Solve each problem. Expansion and Contraction of Gases In 1787, Jacques Charles noticed that g

step 1 For number 59, we're given the equation that relates the temperature of a gas, which is this x,

Solve each problem. Expansion and Contraction of Gases In...

Solve each problem. Expansion and Contraction of Gases $\quad$ In $1787,$ Jacques Charles noticed that gases expand when heated and contract when cooled. A particular gas follows the model2$y=\frac{5}{3} x+455$ where $x$ is the temperature in Celsius and $y$ is the volume in cubic centimeters. (a) What is the volume when the temperature is $27^{\circ} \mathrm{C} ?$ (b) What is the temperature when the volume is 605 cubic centimeters? (c) Determine what temperature gives a volume of 0 cubic centimeters.

Solve each problem.
Expansion and Contraction of Gases $\quad$ In $1787,$ Jacques Charles noticed that gases expand when heated and contract when cooled. A particular gas follows the model2$y=\frac{5}{3} x+455$ where $x$ is the temperature in Celsius and $y$ is the volume in cubic centimeters.
(a) What is the volume when the temperature is $27^{\circ} \mathrm{C} ?$
(b) What is the temperature when the volume is 605 cubic centimeters?
(c) Determine what temperature gives a volume of 0 cubic centimeters.

Key Concepts

Linear Equations

Linear equations describe a constant rate of change between two variables, forming a straight line when graphed. This concept is fundamental in mathematics and science for modeling relationships where increases or decreases in one variable result in proportional changes in another.

Slope-Intercept Form

The slope-intercept form, given as y = mx + b, provides a clear description of a linear equation’s behavior. Here, 'm' represents the slope, or the rate at which the dependent variable changes with respect to the independent variable, and 'b' represents the y-intercept, the value of y when x is zero.

Substitution Method

The substitution method involves replacing a variable with a known value to solve for the remaining unknown. This technique is particularly useful when dealing with linear equations, enabling a step-by-step solution by isolating and calculating one variable at a time.

Inverse Operations

Inverse operations are mathematical procedures that undo each other, such as addition and subtraction or multiplication and division. They are employed to isolate variables within an equation, allowing for the systematic solution of linear equations in algebra.

Mathematical Modeling

Mathematical modeling involves creating equations to represent real-world phenomena. By applying linear equations to situations that exhibit steady, proportional changes, one can predict unknown values and analyze behavior, making complex systems more understandable.

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