Setting up an inequality with absolute value

Maybe you should ask your prof if there is a typo in the problem .And the the absolute value aspect is probably involved by this:|+/- x| = ?Maybe you should ask your prof if there is a typo in the problem .In summary, the problem is to find how accurate the sides of a cube must be measured in order for the volume to be within 1% of 216 cm^3. The problem involves absolute value and requires solving for the value of x, the length of each side of the cube, through the equation (6+Δx)^3=216+2.16=218.16 and (6+Δx)^3=216-2.16=213
  • #1
bnosam
148
0

Homework Statement



I need some help setting up this inequality:
How accurate do the sides of a cube have to be measured if the volume of the cube has to be within 1% of 216 cm^3

Not very good with word problems and for some reason this course never deals with them until now? And this is the first practise question in the chapter on absolute functions.

Homework Equations



Not sure, I know it has to contain an absolute value though



The Attempt at a Solution




Any hints would be great
 
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  • #2
bnosam said:

Homework Statement



I need some help setting up this inequality:
How accurate do the sides of a cube have to be measured if the volume of the cube has to be within 1% of 216 cm^3

Not very good with word problems and for some reason this course never deals with them until now? And this is the first practise question in the chapter on absolute functions.

Homework Equations



Not sure, I know it has to contain an absolute value though



The Attempt at a Solution




Any hints would be great

Why do you think it needs to include an absolute value? When they say 1%, they typically mean within +/- 1%.

Please try to start the problem. We cannot offer tutorial help until you show some effort. That is in the Rules link at the top of the page.
 
  • #3
berkeman said:
Why do you think it needs to include an absolute value? When they say 1%, they typically mean within +/- 1%.

Please try to start the problem. We cannot offer tutorial help until you show some effort. That is in the Rules link at the top of the page.

It's part of the practise sheet titled "Absolute value functions" ;) That's what makes me think I need to have it in here.

Well 1% of a 216 is 2.16.

-2.16 < | x | < 2.16

Something like that look fine, I'm not very sure how to set it up at all, that's the best stab at it I could take
 
  • #4
bnosam said:
It's part of the practise sheet titled "Absolute value functions" ;) That's what makes me think I need to have it in here.

Well 1% of a 216 is 2.16.

-2.16 < | x | < 2.16

Something like that look fine, I'm not very sure how to set it up at all, that's the best stab at it I could take

Okay, but it said that is the volume. What tolerance does each side have to have in order for the volume tolerance to be +/- 1%?
 
  • #5
berkeman said:
Okay, but it said that is the volume. What tolerance does each side have to have in order for the volume tolerance to be +/- 1%?

A cube root?

## - \sqrt[3]{2.16} ≤ | x | ≤ \sqrt[3]{2.16} ##

Like that?
 
  • #6
bnosam said:
A cube root?

## - \sqrt[3]{2.16} ≤ | x | ≤ \sqrt[3]{2.16} ##

Like that?
You're taking a shortcut which may or may not be warranted .

Let x be the length of each side of the cube .

If the cube's volume is exactly 216 cm3 , then [itex]\ x=\sqrt[3]{216\,}=6\,\text{cm}/ .[/itex]

So basically you need to solve
[itex](6+\Delta x)^3=216+2.16=218.16[/itex]

and [itex]\ \ (6+\Delta x)^3=216-2.16=213.84\ [/itex]​
for Δx .
 
  • #7
SammyS said:
You're taking a shortcut which may or may not be warranted .

Let x be the length of each side of the cube .

If the cube's volume is exactly 216 cm3 , then [itex]\ x=\sqrt[3]{216\,}=6\,\text{cm}/ .[/itex]

So basically you need to solve
[itex](6+\Delta x)^3=216+2.16=218.16[/itex]

and [itex]\ \ (6+\Delta x)^3=216-2.16=213.84\ [/itex]​
for Δx .

The only real issue I kind of have with this is the fact, this needs to contain absolute value because the beginning of the page even says "Solve the following questions containing absolute value problems"
 
  • #8
bnosam said:
The only real issue I kind of have with this is the fact, this needs to contain absolute value because the beginning of the page even says "Solve the following questions containing absolute value problems"

And the the absolute valueaspect is probably involved by this:

|+/- x| = ?
 

Related to Setting up an inequality with absolute value

1. What is an inequality with absolute value?

An inequality with absolute value is a mathematical expression that contains an absolute value sign. Absolute value is the distance of a number from zero on the number line. When solving an inequality with absolute value, there will be two possible solutions.

2. How do I set up an inequality with absolute value?

To set up an inequality with absolute value, first identify which variable needs to be isolated. Then, write two separate inequalities without the absolute value sign, one with the variable greater than or equal to zero and one with the variable less than or equal to zero. Finally, combine these two inequalities with an "or" statement.

3. What are the rules for solving an inequality with absolute value?

The rules for solving an inequality with absolute value are:

  • If the absolute value is less than a number, the solution will be between the negative and positive values of that number.
  • If the absolute value is greater than a number, the solution will be any value less than the negative value or greater than the positive value of that number.
  • If the absolute value is equal to a number, the solution will be the positive and negative values of that number.

4. Can an inequality with absolute value have more than one solution?

Yes, an inequality with absolute value can have two possible solutions. This is because an absolute value is always positive, so when solving an inequality with absolute value, there will be two possible values that satisfy the inequality.

5. What are some real-life applications of inequalities with absolute value?

Inequalities with absolute value can be used in many real-life situations, such as:

  • Calculating the range of possible values for a measurement, such as weight or temperature.
  • Determining the amount of error in a measurement or experiment.
  • Solving problems involving distance, rate, and time.
  • Creating boundaries or constraints in optimization problems.

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