A few problems i've come across some trouble with.

[icesalmon]

1. Find the sales necessary to break even (R=C) if the cost C of producing x units is

Given...

Homework Equations

C = 5.5((sqrt(x)) + 10,000 (Cost Equation).
R = 3.29x (Revenue Equation).

The Attempt at a Solution

I thought about what R = C means, your output is equivalent to your input, no? So I followed (R=C) and set the two equations equal; after calculating I come across a quadratic which isn't factorable, so I use the quadratic formula which doesn't yield answers close to the actual value for x which is approximately equal to 3133 units.

Homework Statement

The next problem asks me about a Conveyor design...
"A moving conveyor is built to rise 1 meter for each 3 meters of horizontal change
Find:
A). The slope of the conveyor
B). Suppose the Conveyor runs between two floors in a factory. Find the length of the conveyor if the vertical distance between floors is 10 feet.

Homework Equations

m = (y_2 - y_1) / (x_2 - x_1) The slope formula ( sorry I haven't been aquainted with LaTeX yet, and I didn't have any of the greek letters, delta, copied.)

The Attempt at a Solution

Well, slope is a measure of vertical rise relative to horizontal shifts so the slope, m, is 1 meter up for every 3 meters right. When I make an attempt at the second problem I just think the distance is 20...I know it's completely wrong but I'm at a loss when trying to interperet some of these questions. Thank you all for your time in advance.

Homework Equations

The Attempt at a Solution

 

[eumyang]

Re problem #1: show us what you have for your quadratic. Because I tried it and I was able to get 3133 as one of the solutions.

Re problem #2: Yes, 20 is wrong. This is just a proportional problem. If the conveyor rises 1 meter for every 3 meters of horizontal distance, what would the horizontal distance be if the conveyor rises 10 feet? (You notice that you have two different units, right? Not that it really matters here.)

 

[icesalmon]

Re problem #1: show us what you have for your quadratic. Because I tried it and I was able to get 3133 as one of the solutions.

Re problem #2: Yes, 20 is wrong. This is just a proportional problem. If the conveyor rises 1 meter for every 3 meters of horizontal distance, what would the horizontal distance be if the conveyor rises 10 feet? (You notice that you have two different units, right? Not that it really matters here.)

For Problem #1 I have (x-3039.513678)² = 2.794689628x, I divided by 3.29 on all sides.

For problem #2 the horizontal distance would be 30. I do notice I have feet and meters, the conversion doesn't matter in this step?

 

[symbolipoint]

Recheck your work for mistakes:

For Problem #1 I have (x-3039.513678)2 = 2.794689628x, I divided by 3.29 on all sides.

Equating R and C, a couple of steps should lead to the equivalent of maybe this:

3.29x - 10000 = 5.5$$\sqrt{x}$$,
and further algebraic steps should be able to give this:

3.29²x²-(5.5²+2*32900)x+10⁸=0;

Which only may need a slight bit of calculation before using the solution to Quadratic Formula. Substitute corresponding values.

EDIT: included a multiplication by 2, using asterisk as the multiplication symbol. eumyang in #5 found my mistake in which factor of 2 was missing.

 

[eumyang]

3.29²x²-(5.5²+32900)x+10⁸=0;

This is almost correct; that 32900 should be multiplied by 2.

For Problem #1 I have (x-3039.513678)² = 2.794689628x, I divided by 3.29 on all sides.

I have no idea how you got this. What did you do exactly? Show all steps.

This is what you should do:
$$3.29x = 5.5\sqrt{x} + 10000$$
Subtract 10000 from both sides, square both sides, and put all terms on one side. Your quadratic should look like this afterwards:
$$10.8241x^2 - 65,830.25x + 100,000,000 = 0$$

Re: in problem #2, yes, the different units do not matter.

 

[icesalmon]

I divide by 3.29 to get x = (5.5)/(3.29)(sqrt(x)) + 10,000/3.29 or 3039.51678
I move 10000/3.29, or 3039.51678, over to the right and get ( x - 3039.51678 ) = 1.7sqrt(x)
I square both sides so I can get that root(x) out of the way to get ( x - 3039.51678 )² = 2.794689628x
I factor out the left and move the 2.794689628x over
It doesn't factor, so I use the quadratic formula.

 

[eumyang]

I divide by 3.29 to get x = (5.5)/(3.29)(sqrt(x)) + 10,000/3.29 or 3039.51678
I move 10000/3.29, or 3039.51678, over to the right and get ( x - 3039.51678 ) = 1.7sqrt(x)
I square both sides so I can get that root(x) out of the way to get ( x - 3039.51678 )² = 2.794689628x
I factor out the left and move the 2.794689628x over
It doesn't factor, so I use the quadratic formula.

If you really want to divide by 3.29 first, then after following your steps, you should get this for your quadratic (approx.):
$$x^2 - 6,081.82x + 9,238,643.40 = 0$$

I'm still getting ~3133 as one of the solutions.

 

[icesalmon]

If you really want to divide by 3.29 first, then after following your steps, you should get this for your quadratic (approx.):
$$x^2 - 6,081.82x + 9,238,643.40 = 0$$

I'm still getting ~3133 as one of the solutions.

Got it, I must have put the numbers in incorrectly. Although a goofy mistake to say the least one that has plagued me for a while. Thanks for your time.