Function Word Problem , and a factor question

[waloshin]

Q: The sum of a number and twice its reciprocal is 3. What is the number?

What I got:

Let n = the number

n + 2(1/n) = 3

Q: Factor 2x^3 - 3x^2 -3x +2 completely

Do you take -3x^2 -3x +2

Then factor that?

Q: Garrett ate 60 marshmallows in the same time that cory ate 55. If garrett ate 1 marshmallow per minute more than cory, thn how many did each it per minute?

I have 60 = 55

60/1 = 55

 

[Eraserhead]

Homework?

 

[fireshot91]

Same exact thread?

 

[Malfoy]

Q: The sum of a number and twice its reciprocal is 3. What is the number?

What I got:

Let n = the number

n + 2(1/n) = 3

Q: Factor 2x^3 - 3x^2 -3x +2 completely

Do you take -3x^2 -3x +2

Then factor that?

Q: Garrett ate 60 marshmallows in the same time that cory ate 55. If garrett ate 1 marshmallow per minute more than cory, thn how many did each it per minute?

I have 60 = 55

60/1 = 55

for the first queston you are overcomplicating it.


2 + 2(1/x) = 3
2 + 2/x = 3
2x + 2 = 3x <=multiple everything by x to get rid of denominator
2 = x <= subtract 2x from each side

for the 2nd one

you know in the same time, one eats 55, the other eats 60 and where the one eats N in one minute the other eats n + 1. This one took me a bit of time cause I approached it wrong at first.


55/ n = 60/(n+1)

because we know the totals, 55 and 60 are in the same amount of time they are set to each we know each of their rates, so if we were to divide them we would know how long it took them to do this.


(n+1) * (55/n) = 60 <=multiple both sides by n+1 to get rid of the denom on the right. You could try doing it with just N but well thats just making life more difficult.

(55/n +55)/n = 60 <=if u dont see why i did that, resign from the board please

55n/n +55/n = 60 <= just broke them up
55 + 55/n = 60 <= god rid of an N

55n + 55 = 60n <=multipled by n to get rid of a denominator

55=5n <=subtracted 55 on all sides
n = 11 <= divided by 5


garrett hate 12 marshmellows a minute while cory ate 11.

When I'm in your neck of the woods, I'll expect lunch.

 

[dommeister]

Waloshin,
You are on the right track with Question 1 and Malfoy answered it for you.

A shorter way would be: 2 + 2(1/x) = 3
Subtracting 2 from both sides gives you: (2/x) = 1
Rewrite both sides as a fraction: (2/x) = 1/1
Invert (flip) the fraction on both sides: (x/2) = 1/1
Multiply both sides by 2: x = 2


Question 2

My approach to solve y = 2x^3 -3x^2-3x+2 is the following:

Step 1: Substitute the x value with whole numbers (integers) through trial and error to obtain a y = 0 value.
Step 2: In this case there are 2 integer values (x = 2) and (x = -1)
Step 3: Rearrange to obtain (x - 2)= 0 and (x +1) = 0.
(These are two of your three factors)
Step 4: Expand these values to obtain a quadratic equation. In this case it is (x^2 -x -2).
Step 5: Use trial and error to multiply the quadratic equation to obtain the original equation y = 2x^3 -3x^2-3x+2
2x(x^2 -x -2) and -1(x^2 -x -2).

Your third factor is the values outside of the brackets in the above line highlighted in bold.

Your answer would be (2x-1) (x-2) (x+1)

Question 3:

Again, Malfoy calculated this question correctly. Another way to look at it is shown below.

Let n= Number of marshmallows Garret ate per minute.
Therefore n-1 = Number of marshmallows Cory ate per minute
The below equation shows that Garret and Cory ate in the same timeframe

Garrett = Cory
60/n = 55/(n-1)
60(n-1) = 55n
60n-60 = 55n
5n-60 = 0
5n = 60
n = 12 marshmallows per minute.
Therefore Garrett ate 12 marshmallows per minute.
Cory ate n-1 marshmallows per minute (12 -1) = 11 per minute

Calculation check

Calculate the time both people ate their marshmallows. It should be equal as stated in the question.

Garrett: 60/n = 60/12 = 5 minutes
Cory: 55/(n-1) = 55/(12-1) = 5 minutes

Both times are equal

Conclusion: Garrett ate 12 marshmallows per minute and Cory ate 11 marshmallows per minute; both over a 5 minute period.

It is useful to do a calculation check as this can either validate your answer or allow you to troubleshoot your calculation to see if you've made a mistake. Handy especially during exams and it shows that you are more thorough in your work (It's like having a back up plan).

There is usually more than one way to solve mathematical problems as Malfoy and I have shown.

I am a slow typer and was still replying to your post when Malfoy posted his reply which is why I answered all three questions.

Dominic