Need help with pre-cal questions!

M

Mumtaaz

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It takes Karl 15 minutes to clean his room. It takes Jesse at least twice as long to clean her room. Which inequality expresses this relationship, if x is equal to the amount of time it takes Jesse to clean her room?

The formula for finding the volume of a square pyramid is V = 1/3 s^2 h. The length of the side of a model pyramid is (x + 2) cm. The height of the pyramid is (x - 1) cm. If the volume of the pyramid is 12 cm^ 3 , determine the length of the side and the height of the pyramid.

A marine biologist is testing a new under water probe. The probe is catapulted from the ship into the air, descends under water to a predetermined depth, and then returns to the surface where it can be collected. The function that models the probe’s path is f(x) = 15x ^2 - 195x + 450, where x is time measured in seconds. The probe enters the water at 3 seconds. How long is the probe under water?

Explain how can you use the zeros of a quadratic function to help you determine where the function has a positive rate of change and a negative rate of change.

If anybody could help, it would be greatly appreciated :)
 
Mumtaaz said:
… The formula for finding the volume of a square pyramid is V = 1/3 s^2 h. The length of the side of a model pyramid is (x + 2) cm. The height of the pyramid is (x - 1) cm. If the volume of the pyramid is 12 cm^3 , determine the length of the side and the height of the pyramid …
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Hi Mumtaaz. How far did you get, in the exercise above? I would begin by substituting the given expressions for s and h, in the volume formula.

V = (1/3) (s^2) (h)

s = x + 2

h = x - 1

What expression do you get for V?

Are you allowed to use technology, when finding roots of cubic polynomials?

PS: Please start new threads for different exercises. Here's a link to the forum's guideline summary.

?
 
Hi, welcome to the forum!

You asked for help and this is a great place for that. At FMH we prefer that the student solves their own problem with assistance from the forum helpers. It then makes sense that you need to be actively involved in solving your own problem. So please go ahead and show us the work you have done so far so we know how you want to solve your problem and we can also see any errors you made. Thanks.
 
Of course, thanks, some of them I have an idea and others I have no clue.
 
Hello Otis,

I put the values in and I tried to simplify to a basic expression so I could maybe use quadratic formula? This is what I have so far, 12=(x^2+4x+4) / 3 (x-1), I simplified it all the way to this equation, x^3/3 +x^2 - 40/3 = 0
 
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Mumtaaz said:
Of course, thanks, some of them I have an idea and others I have no clue.
Click to expand...
Just telling us that you have an idea is not the same as telling us you have an idea. Seriously, if you want help you will receive the help that you need to do finish your problems but in the end it will be you who solve your problem. That will open happen if you tell us what you know and exactly where you need help.
 
1st problem. It takes Karl 15 minutes to clean his room. It takes Jesse at least twice as long to clean her room. So it takes Jesse at least 30 minutes to clean her room. If x is how long it takes Jess to clean her room and it take Jesse at least 30 minutes to clean her room can you come up with an inequality that relates x and 30?
 
Mumtaaz said:
… maybe use quadratic formula? This is what I have so far …

x^3/3 + x^2 - 40/3 = 0
Click to expand...
Hi Mumtaaz. Your equation matches mine. But that is a cubic equation (3rd-degree polynomial), so we can't use the quadratic formula.

The quadratic formula is for finding roots of 2nd-degree polynomials.

Does your class use graphing calculators (or other software), to solve cubic equations?

?
 
Mumtaaz said:
Hello Otis,

I put the values in and I tried to simplify to a basic expression so I could maybe use quadratic formula? This is what I have so far, 12=(x^2+4x+4) / 3 (x-1), I simplified it all the way to this equation, x^3/3 +x^2 - 40/3 = 0
Click to expand...
Multiply by 3 will get you x^3 + 3x^2 -40 = 0. Now it is time to use the rational root theorem to find and test all possible rational roots. Can you list the possible rational roots??
 
Jomo said:
… Now it is time to use the rational root theorem …
Click to expand...
That might be a possibility, in Mumtaaz's class, Jomo. It will show that the root is not rational. What's next, for Mumtaaz?

;)
 
Otis said:
That might be a possibility, in Mumtaaz's class, Jomo. It will show that the root is not rational. What's next, for Mumtaaz?

;)
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After verifying that the rational root test does in fact fail, then and only then (IMO) should Mumtaaz start looking at using software. Of course I am teaching teaching the course. Possibly the instructor tells their students to use their software whenever it make life easier.
 
Jomo said:
After verifying that the rational root test does in fact fail, then and only then (IMO) should Mumtaaz start looking at using software. Of course I am teaching teaching the course. Possibly the instructor tells their students to use their software whenever it make life easier.
Click to expand...
What software should I use and how do I use it?
 
Otis said:
Hi Mumtaaz. Your equation matches mine. But that is a cubic equation (3rd-degree polynomial), so we can't use the quadratic formula.

The quadratic formula is for finding roots of 2nd-degree polynomials.

Does your class use graphing calculators (or other software), to solve cubic equations?

?
Click to expand...
Oh, No we don't use software, we also don't use graphing calculators. The teacher hasn't mentioned that unfortunately.
 
Mumtaaz said:
?
I haven't learned rational root theorem
Click to expand...
You can use the quadratic forum if you have a quadratic equation. Unfortunately you have a cubic equation because of the x^3 term. You can use Wolfram Alpha to find the roots. Just type in the equation and hit enter.
 
Jomo said:
You can use the quadratic forum if you have a quadratic equation. Unfortunately you have a cubic equation because of the x^3 term. You can use Wolfram Alpha to find the roots. Just type in the equation and hit enter.
Click to expand...
Okay, thanks, I will try that
 
Jomo said:
You can use the quadratic forum if you have a quadratic equation. Unfortunately you have a cubic equation because of the x^3 term. You can use Wolfram Alpha to find the roots. Just type in the equation and hit enter.
Click to expand...
So the positive x value is the both the side length and the height?
 
Jomo's latest suggestion means using the web site wolframalpha.com

Click the 'Approximate forms' button, to see a decimal approximation for x.
 
Otis said:
Hi. Do you mean the teacher hasn't said anything about solving cubic equations?

:confused:
Click to expand...
She's only uploaded a small video about factoring, I know how to factor it using long division or synthetic division but other than that, nothing.
 
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