Non-Linear Equations - Solutions

Non-Linear Equations: Final Exam Prep Math II Nome: Key Directions: The following questions are sample items similar to those found on the EOC Exam. Answer each to the best of your ability. 1. A company manufactures DVDs. The company spent $247,000 to develop its process for manufacturing the DVDs. The company spends an additional $1.25 to manufacture each DVD. Which function represents the average total cost per DVD, y, for the company to manufacture x total DVDs? A y = X 1.25x ELE B y = 1.25x X C y= X 1.25x + 247,000 D Y = 1.25x+ 247,000 X X= # of DVDS y= Total cost per DVD y= Experises (cost) 1.25x+247000 = 1 # of DVDS X 2. The volume, V, of a certain gas varies inversely with the amount of pressure, P, placed on it. The volume of this gas is 175 cm³ when 3.2 kg/cm² of pressure is placed on it. What amount of pressure must be placed on 400 cm³ of this gas? A 1.31 kg/cm² V=K 112 400= 360 P B 1.40 kg/cm² C 2.86 kg/cm² D 7.31 kg/cm² 175 = K 3.2 4000 560 P: 560 40x) 1.4 K= 560 3. An investment has a balance of $2,000 and earns 3.2% interest each year. If $150 is added at the end of each year by the account holder and no money is withdrawn from the investment, which represents a function that can be used to calculate the investment balance for successive years? A 0.03281+ 2,000, B = 150 1=1+0.032 = 1.032 more than I means growth Beginning Amt (B.)=2000 B BB = 0.0328-1 + 150, B = 2,000 C Bn1.0328-1 + 2,000, Bo 150 D B1.0328-1 +150, B2,000 4. The value, V, of a car can be modeled by the function V(t) 13,000(0.82), where t is the number of years since the car was purchased. To the nearest tenth of a percent, what is the monthly rate of depreciation? A 1.5% B 1.6% C 9.2% D 18.0% y=a(1-r) T t rate of deprecication -r=0.82 -=-0.18 5. Which expression is equivalent to (8wxyz)? V= 0.18 18%. 6. Which expression is equivalent to 19 X 4wy 10 3 16xy xy A 8 w x y z A 24x3y -3 2 6 w x y z 4w Sy B 8 3 24x 16 X Y 64xY B 2wy C L 4w y D 2wy Y X" y 64 x²y C 64 x 24 64x D 12 7. A marathon is roughly 26.2 miles long. Which equation could be used to determine the time, t, it takes to run a marathon as a function of the average speed, s, of the runner where t is in hours and s is in miles per hour? A 26.226.25 B t = 26.2- 5 26.2 C t = 26.2s 26.2 t= 5 D distance = (rate(time) d= st 26.2: St t= 26.2 The time, t, in hours, that it takes x people to plant n trees varies directly with 8. the number of trees, and inversely with the number of people. Suppose 6 people can plant 12 trees in 3 hours. How many people are needed to plant 28 trees in 5 hours and 15 minutes? 15 min 0.25 hrs A 6 tirme (#of trees) K B 7 Hof ppl 5.25 28(1.5) x = 28 (1.5) 5.25 C 8 t=nk 3= 12K 18:12K K=1.5 D 9 X X8 The force, F, acting on a charged object varies Inversely to the square of its distance, r, from another charged object. When the two objects are 0.64 meter apart, the force acting on them is 8.2 Newtons. Approximately how much force would the object feel if it is at a distance of 0.77 meter from the other object? A 1.7 Newtons F= F= 3.35872 (077) B 5.7 Newtons 8.2 K C 11.9 Newtons ( 0.64)2F=5.67 D 12.9 Newtons K= 3.35872 10. The cost of a newspaper advertisement is a function of its size. A company wants its advertisement to have a height that is twice its width. The newspaper charges a flat rate of $50 plus an additional $10 per square inch. L The company can spend no more than $2,050 on the advertisement. What is the maximum height of an advertisement that the company can afford? A B 5 inches 10 inches h=2w Cost=10(Areo) +50 C 15 inches 10(2²) +50 ≤ 2050 D 20 inches ZN 20w² 2000 WEID W² 100 W n 20 11. The function f(x) = 85 X models the volume of a gas in a balloon under x units of pressure at a constant temperature. Which best describes the domain of f(x)? A 0 < x ≤ 85 0 ≤ x ≤ 85 C x > 0 951 x20 Volume= 95 Pressure ← can't be zero 85 12. Which expression is equivalent to (3x + 17x-1)+(2x-6)? (A) x+17x³-7 3x5+17 x3-1-2x5-6 B x11x-1 3-7 C 5x5 + 17x³ +7 D "6x + 17x3 +6 13. Alberto and Janet start running at the same time in a straight-line path in the same direction. Alberto is 1,080 inches behind Janet. 36 1080 m = 30 yds Alberto runs at a constant rate of 1,440 feet per minute. 1440ft 400 yds Byd Cols sec Janet runs at a constant rate of 6 yards per second. 3 ft 1 sec After approximately how many seconds will Alberto pass Janet? A 15 seconds X= time Janet 6x +30 B 20 seconds Alberto Bx C 25 seconds D 8x=6x+30 30 seconds 2x=30 x=15 14. The equations = 2√5x can be used to estimate the speed, s, of a car in miles per hour, given the length in feet, x, of the tire marks it leaves on the ground. A car traveling 90 miles per hour came to a sudden stop. According to the equation, how long would the tire marks be for this car? A 355 feet S=2Sx B 380 feet S= speed =90 X= length of tire marks C 405 feet 90=2√5x D 430 feet 45 = √5x 45²= (√x)² 2 2 2025 = SX x= 405