Part 1: What is the formula for the volume of a rectangular solid? Find an object in your residence that has the shape of a rectangular solid. Measure and record the length, width, and height of your object in either centimeters (to the nearest 10th of a centimeter) or inches (to the nearest quarter of an inch). Compute the volume of your solid and include units with your answer. Include the type of object, the measurements, and show how you obtained the volume.
Part 2: Using the Library, web resources, and/or other materials, find a real-life application of a linear function. State the application, give the equation of the linear function, and state what the x and y in the application represent. Choose at least two values of x to input into your function and find the corresponding y for each. State, in words, what each x and y means in terms of your real-life application. Please see the following example. Do not use any version of this example in your own post. You may use other variables besides x and y, such as x and W depicted in the following example. Be sure to reference all sources using APA style.
The average lifespan of American women has been tracked, and the linear model for the data is A = 0.2t + 73, where t = 0 corresponds to 1960. This implies that in 1980, t = 20, women lived an average of 77 years. A = 0.2(20) + 73 = 77. In addition, in 2000, t = 40, women lived an average of 81 years. A = 0.2(40) + 73 = 81.
Part 1: The formula for the volume of a rectangular solid is given by V = lwh, where l is the length, w is the width, and h is the height of the solid. To find an object in your residence that has the shape of a rectangular solid, look for an object that has three pairs of parallel faces and right angles between the faces (e.g., a box, a book, a smartphone).
Once you have selected an object, measure and record the length, width, and height of the object in either centimeters (to the nearest 10th of a centimeter) or inches (to the nearest quarter of an inch). For example, let's say you have a box as your object with the following measurements:
Length = 15 cm
Width = 10 cm
Height = 8 cm
To compute the volume of your solid, substitute the measurements into the volume formula: V = lwh. Using the measurements from the example:
V = 15 cm * 10 cm * 8 cm = 1200 cm³
Therefore, the volume of the rectangular solid is 1200 cubic centimeters (cm³).
Part 2: A real-life application of a linear function is predicting the cost of gasoline based on the number of gallons purchased. Let's assume that the cost per gallon remains constant. In this case, the linear function can be expressed as C = mx + b, where C is the total cost, x represents the number of gallons, m is the constant cost per gallon, and b is any fixed costs.
Let's say the cost of gasoline is $2.50 per gallon and there are no additional fixed costs. The linear function for this application would be C = 2.50x.
To find corresponding values of C for different values of x, we can substitute different values into the equation. Let's choose two values:
For x = 5 gallons: C = 2.50 * 5 = $12.50
For x = 10 gallons: C = 2.50 * 10 = $25.00
In this case, x represents the number of gallons of gasoline purchased, and y (or C) represents the total cost in dollars. So, if you purchase 5 gallons of gasoline, the corresponding cost would be $12.50. Similarly, if you purchase 10 gallons, the cost would be $25.00.
Please note that the example provided above is hypothetical, and real-world gasoline prices may vary. Additionally, appropriate APA-style references should be provided when using information from external sources.