Question

HELPPPP PLSSSS

6.7.4 - Rational Expressions and Functions Unit Portfolio

You need to do all three tasks in order to get all of the points. Use this document with the directions so you can make sure you understand and answer all of the questions.


Task 1:
Use something like a cereal box. To find the surface area you will find the area for all 6 sides. SA = 2lw + 2wh + 2lh. Using this formula will give you the surface area of each of the sides, including the top and bottom.
Then find the volume by multiplying the length x width x height.
Remember that a ratio is like a fraction -- it's just a comparison between two numbers. Like a fraction, it should always be reduced. For example, if we have a fraction of 4/6,that can be written as a ratio as 4:6. But since 4 and 6 share a factor of 2, this ratio should be reduced by a factor of 2, which would make it 2:3 (read as "2 to 3").
A ratio of 200:100 means that the surface area is about 2 times larger than the volume of the package.]

Task 2:
See Problem 3 on p. 681 of the online textbook for a similar example that will be helpful in figuring this one out. Please make sure that you answer each of the questions.

Task 3:
Remember that inverse variation is any equation in the form xy = k. What that means is that the product of two variables, x and y, is always constant, meaning always the same. Use that idea to complete this task. In other words, x can be your number of people you invite and y can be the cost for each person. If you have a lower cost, does that increase or decrease the number of people you can invite?

Answer 1

To find the surface area and volume of a cereal box, use SA = 2lw + 2wh + 2lh for surface area and l x w x h for volume. Ratios like 200:100 should be simplified to 2:1. Inverse variation is represented by the equation xy = k, indicating that the product of two variables remains constant.

Understanding Surface Area, Volume, Ratios, and Inverse Variations

To calculate the surface area of a cereal box, you use the formula SA = 2lw + 2wh + 2lh, where l is length, w is width, and h is height.

This formula accounts for all six sides of the box.

To find the volume, simply multiply the length by the width by the height (l x w x h).

A ratio is a comparison between two numbers and can be reduced to its simplest form.

For instance, a ratio of 200:100 simplifies to 2:1, indicating that the first quantity is twice as large as the second.

In Task 3, you're dealing with inverse variation, described by the equation xy = k.

In this scenario, x could represent the number of people you invite to an event, and y could be the cost per person.

If the cost per person is lower, then you can afford to invite more people, meaning that as y decreases, x increases to maintain the same product k, which is the total cost.