two review questions

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yfelix45

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Joined
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hello,

Thanks for the help on your forum.

These are questions I am reviewing for my final test and would like to know where I went wrong because it was never explained to me. Below are the questions and my answers to each question.
Can you help?

Thanks
yfelix45






    2. The profit, P, of a video company in thousands of dollars, is given by P = -5x² + 550x – 5000 , where x is the amount spent on advertising, in thousands of dollars.


(a) Determine the amount spent onadvertising that will result in a profit of $0. In other words, theamount that must be spent on advertising in order in order to breakeven.
My answer:

P = -5x² + 550x – 5000 b² = [1/2(110)]² = 3025
P = -5(x² + 110x) = - 5000
P = -5(x² +110x + 3025 –3025 ) - 5000
P = -5(x² + 110x +3025)15125 – 5000
P = -5 (x + 110)² + 10125
P = 110, x = 10125
The vertex (110, 10125)-5(x-10(x-100) x= 10 x= 100








  1. The profit, P, of a video company
    in thousands of dollars, is given by P = -5x² + 550x – 5000 ,
    where x is the amount spent on advertising, in thousands of
    dollars.








(a) Determine the amount spent on
advertising that will result in a profit of $0. In other words, the
amount that must be spent on advertising in order in order to break
even.







P = -5x² + 550x – 5000
b² = [1/2(110)]² = 3025


P = -5(x² + 110x) = - 5000



P = -5(x² +110x + 3025 –
3025 ) - 5000



P = -5(x² + 110x +
3025)15125 – 5000


P = -5 (x + 110)² + 10125


P = 110, x = 10125


The vertex (110, 10125)
-5(x-10(x-100) x= 10 x= 100









  1. A jet flew from Tokyo to Bangkok
    a distance of 4800km. On the return trip the speed was decreased
    by 200km/h. If the difference in the times of the flight was
    2hrs. What was the jet's speed from Bangkok to Tokyo?


My answer:
Speed was was reduced by 200km/h on
the return trip, x – 200 represents the reduced speed.





DESTINATION


 DISTANCE d(km)


 SPEED km/h


 TIME d/s


Tokyo to


Bangkok


 4800


 x


 4800/x


Bangkok to


Tokyo


 4800


 x – 200



4800/x – 200



Total









- 2hrs








4800/x + 4800/x – 200 = 2

= 4800/x x(x – 200 ) + 4800/x – 200 x (x – 200 ) = 2x (x – 200 )


= 4800 x – 960000 + 4800x = 2x²– 400x



= 2x² + 400x – 960000 = 0


= (2x + 400 )(x – 2400 ) = 0

= 2x = - 400 or x = 2400

= x = -400/2

x= - 200


The jet speed from Bangkok to Tokyo is
2400 km/h
 
Last edited:
Hi Felix. Your post is a mess. Your formatting is difficult to read, and you made several typographical errors. In the future, please follow the guidelines in the post titled Read Before Posting regarding previewing, proofreading, and correcting your posts prior to submitting.


I have some time (you are lucky today as I often ignore messes) to decipher your typing on the first exercise and comment.

They want you to find a positive value for x that causes the profit polynomial to equal zero (i.e., the positive x-intercept, not the vertex). In other words, solve the following equation.

-5x^2 + 550x - 5000 = 0

Your typing below looks like you are trying to Complete the Square. This method is one valid approach, but using factoring or the Quadratic Formula might be simpler for you. (If you decide to use the Quadratic Formula or factoring, then divide both sides of the equation above by -5 before starting.)


yfelix45 said:
P = -5x² + 550x – 5000

b² = [1/2(110)]² = 3025

P = -5(x² + 110x) = - 5000

P = -5(x² +110x + 3025 – 3025 ) - 5000

P = -5(x² + 110x + 3025)15125 – 5000

P = -5 (x + 110)² + 10125

P = 110, x = 10125

The vertex (110, 10125)
Click to expand...

I highlighted in red what looks incorrect. I'm not sure which errors are typographical; hence, I simply provide below the steps as I would have texted them. Please compare.

P = -5x^2 + 550x - 5000

P = -5(x^2 - 110x) - 5000

(b/2)^2 = (110/2)^2 = 3025

P = -5(x^2 - 110x + 3025) - 5000 + 5(3025)

P = -5(x^2 - 110x + 3025) + 10125

P = -5(x - 55)^2 + 10125

Remember: x^2 + bx + (b/2)^2 always factors as (x + b/2)^2

At this point, you may let P = 0 and solve for x.

-5(x - 55)^2 + 10125 = 0

The last step will be stating your final answer using a complete English sentence.

If you find something in my post that you do not understand, please ask a specific question.

Cheers ~ Mark :cool:
 
Last edited:
thanks and resubmitting my question for better viewing

hello,



Thanks for your help. I am resubmitting my review questions. I would to know where I went wrong in both questions.


    1. The profit, P, of a video company in thousands of dollars, is given by P = -5x[FONT=Times New Roman, serif]²[/FONT][FONT=Times New Roman, serif] + 550x – 5000 , where x is the amount spent on advertising, in thousands of dollars.[/FONT]


[FONT=Times New Roman, serif](a)Determine the amount spent on advertising that will result in aprofit of $0. In other words, the amount that must be spent on advertising in order in order to break even.[/FONT]


[FONT=Times New Roman, serif]P= -5x[/FONT][FONT=Times New Roman, serif]²[/FONT][FONT=Times New Roman, serif]+ 550x – 5000 b[/FONT][FONT=Times New Roman, serif]²[/FONT][FONT=Times New Roman, serif]= [1/2(110)][/FONT][FONT=Times New Roman, serif]²[/FONT][FONT=Times New Roman, serif]= 3025[/FONT]
[FONT=Times New Roman, serif]P= -5(x[/FONT][FONT=Times New Roman, serif]²[/FONT][FONT=Times New Roman, serif]+ 110x) = - 5000 [/FONT]
[FONT=Times New Roman, serif]P= -5(x[/FONT][FONT=Times New Roman, serif]²[/FONT][FONT=Times New Roman, serif]+110x + 3025 – 3025 ) - 5000 [/FONT]
[FONT=Times New Roman, serif]P= -5(x[/FONT][FONT=Times New Roman, serif]²[/FONT][FONT=Times New Roman, serif]+ 110x + 3025)15125 – 5000[/FONT]
[FONT=Times New Roman, serif]P= -5 (x[/FONT][FONT=Times New Roman, serif] [/FONT][FONT=Times New Roman, serif]+110)[/FONT][FONT=Times New Roman, serif]² + 10125[/FONT]
[FONT=Times New Roman, serif]P= 110, x = 10125[/FONT]
[FONT=Times New Roman, serif]Thevertex (110, 10125)[/FONT]







      1. [FONT=Times New Roman, serif]A jet flew from Tokyo to Bangkok a distance of 4800km. On the return trip the speed was decreased by 200km/h. If the difference in the times of the flight was 2hrs. What was the jet's speed from Bangkok to Tokyo?[/FONT]

        [FONT=Times New Roman, serif]Speed was was reduced by 200km/h on the return trip, x – 200 represents the reduced speed. [/FONT]


DESTINATION
 DISTANCE d(km)
 SPEED km/h
 TIME d/s
Tokyo to
Bangkok
 4800
 x
 4800/x
Bangkok to
Tokyo
 4800
 x – 200
4800/x – 200
Total



- 2hrs


[FONT=Times New Roman, serif]4800/x+ 4800/x – 200 = 2[/FONT]
[FONT=Times New Roman, serif]= 4800/x x(x – 200 ) + 4800/x – 200 x (x – 200 ) = 2x (x –200 )[/FONT]
[FONT=Times New Roman, serif]= 4800 x – 960000 + 4800x = 2x[/FONT][FONT=Times New Roman, serif]²[/FONT][FONT=Times New Roman, serif]– 400x[/FONT]
[FONT=Times New Roman, serif]= 2x[/FONT][FONT=Times New Roman, serif]²[/FONT][FONT=Times New Roman, serif]+ 400x – 960000 = 0 [/FONT]
[FONT=Times New Roman, serif]=(2x + 400 )(x – 2400 ) = 0[/FONT]
[FONT=Times New Roman, serif]=2x = - 400 or x = 2400[/FONT]
[FONT=Times New Roman, serif]=x = -400/2[/FONT]
[FONT=Times New Roman, serif]x=- 200 [/FONT]
[FONT=Times New Roman, serif]Thejet speed from Bangkok to Tokyo is 2400km[/FONT]




thanks

yfelix45
 
Last edited:
yfelix45 said:
I am resubmitting

I would to know where I went wrong
Click to expand...

Okay -- I will try commenting again on exercise 1.

This time, I hope not to overwhelm you with a lot of information. So, let's take it one step at a time. :cool:


YOUR FIRST MISTAKE IN EXERCISE 1

You found the vertex coordinates. The exercise does not ask for the vertex coordinates.

The exercise is asking for the positive x-intercept.

In other words, solve this equation for x:

-5x^2 + 550x - 5000 = 0


Please let me know whether you understand what I posted above, and then I will comment on what I view as your second mistake.

Cheers ~ Mark :cool:
 
reply to mmm4444bot and denis

hello mmm4444bot,

I understand that I should use the equation to find the x-intercepts and not find the vertex. I got it thanks!!



Denis: thank you for pointing out my mistake in my starting equation.

yfelix45
 
thank you

hello,

Thank you to denis for pointing me the right direction. I could not respond to anyone last night because my internet decided to play connect/ not connect. I thank you for your help on the forum and I always appreciate the help I receive.

Thanks

yfelix45
 
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