Question

The pressure in a vessel is increased by \(12 \%\) to \(130 \mathrm{~N} \mathrm{~m}^{-2}\). Calculate the original pressure.

Short answer

Answer: The original pressure in the vessel was approximately 116.07 N/m².

Step-by-step solution

Set up the equation

Let x be the original pressure. After increasing the pressure by 12%, the final pressure is 130 N/m². We can write this as: x + 0.12x = 130

Combine the terms

Combine the terms with x: 1x + 0.12x = 1.12x So, the equation becomes: 1.12x = 130

Solve the equation

To solve for x, divide both sides of the equation by 1.12: x = \frac{130}{1.12}

Calculate the value of x

Perform the division to find the value of x: x \approx 116.07

State the final answer

The original pressure in the vessel was approximately 116.07 N/m².

Key concepts

Understanding Percentage Increase

When we talk about percentage increase, it refers to how much a value has grown in relation to its original amount. In this problem, we are dealing with the pressure inside a vessel that has increased by 12%. This means the new pressure is 112% of the original pressure. If we consider the original pressure to be 100%, then adding 12% more results in the total pressure rising to 112% of its initial value.

• To calculate a percentage increase, you multiply the original value by (1 plus the percentage increase expressed as a decimal).
• In this example, if the original pressure is denoted as \( x \), a 12% increase can be written as \( x + 0.12x \) which simplifies to \( 1.12x \).
• This equation captures how the original pressure transforms to the increased pressure level.

Grasping this concept is crucial because many real-life applications require calculating percentage changes, from science experiments to financial assessments.

Pressure Calculation Made Simple

Calculating pressure is important in a variety of scientific and engineering contexts. Pressure is generally defined as the force exerted per unit area and is measured in units like newtons per square meter (N/m²), also known as Pascals.
In this problem, instead of calculating the force or area independently, we are examining how pressure changes over time with a given percentage increase.

• Understanding the way pressure transforms helps predict how it affects its surrounding environment, in this case within a vessel.
• The question presents the final pressure as 130 N/m², after the pressure itself has gone through an increase.
• To determine the original value, the change is expressed as an equation accounting for the pressure increase.

Knowing how to handle these fundamental problems is valuable for anyone studying physics, chemistry, or engineering.

Solving Equations to Find Unknowns

In mathematics, solving equations is a critical skill for finding unknown values. The exercise at hand required solving the equation \( 1.12x = 130 \) to determine the original pressure inside a vessel before a 12% increase occurred.

• The purpose of solving the equation is to isolate the unknown variable \( x \).
• This process usually involves combining like terms, moving variables across the equation, and performing arithmetic operations until the unknown is isolated.
• In this exercise, dividing both sides by 1.12 allows for the solution of \( x \), providing the original pressure value.
• Remember to perform any division or multiplication carefully to maintain precision in your final answer.

Equation solving is an essential tool not only in algebra but across disciplines like physics and engineering, where it is used to model and solve real-world problems.