# 97.9747 = sinh (6.2737x10^9) How did they solve this?

• j2dabizo
In summary, the conversation is discussing an equation involving the hyperbolic sine function and how the value of 5.2779 was obtained from the given expression. One person suggests using the inverse hyperbolic sine function, while another realizes their mistake and provides the correct solution.
j2dabizo
97.9747 = sinh (6.2737x10^9) How did they solve this??

## Homework Statement

Just an equation that I don't understand how they calculated.

97.9747 = sinh(6.2737x109)...
6.2737x109 = 5.2779

how did they get the 5.2779 ??

## The Attempt at a Solution

Can't you just take arcsinh?

That's not even close to correct. What context is this being brought up and are you sure you read it correctly or is not a typo?

j2dabizo said:

## Homework Statement

Just an equation that I don't understand how they calculated.

97.9747 = sinh(6.2737x109)...
6.2737x109 = 5.2779

how did they get the 5.2779 ??

## The Attempt at a Solution

nevermind..had a brain fart ...just sinh-1(97.9747)

As a scientist, it is important to understand the methods and processes used to solve equations. In this case, the equation in question is a hyperbolic sine function, which can be solved using a calculator or a computer program.

To solve this equation, the first step is to isolate the variable (x) by taking the inverse hyperbolic sine (sinh^-1) of both sides:

sinh^-1(97.9747) = sinh^-1(sinh(6.2737x10^9))

Next, we can use the property of inverse functions to simplify the equation:

97.9747 = 6.2737x10^9

Finally, we can solve for x by dividing both sides by 6.2737x10^9:

x = 97.9747 / 6.2737x10^9

By using a calculator or computer program to solve this equation, we can get the result of x = 5.2779. Therefore, the 5.2779 was obtained by solving the equation using mathematical principles and tools.

## 1. What is the significance of the numbers in this equation?

The numbers in this equation represent a mathematical relationship between two values: 97.9747 and 6.2737x10^9. The equation is solved by using the mathematical operation of hyperbolic sine (sinh).

## 2. How is this equation solved?

The equation is solved by plugging in the value of 6.2737x10^9 into the sinh function. This function is then evaluated using a mathematical algorithm to calculate the result of 97.9747.

## 3. What is the purpose of using scientific notation in this equation?

Scientific notation, represented by the "x10^" format, is used to express very large or very small numbers in a more compact form. In this equation, it is used to represent the value of 6.2737x10^9, which is a very large number, in a more manageable way.

## 4. What is the relationship between the numbers in this equation?

The numbers in this equation are related by the mathematical operation of hyperbolic sine. This operation takes the value of 6.2737x10^9 and calculates its sinh value, which is then equal to 97.9747.

## 5. What is the practical application of this equation?

This equation may have various practical applications, depending on the context in which it is used. However, in general, it represents a mathematical relationship that can be used to solve problems related to hyperbolic sine and its inverse function.

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