Functions Questions and Answers

5 Engineers study different shapes for storage tanks for liquid important component of rocket fuel One engineer is testing both the spherical and cylindrical designs below Both shapes have the same radius x The height 2 of the cylinder is 2x The engineer wants to choose the tank that has the least ratio of surface area to volume Surface area 4x Volume 3x 2x Surface area 2 x 4x Volume 2x4 Part A Write a function f to represent the ratio of surface area to volume for the sphere Simplify Part B Write a function g to represent the ratio of surface area

Why Didn t Klutz Do Any Homework on Saturday Either multiply or factor as directed and find your answer in the adjacent answer column Write the letter of that exercise in the box that contains the number of the answer 4 16a b 13 49a 1 a 25 Multiply a 5 a 5 D 2 3a 2 3a E 7a 1 7a 1 N a 6 a 6 A 4a b 4ab 2a 5b 2a 5b Factor En 49 A n 1 N 81 n H 4n 9 49n 16 E 144 25n 1 2 3 6 17 4a4 25b 15 4 9a 12 4a 36 24 a 36 1 2n 3 2n 3 10 12 5n 12 5n 8 n 1 n 1 5 7n 3 7n 3 2 n 7 n 7 18 9 n 9 n 20 7n 4 7n 4 5 4 8 7 6 Factor S x y 4x 49y W 81x 100y E 36x 121y O9x 64y Nx4 400 Factor HOBO C 25a 9b4 W a b 36 16 a b6 K a b c8 N 48 6 225 D 3 9x 10y 9x 10y 5 x y x y 7 x 20 x 20 11 6x 11y 6x 11y 16 3x 7y 3x 7y 22 2x 7y 2x 7y 23 3x 8y 3x 8y 19 4 a b 4 a b 14 2a 15 2a8 15 21 a b a b 12 ab c ab c 9 ab 6 ab 6 16 5a 3b 5a 36 10 4 ab 4 ab 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

23 Add the Data table here Speed r min Output Current lo A 24 Add the plotted graph here 1800 1799 1796 1797 1804 1790 1801 1792 0 106 0 249 Torque Nm 0 21 0 421 0 250 0 310 0 442 0 560 0 790 1 002 1 150 1 310 0 306 0 442 E1 AC V OUTPUT CURRENT IO VS TORQUE T 0 7 130 5 129 2 126 7 107 6 118 8 113 6 110 8 106 2 0 985 12 AC A 1 324 1 571 0 56 0 788 1 002 1 146 Torque N m 0 106 0 21 0 421 0 7 0 985 1 324 1 571 1 855 1 855 1 31 Speed r min 0 300 0 296 0 295 0 294 0 287 0 287 0 287 0 287 Does this graph confirm that the separately excited dc generator is equivalent to a torque to current converter with higher torque producing greater speed Ans Yes

The Corner Frame Shop wants to know the effect of different inventory costing methods on its financial statements Inventory and purchases dat June are Click the icon to view the inventory and purchases data If The Comer Frame Shop uses the LIFO method cost of goods sold will be OA 21 200 B 21 240 OC 20 900 OD 22 340 Data table Jun 1 Beginning inventory Units 2 500 Unit Cost 11 00 Total Cost X 27 500

The distance to the surface of the water in a well can sometimes be found by dropping an object into the well and measuring the time elapsed until a sound is heard If t is the time in seconds it takes for the object to strike the water then t obeys the equation s 16t where s is the distance in feet Solving for t we have t 5 4 Let to be the time it takes for the sound of the impact to reach your ears Since sound waves travel at a speed of approximately 1100 feet per second the time to travel the distance s is t s 1100 Now t t is the total time that elapses from the moment that the object is dropped to the moment that a sound is heard We have the equation 5 Total elapsed time t t 1 4 S 1100 Falling object 5 Sound waves S 1100 Find the distance to the water s surface if the time elapsed from dropping a rock to hearing water is 7 0 seconds S feet Round to the nearest hundredth as needed

of 2 ences View transaction list Journal entry worksheet 2 Note Enter debits before credits Date August 31 31 the perpetual inventory system is used 3 Record the entry to close the income statement accounts with debit balances 4 General Journal Debit Credit

Use number bases to answer the question Suppose you have four quarters three nickels and two pennies Using base five determine the place value for each coin quarter 5 nickel penny 5 5 Use base five to write a numeral to indicate how many cents you have cents five

Change the number to base ten 441 five

Compute the cost assigned to ending inventory using LIFO Note Round your average cost per unit to 2 decimal places Date January 1 February 10 Total February 10 March 13 Total March 13 March 15 Total March 15 Goods Purchased of units Cost per unit of units sold Perpetual LIFO Cost of Goods Sold Cost per unit Cost of Goods Sold of units 600 at Inventory Balance Cost per unit 40 00 Inventory Balance 24 000 00

Find the quadratic polynomial whose graph goes through the points 1 5 0 4 and 2 26 f x 0

The system 7x 35 y x 4y 5x 25 y has the solution x 20 z 2z 15 z y 0 0 0 Z

In how many different ways can you pick 2 people from among 3 people 1 5 3 C

Let A n s and B a b c Use this information to complete parts a though c belo a Find Ax B Choose the correct answer below O A a n b n c n a s b s c s OB axn bxn cxn axs bxs cxs O C n a n b n c s a s b s c OD nxa nx b nx c s a s x b s x c b Find BX A Choose the correct answer below OA nxa nx b nx c s x a sx b sxc OB a n b n c n a s b s c s a s b s c OC n a n b n c OD axn bxn cxn axs bxs cxs c Does A x B BXA

If a statement and its converse are both true which of the other forms inverse and contrapositive are also true if any Choose the correct answer OA Both the inverse and the contrapositive are true OB Only the contrapositive is true OC Neither the inverse nor the contrapositive are true OD Only the inverse is true

2 x 1 Label the appropriate functions as g and h et f x 0 Oy x 1 2 x 1 2 1 Write f as a composition g h of two functions g and h in two different ways g h and g2 0 O O y y x 2 X N x 81 h Answer Bank 82 h

15 If a thermometer indicates 40 degrees Celsius what s the temperature in degrees Fahrenheit OA 54 F OB 72 F OC 22 F OD 104 F

11 Which prefix means 1 10 of a unit in the metric system OA Milli OB Hecto OC Centi OD Deci

1 The English measurement system is primarily used by what country OA United States O B England O C Ireland OD Italy

8 Use the following table to calculate GDP in this economy Corporate Profits R D Government expenditure Proprietors Income Interest Taxes Net Foreign Factor Income Wages Rents Residential Investment Personal Saving Transfer Payment 400 40 400 50 70 300 30 1000 300 200 250 60 9 Why does GDP underestimate the actual amount of output produced in an economy

A sculptor is designing her new triangular masterpiece In her scale drawing the shortest side of the triangular piece to be made measures 4 cm The longest side of the drawing measures 39 cm The longest side of the actual triangular piece to be sculpted must be 11 9 m long How long will the shortest side of this piece be The shortest side of the sculpture measures m Round to the nearest tenth

7 Define Gross Domestic Product GDP from the expenditure approach and the income approach In other words what are the components of GDP from each approach

20 Which set is an example of like fractions O A 2 and 23 O B 74 and 4 O C 12 and 32 O D 1010 and 5

1 Using the graph on the right give the value of each statement a lim f x c lim x e f 1 b f 1 d limf x 14 2 f lim f x sto

Find CA as a function A At t 0 SA CAO and t t CA CA Vo CAO VOCA K 1 1 So JCA dt

The kinematic viscosity is defined as the ratio between the viscosity and the density v p Find the dimension and the unit in both the BG system our textbook calls it US system and Sl system recall viscosity is defined from the Newton s law of viscosity

Evaluate the expression using exponential rules Write the result in standard notation 4 8x10 40 10

Brandon works as an animal trainer training service dogs for people with disabilities He earns 635 27 per week Brandon is single and claims one withholding allowance What is the amount of federal income tax that will be withheld from Brandon s weekly paycheck

14 The prefix kilo in the metric system means O A 10 O B 1 000 000 O C 1 000 O D 100 units

O A 22 300 000 cg O B 023 cg O C 223 000 cg OD 0023 cg

rove that for a b 0 and neN a n b n a b al i mz i 1 al j ng i 1

4 Identify the vertical and horizontal asymptotes of the function 2 x 3 f x 2 4 x 4x 5 amro 08 zi sontzizen erit new tiupio ert ni s

5 Graph the function labeling all vertical or horizontal asymptotes f x 3x 6x 2 x 3x 28

2 The time t to empty a water tank varies inversely as the rate of pumping p A pump can empty a water tank in 30 minutes at the rate of 150 gallons per minute Part A Write the equation of the inverse variation Part B How long will it take to empty the water tank at a rate of 250 gallons per minute

1 The voltage V in volts in an electrical circuit varies inversely as the resistance F ohms The voltage in the circuit is 10 volts when the resistance is 120 ohms Part A Write the equation of the inverse variation Part B Find the voltage in the circuit when the resistance is 80 ohms

2 1 Several transformations of f x x combine to result in the graph of function g shown to the right Explain in words what transformations of f result in this graph

0 5 0 5 5 The graph of the function f is shown below The domain of f is 0 50 Find the domain and range of g x 4f x 10 20 30 40 50

3 The graph below represents function f Graph g x 2f x 1 2

2 What is the equation for function g which is f x 2x 3x 1 reflected across the x axis

A tank initially contains 4 gallons of pure water A salt solution containing 1 2 lb of salt per gallon is then poured into the tank at 4 gallons per minute while the well mixed solution is simultaneously drained at 3 gallons per minute Find the amount of salt in the tank after 4 minutes Simplify your final answer it should be given in the form a b where a and b are positive integers

The process to determine which normal human the source of the person s problem V matter most uses knowledge from the ability to ask relevant 2 and an understanding of and an attitude that finding

Multiply 3x 4x 2x 5 2 3x 4x 2x 5 Simplify your answer

The legislature in a state has 42 seats Apportion these seats to the five counties below using Jefferson s method

A manager of a store that sells and installs spas wants to prepare a forecast for January February and March of next year Her forecasts are a combination of trend and seasonality She uses the following equation to estimate the trend component of monthly demand F 60 5t where t 0 in June of last year Seasonal relatives are 87 for January 91 for February and 1 02 for March What demands should she predict Round your answers to 2 decimal places Answer is complete but not entirely correct Forecast Month January of the next year February of the next year March of the next year 82 65 x 91 00 107 10

Label all of the Parts of Speech N Noun V Verb PN Pronoun Adj Adjective Adv Adverb P Preposition Rain forests are tropical places with tall trees and tons of rain

Parent function f x x is translated 2 units to the left and reflected across the x axis to result in function g A Write an equation for g B f is graphed below Graph g 2 0 2

10 Write a quadratic function with real coefficients that has a root of 3 i

9 Write a quadratic function with rational coefficients that has roots 7 and 7

2 What is the remainder if f x x 5x 6x 10 is divided by x 33

2 Use synthetic division to divide x x 3 6x 4x 8 by x 2

10 What s the product of 3 23 and 14 OA 54 OB 52 45 O C 4245 O D 52 415