Need help solving quadratic problems

[silver1]

I would really appreciate it if someone could explain the steps to solving the following:

1) A large bottle of shampoo is 20cm tall and cylindrical in shape.

a. write a formula for the volume of the bottle in terms of its radius
b. what radius should the bottle have if it must hold 240 milliliters of shampoo? (a milliliter is equal to 1 cubic centimeter)

2) Solve by extraction of roots:

2a) 81(x + 1/3)^2 = 1

2b) 2(5x - 12)^2 = 48


Thanks for any help in advance

 

[tkhunny]

You should start by writing the requested formula. Did you do that?

 

[silver1]

You should start by writing the requested formula. Did you do that?

That's actually the first step I got stuck on, lol. My teacher didn't go over these types of problems in class, just assigned as homework.

I know that volume = L * W * H but im confused by the wording "in terms of its radius". I'm not sure how that looks written out. I also have a terrible head cold right now so I'm having trouble even with the most basic things it seems

 

[silver1]

Well, whadda heck does your teacher do in class? Clean his finger nails?

Pretty much. He has a habit of going over an example or two the easier problems in a chapter, expecting you to know the rest based on your knowledge from last semester, and then assigning homework that includes a few problems that he didn't go over in class. This is some of those unfortunately. I tend to be a student that needs to be refreshed on stuff after a long summer so his expectations don't work too great with me personally. I tend to look for help a lot.

 

[tkhunny]

Volume of Right Circular Cyllinder \(\displaystyle \pi r^{2}h\)

 

[HallsofIvy]

That's actually the first step I got stuck on, lol. My teacher didn't go over these types of problems in class, just assigned as homework.

I know that volume = L * W * H but im confused by the wording "in terms of its radius". I'm not sure how that looks written out. I also have a terrible head cold right now so I'm having trouble even with the most basic things it seems

In other words, you do not know anything! "L*W*H" is the volume of a rectangular solid". I suspect that your text book has a formula for volume of a cylinder. Look it up in the index. Or, since you clearly can get on the internet, "google" the words "cylinder" "volume". I did that and it took less than a minute to get the formula.'

I see now that tkhunny has given you the formula.

"Assigning homework that includes a few problems that he didn't go over in class." Why in the world would he assign problems that he did go over in class! Sounds to me like he is assuming (or, perhaps, "hoping") that you can do some things for yourself- like look up the formula for volume of a cylinder.

 

[mmm4444bot]

2a) 81(x + 1/3)^2 = 1

2b) 2(5x - 12)^2 = 48

The strategy for solving these equations is to first isolate the squared expression on one side of the equation, followed by taking the square root of both sides. You may then solve for x in the usual way and simplify.

Here's a short video showing an example.

Please show what you're able to try or ask specific questions.

PS: For future reference, it's better at this site to begin a new thread for each new exercise. Cheers :cool:

 

[silver1]

The strategy for solving these equations is to first isolate the squared expression on one of the equation, followed by taking the square root of both sides. You may then solve for x in the usual way and simplify.

Here's a short video showing an example.

Please show what you're able to try or ask specific questions.

PS: For future reference, it's better at this site to begin a new thread for each new exercise. Cheers :cool:

That video helped a lot, thank you.