feet, for instance, multiply 10 by 3.28, which is 32.8 ft. Therefore, 10 meters = 32.8 feet.

Converting from metres to feet: 3.28084 metres are nearly equal to one metre. Add 3.28084 feet to the given metre value to convert it to feet. Add 3.28084 feet to the given metre value to convert it to feet. For instance, the conversion of 5 metres to feet is as follows: We are aware that the conversion factor for 5 metres to feet is 3.28084.

30 m * 3.280839895 ft/m =98.4251968504 ft

So, 30 metres is roughly equivalent to 98.4 ft.

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Answer:

2*4*3

Step-by-step explanation:

The number of blocks is the same as the volume. So start with the formula for the volume of a rectangular prism, that being length*width*height. Then use the picture to count out that the length is 4 blocks, width is 2 blocks and height is 3 blocks. Then we can plug these values into our equation and get the answer: 2*4*3

Cody's profit from selling 9 scarves at $25 each, after spending $34 on materials and paying a $10 fee to sell at the craft fair, was $181.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

To calculate Cody's profit using the expression np - (m + 10), we need to substitute the given values:

n = 9 (number of scarves sold)

p = $25 (price per scarf)

m = $34 (amount spent on materials)

Using these values, we can calculate Cody's profit as:

= np - (m + 10)

= (9 * 25) - (34 + 10)

= 225 - 44

= $181

Therefore, Cody's profit from selling 9 scarves at $25 each and spending $34 on materials is $181.

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(a) The expected profit of this policy to the insurance company is $520.10.

(b) The interpretation value of expected profit in (a) in the context of the problem is small probability of the policyholder's death.

(a) The expected profit to the insurance company can be calculated as follows:

Expected Profit = (Probability of Survival * Premium) - (Probability of Death * Death Benefit)

Probability of Survival = 0.997

Probability of Death = 1 - Probability of Survival = 1 - 0.997 = 0.003

Premium = $780

Death Benefit = $250,000

Expected Profit = (0.997 * $780) - (0.003 * $250,000) = $520.10

Therefore, the expected profit to the insurance company from selling this policy is $520.10.

(b) The expected profit of $520.10 represents the average profit that the insurance company can expect to earn from selling this type of policy to similar customers over time.

In the context of this problem, it means that if the insurance company sells many policies like this one, they can expect to make a profit of about $520.10 per policy, on average, after accounting for the small probability of the policyholder's death.

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Answer:

Below

Step-by-step explanation:

21 is to 27    as x-3   is to    x-1

21/27 =  x-3/x-1    cross multipliy , solve for x = 10

Answer:

Step-by-step explanation:

x-3/21 = x-1/27

27(x-3) = 21(x-1)

27x-81 = 21x-21

27x-21x = -21+8

6x = 60

x = 60/6

x = 10

_____________________

Hope this helps! :)

The value of the markup is $12

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

Original $10.00 percent of markup: 20%​

The markup price is calculated as

Markup Price = Original; * (1 + Markup)

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

Markup Price = 10 * (1 + 20%)

Evaluate

Markup Price = 12

Hence, the price is $12

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The numbers between 20 and 30 are: 21,22,23,24,25,26,27,28,29 Even numbers, other than 2 are not prime because by definition of being even they are divisible by 2.

Prime numbers are numbers that can only be divisible by themselves or 1. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. In this tutorial, you will learn how to check if a number is a prime number. We will discuss how to write a prime number program in python – this program prints numbers that are prime numbers within a given range.

There is just one perfect number between 20 and 30. The number 28 is a perfect number. Its factors are 1, 2, 4. 7, 14, and 28. Why is 2 the only prime number? Two is a prime because it is divisible by only two and one. All the other even numbers are not prime because they are all divisible by two. That leaves only the odd numbers.

Hence, The numbers between 20 and 30 are: 21,22,23,24,25,26,27,28,29 Even numbers, other than 2 are not prime because by definition of being even they are divisible by 2.

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Amanda's answer correct is not correct. The correct answer is 4 R2, because she might have incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead

Amanda's answer, 3 R10, is not correct.

When we divide 34 by 8, we want to know how many times 8 goes into 34, and what is left over. We start by dividing 8 into the first digit of 34, which is 3. 8 cannot go into 3, so we move on to the next digit, which is 34.

We can see that 8 goes into 34 four times, because 8 x 4 = 32. This means that the whole number part of the answer is 4.

But there is still a remainder left over. To find the remainder, we subtract 32 from 34, which gives us 2.

Therefore, the correct answer is 4 R2.

Amanda's mistake may have been to incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead.

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The quotient of 25 divided by 25,704 is approximately 0.00097 (rounded to five decimal places).

When splitting huge numbers, the task is divided into several sequential steps using the long division approach. The dividend is divided by the divisor, just like in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.

The long division for 25 divided by 25,704 is shown below:

code :

0.00097

-------

25704 | 25.00000

      0

      --

     250

     257

     ---

      -7

As a result, the result of 25 divided by 25,704 is almost 0.00097. (rounded to five decimal places).

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Answer:36

Step-by-step explanation:360 * 0.1 = 36 or 360/10 = 36

The method to convert milimeter to meters will be through multiplication of [tex] {10}^{-3} [/tex] with the quantity in milimeter.

The abbreviation mm is representative of milimeters. Now, we know that milimeters is 1/1000 meters and hence is smaller unit in comparison to meters.

Based on the above mentioned fact, we can multiply the same number (smaller unit) with negative exponent. It will be carried out like this -

Quantity in meters = quantity in milimeter ×

[tex] {10}^{-3} [/tex], where [tex] {10}^{-3} [/tex] has negative exponent. Let us say we have 10⁹ milimeters and need to convert in into meters.

So, quantity in meter = 10⁹ × [tex] {10}^{-3} [/tex],

Performing multiplication which will be done through subtraction of powers

Quantity in meters = 10⁶ meters

Hence, mm to meters will be multiplication with [tex] {10}^{-3} [/tex].

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The required proof is inductively and deductively that the sum of six consecutive numbers is divisible by 3 in the solution part.

Deductive reasoning is a method of reasoning in which conclusions are drawn based on premises that are known or assumed to be true.

Let's assume that the six consecutive numbers are n, n+1, n+2, n+3, n+4, and n+5.

We have to show that the sum of these numbers is divisible by 3.

First, we can express the sum of the six numbers as follows:

n + (n+1) + (n+2) + (n+3) + (n+4) + (n+5)

Simplify the expression by combining like terms:

6n + 15

Next, factor out 3 from the expression:

6n + 15 = 3(2n + 5)

Since 2n + 5 is an integer, we can see that 3(2n + 5) is divisible by 3. Therefore, the sum of six consecutive numbers is divisible by 3.

This is an example of deductive reasoning because we started with a premise (the assumption that the six consecutive numbers are n, n+1, n+2, n+3, n+4, and n+5) and used logical steps to arrive at a conclusion (that the sum of the six numbers is divisible by 3).

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The Inverse tangent is defined as the mathematical function that returns the angle whose tangent is a given number and the step to calculate the inverse tangent has been explained

Inverse tangent (also known as arctangent) is a mathematical function that returns the angle whose tangent is a given number. The inverse tangent function is denoted by "tan^-1" or "arctan".

To calculate the inverse tangent of a number, you can follow these steps:

Determine the input value (the number whose inverse tangent you want to find).

Use the inverse tangent function on your calculator.

The output of the inverse tangent function will be in radians. If you want the result in degrees, you can convert it using the formula: degrees = radians * (180/π), where π (pi) is approximately 3.14159

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Steps per mile is a measure of how many steps a person takes to walk one mile, Which is 2000 steps.

It takes over 2,000 steps to walk one mile and 10,000 steps would be almost 5 miles, as the average person has a stride length of approximately 2.1 to 2.5 feet.

The number of steps required to walk a mile can vary from person to person depending on their height, weight and stride length. And Generally, taller people with longer strides take fewer steps per mile, while shorter people with shorter strides take more steps per mile.

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The total surface area is 46.43 square centimeter.

The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.

Given that, the area of the rectangle is 34.56 cm².

Here, the diameter is 2.75 cm, so radius =2.75/2=1.375 cm

Cylinder is made up of 1 rectangle and 2 circles.

Now, area of 2 circles =2πr²

= 2×3.14×1.375²

= 11.87 cm²

So, total surface area = 34.56+11.87

= 46.43 cm²

Therefore, the total surface area is 46.43 square centimeter.

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After 32 weeks, the population of bumble bees will be 6.77315 x 10¹⁴ bees.

The population of bumble bees triples every week, so the common ratio is 3. The starting population is 20 bees.

The formula for a geometric sequence is:

a_n = a_1 * rⁿ⁻¹

where,

a_n = the nth term in the sequence

a_1 = the first term

r = the common ratio

n = the number of terms.

Using this formula, we can find the number of bees after 32 weeks:

a_32 = 20 * 3³²⁻¹

a_32 = 20 * 3³¹

a_32 = 6.773150 × 10¹⁴

Therefore, after 32 weeks, the population of bumble bees will be approximately 6.77315 x 10¹⁴ bees.

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