Question

17. The profit, P, of a video company, in thousands of dollars, is given by P=-57 +550x-5000, where x is the amount spent on advertising, in thousands of dollars Determine the amount spent on advertising that will result in a profit of $0. In other words, determine the amount that must be spent on advertising in order for the company to break even Describe the relationship between your solution and this graph of the corresponding relation (6 marks) 11000 10000 -9000 5000 Profit ($10001 7000 5000 5000 4000 3000 2006 1000 20 40 100 120 60 80 (51000) 18. Ajet flew from Tokyo to Bangkok, a distance of 4800 km. On the return trip, the speed was decreased by 200 km/h. If the difference in the times of the flights was 2 hours, what was the jet's speed from Bangkok to Tokyo? (13 marks)

please answer ALL questions. thank you.

Answer 1

Page No: Page - Date. solution 2 on O 10) x = 10 (17 P = -5% +550 - 5000 The amount spent advertising that will result in a profit of so Pro -5x2 +5500-5000 => +592 +500+ soon 5 5000 a sx (2-10) + 500 (x - 10 -> (x-10) (-5x+500) 500 - a=t Do KE 100 The amount spent on ů to thousand dollars ar thousand dollars Answer) part 1 Here when x-10 , Profit P=0 and when a=100 Profit P = 0 -52- OS XOR + Now, as ix increases the profit increase. when x = 20 RE-5X(20)? + 550x20 -501d 2000 + 11000 - 5000 4000 Io the graph it is clearly seen that P = d 1-2 Chihen NE 20, P = 4000- similarly as a increase P also incron advertising thousand Part 2 n=10

Page No: Date Page 2 Now when a=50 P- - 5 (50)2 + 550X50 -5000 = -5x2500 + 275-00 - 5000 = - 12500-5000 + 27500 =-17500 + 27500 1oooo anten a=50 the profit is highest col and Da lovoo OS 60 10000 Now as a increase the value of dearen i samo same as when 25 -5(60) + 550X60 - soco - 18ovo +33010 - sooo fallcb So, the value of P remein same for x ²50 and x-60, when a=70, P=-570) +550x70 -5000 24500 +38500 -5000 qoro. It is clearly show is the when &=70 the value graph of P29000. - Now as a increase the value of P. docreare when x=90 g P = -5/90) +550x90 -5000 - 40,500 + 49500-5000 E 4000

Page No Page 73 Date. (201) 7 tard 16ooo 9000 8000 Zobo Gas Foro 3000 2007 600 g 10 20 30 40 50 60 70 80 90 100 2 ($1000) when x= 10 20 P = Lovo x = so P = lors p = lovoo (ory 2= 70 P E qovo. x=90, PE 4000 So, this graph ies right for the correspond- ing relation (18) Distance between Tokyo and Bangkok Logool = 4800 km jet flew from Tokyo to Bangkok at na km/h. let, a 7 4800 hour ". Time taken for going decreased rookon/h On returning ". The speed is (x-200) Km/h 4800 Time taken for returning read speed hour (2-00

Page No: Date. Page - 4 1927 Was a -2 2 x 200 2 The difference in times of flight 2 hours 4800 4800 4800x 48 cox # 96 000 x(x-200) conso => 222 - 4000. 9 Govo 20 => 2(x 2con a 4800 coo) = 800x + 600x - 48000 x (2809) 600/x=800) 0 = (x 800) (x + 600) x = 8co or R.20 God a cannot be negetive. Sox = 800 kn/h . The jets speed from Bangkok 6.800 800-200) koch = 6oo kon/hour. Animer No to Tokyo Cinere

Page No: Date. Page 5 19). The roots of the quadratic equation is (2 + 3) (2-3) The equation passes through the point (2,10) So, the equation can be written as y = a (x-x) (2-x2) a{x-(2+3)}{ (+63-13) where in, = 2+√3 x2 = (2-3) .: Y= a (2+2 -13) (2 x+243) = a {la-z? 80035 afx² - 4x +43) ala²4n+1) Now, the equation passes through (2, 10) :.: 10) = 12:1254.2+1). S 10 = a (-3 (ans) (4-8 +1) 3 i. The requered equation is - y = 10 (3? - 42+1) borit - 3y = orzy - 3y = - 10 (x²-4*+1) Answer - 10xt 40x 510

Page No: Date ① The croots are a let, the equation is Y = a (x-x) (x-x2) a(x-3)(2+4) .: 3y = a (32-1) (a+h) + "3 The requetion passes through (1,5) 3x5 = 2 ( 3 - 1) 1+4) 15 - å 245 To z 2 CoreThe o required equation is 3y = 3 (3x-1)(2+4)* Gy=3 (3x-1) (2+4) Answer) The equation of line y = 3x+5. quadratic equation function is f(a)= 3 2 2 - 2 0 - 4 sh To find the point of intersection we write 3222x - 4 = 3x45 com

Page No. Page - 7 Date. 2 -> 3x - 20-4 = 3a +5 = 32²-5n-a. -(-5)+ Vesga - 4,3.6-9) uring the formula a22 & bate=0 but ✓ 6²-4ac 2.3. aa 5 & 125 +108 6 5133 The roots are 57 J133 6 Annen