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Question 570883: Ticket Sales
Living in or by a metropolitan area has certain advantages. Entertainment opportunities are almost boundless in a major city. Events occur almost every night, from sporting events to the ballet. Tickets to these events are not available long; and quantity of tickets demanded can often be modeled by quadratic equations.
Application Practice
Answer the following questions. You must use Equation Editor or MathType when writing mathematical expressions or equations. Working in a new MS Word file, provide solutions and answers to all problems, clearly labeling your work. You must show your steps or provide verbal explanations (where appropriate) to receive full credit. Use textbook examples as your guide as to what level of detail is expected.
1. Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day n. ( is the day tickets go on sale, Day 1).

[Note: Function f(n) “maps” the days (dates) when tickets are sold to the corresponding number of tickets sold on each specific day (date), so f(15) would denote the number of tickets sold on the 15th day of ticket sales]
a. Does the graph of this equation open up or down? How did you determine this?

b. Describe what happens to the tickets sales as time passes.
c. Use the quadratic equation to determine the last day that tickets will be sold.
Note. Write your answer in terms of the number of days after ticket sales begin.

d. Will tickets peak or be at a low during the middle of the sale? How do you know? After how many days will the peak or low occur?

e. How many tickets would be sold on Day 4? On Day 13? On Day 32?

f. How many tickets will be sold on the day when the peak or low occurs?

g. What is the point of the vertex? How does this number relate to your answers in parts d. and f?

h. How many solutions are there to the equation ? How do you know?

i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
j. (Optional – advanced) How many tickets in total will be sold during the entire period when tickets are sold?
[Hint: One can, of course, take this problem “heads on”, calculating the number of tickets sold on each day that tickets are sold (e.g. for all n when f(n)>0). However, this will involve way too much work, as you probably have seen in e. We need to “speed up” the process. How? Well, if a constant number of tickets (e.g. 100 tickets) were sold on days 1 through k, we know that the total number of tickets sold would be 100*k. You should use your answer to c. above as your actual k.
What if ticket sales were proportional to the day number, e.g. 1 ticket sold on Day 1 and k tickets sold on Day k? Formula for the sum of an arithmetic progression (specific to this case) would yield the number of tickets to be . Now if the proportionality coefficient were to be not 1 but some “b”, then the formula would simply be: (do you see why?)

The most challenging is probably the formula for the total number of tickets sold if ticket sales were directly proportional to the square of the day number: . Try this formula to see if it works for the first few sums of squares (e.g. 1+4+9, here k would be 3).
Of course, if there was a proportionality coefficient different from 1, say “a”, then the formula would simply be:
Now, all you have to do would be to understand that the quadratic function’s three separate elements may be evaluated separately using the above formulas for the entire domain of days when tickets are sold, and the total can be arrived at much quicker than taking the problem “head on”]
I am totally confused on this problem and not matter what I did I cannot figure it out. Please help.
Click here to see answer by richard1234(4789)

Question 571016: my homework question reads:
an object is thrown upward from the top of a 256ft tower at a velocity of 96ft/sec. Find the height after 3 seconds.
I know I need to use the quadratic equation, but I don't know what to do next.
3t=-16t^2+96t+256
16t^2-93t-256=0
Thanks for your help!
Click here to see answer by KMST(578)

Question 570939: x^2-6x-28=0
Click here to see answer by jim_thompson5910(21667)

Question 570835: I am having a hard time solving this equation quadratic in form:
9x(to the 4th power)=85x(squared)-196.
I know it then becomes 9x(to the 4th power)-85x(squared)+196=0.
Then u = x squared. So then it becomes 9u squared-85u+196=0
Now I'm stuck on how to solve the equation from here because I don't think I factor here???
Click here to see answer by mananth(10541)

Question 570705: I need to solve : f(x)=(1)/(3) (x+4)^(2)+3 for the vertex, and the line of symmetry..Have been working on this one problem for about 20 minutes now.
Click here to see answer by scott8148(5879)

Question 570645: Solve the equation by factoring.
(2x/x+3)+(5/x)-4=(18/x^2+3x)
--------------------------------
I have gotten this far with the problem....
LCM = X(x+3) thus I have 2x^2+5x+15-4x^2-12=18--->-2x^2+5x+3=18--->-2x^2+5x-15=0

I think my problem is the (-2x^2) which I got from 2x^2-4x^2 and the (-4x^2) is from multiplying the LCM (x(x+3))to -4.
Could you show me where my error is?
Thank you
Kenneth
Click here to see answer by Earlsdon(6098)

Question 570512: please help me solve this problem 2x to the second power -3=1
Click here to see answer by jillfired(1)

Question 570434: the value of d in this equation: d-34.8=5.3
Click here to see answer by solver91311(12118)

Question 569602: 1/a+1/b+1/x=1/a+b+x ,a#0,b#0,x#0,x#-(a+b).
Click here to see answer by Alan3354(21551)

Question 569574: Find Y in the following equation:

Click here to see answer by JBarnum(1826)

Question 569421: Q. Obtain the values of k such that x^2-6x+k=0 has real roots.
is it to solve by making b^2-4ac=0
i got the answer as
k=9
also
Calculate the value of if the difference between the roots of x^2-6x+k=0 is 3
i got the answer as k=27/4
please can u help me to varify my answers.. i will be happy to forward u the steps which i prepared in word. to ur email.
Thanks
Click here to see answer by richard1234(4789)

Question 569254: How do you know if a quadratic equation will have one, two, or no sloution?
Click here to see answer by richard1234(4789)

Question 569266: How do you find a quadratic equation if you are only given the solution? Is it possible to have different equadratic equations with the same solution?
Click here to see answer by richard1234(4789)

Question 569428: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax2 + bx + c = 0.
Solutions: -9 and 6.

Click here to see answer by stanbon(48510)

Question 569221: y=x-1
y=-x=1

Click here to see answer by Alan3354(21551)

Question 569208: Which of the binomials below is a factor of this expression? 25x2 - 9y2 z2
Click here to see answer by stanbon(48510)

Question 569093: how do i find the solution of x2-x+3/16=0 by factoring?
Click here to see answer by Alan3354(21551)

Question 569115: How do you solve this quadratic equation explain process.
te{5/3,3/2}
Click here to see answer by Alan3354(21551)

Question 569015: One leg of a right triangle is 7 miles longer than the other. The hypotenuse is equal to 13 miles. How long is the shorter leg?
The correct answer is 5 miles.
please help me see how to do this!
Click here to see answer by Alan3354(21551)

Question 569018: One leg of a right traingle is 3 inches shorter than the hypotenuse. The other leg is equal to 8 inches. How long is the first leg?
The correct answer is 55/6 inches, but I can't figure out how ot get it. Please help me!
Click here to see answer by stanbon(48510)

Question 568822: whats the quadratic equation for the table x=1 and 3 when y =0 for both of them?
Click here to see answer by stanbon(48510)

Question 568702: Model with a quadratic equation, then solve.
Find the dimensions of a square picture that make the area of the picture equal to 75% of the total area enclosed by the frame. The total length of the side is 12inches, including the frame.
I thought y=axsquared for the equation
144=0.75x2
192=x2
x=13.9 But this is larger than the length of the picture frame???

Click here to see answer by KMST(578)

Question 568741: x^2+3x+8=5
Click here to see answer by jim_thompson5910(21667)

Question 568662: 3x^2-x-5=0
Click here to see answer by jim_thompson5910(21667)

Question 568627: I have no idea why I got a certain answer. This is my problem: 5/6x+30=x then I multiplied both by 6 and added them together to get 185. Am I correct? If so, how does that answer work?
Click here to see answer by nyc_function(2626)

Question 568520: how do you completely factor y5-26y
Click here to see answer by jim_thompson5910(21667)

Question 568196: a pool is to be 30 feet wide and 90 feet long. A walkway is to be built around the entire pool. if the combined area cannot exceed 4000 square feet what are the possible widths of the walkway?

Click here to see answer by mananth(10541)

Question 566230: how do you solve the equation 4p^2-90=-9p?
Click here to see answer by jim_thompson5910(21667)

Question 567835: How do you get the quadratic equation if you are given a table of values?
Click here to see answer by issacodegard(60)

Question 567780: The quadratic equations are difficult. I need help with this equation.
Write a quadratic equation having the given numbers as solutions - sqrt5 and 8sqrt5.
Click here to see answer by Alan3354(21551)

Question 567571: Tell whether y=-3x^2+18x-20 has a minimum value or a maximum value?Then find the minimum or maximum value.
Click here to see answer by lwsshak3(2915)

Question 567351: A box with an open top is constructed from a rectangular piece of cardboard which is initially 30 inches long and 23 inches wide. The box will be formed by removing squares of length x inches from each corner and then folding up the sides (as shown below). Express the volume (V) of the box as a function of x.
I've been trying to figure out this problem for a while, any help is greatly appreciated!!! Thanks!
Click here to see answer by ankor@dixie-net.com(12684)

Question 567353: A flag is raised while an onlooker watches from a distance of 21 feet away from the base of the flag pole (see the figure below). The flag rises vertically at a rate of 8 inches per second. Let t denote the time (in seconds) after the flag begins to rise (For simplicity, assume that when the flag begins to rise it is 0 inches above the ground). Express the distance d (in feet) between the flag and the onlooker as a function of t.
All of the answers I come up with are incorrect! Any help is greatly appreciated!!! Thanks!
Click here to see answer by ankor@dixie-net.com(12684)

Question 567184: -4x+5y=20 in y-intercept form and graph
Click here to see answer by mananth(10541)

Question 566846: 4/7,7 WHATS THE QUADRATIC EQUATION?
Click here to see answer by solver91311(12118)

Question 566456: factor and solve the following quadratic equation.
4x^2+10x=x^2-x+4
Click here to see answer by mananth(10541)

Question 566320: Find two consecutive negative integers such that the sum of their squares is 113.
Click here to see answer by ad_alta(170)

Question 566000: The directions are: Solve over the complex numbers
The problems are b-3 sqrt of b -10=0 (b minus 3 times the square root of b minus 10 equal 0.
and 2x-9 sqrt x + 4=0 (2x minus 9 times the square root of x plus 4)
The title of the paper is the Discriminant: equations in quadratic form. Since there is no squared number in these I don't know how to begin doing them.
Thank you!
Click here to see answer by stanbon(48510)

Question 565891: A 24-inch-wide sheet of metal is to be bent into a rectangular trough with the cross section shown in the illustration. Find the dimensions that will maximize the amount of water the trough can hold. That is, find the dimensions that will maximize the cross-sectional area.(depth and width = 24 inches)
Click here to see answer by solver91311(12118)

Question 565872: 3(x-5)2=21
Click here to see answer by ad_alta(170)

Question 565869: 4x2-3=9
Click here to see answer by ad_alta(170)

Question 565570: What is the lenghts of the legs?
The hypotenuse of a right triangle is 4 cm long. One leg is 1 cm longer than the other. Find the lengths of the legs. Round to the nearest tenth.
Thank You =)

Click here to see answer by ankor@dixie-net.com(12684)

Question 565690: Solve,
x + y = 6
y = 2x - 3
I'm completely lost
Daren
Click here to see answer by ankor@dixie-net.com(12684)

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