Questions

4 Let f n 3n 5 and g n n be two functions defined on Z Which of the functions f g fog gof are injective Please explain precisely why 5 Show that the operation r y x y xy is commutative associative and distributive with respect to x y x y 1 Which element is the inverse of 4 with respect to

Solve the following for x a 3x 11 2 b x5 2 2x 1 c 3x 1 2 x 3 2 marks 2 marks 2 marks

Find the quotient and remainder for x 4x 4x 10 x 3 5 marks

A school had a fund raising event The revenue came from three resources ticket sales auction sales and donations Ticket sales account for of the total revenue auction sales account for of the total revenue What fraction of the revenue came from donations of the revenue came from donations

Topographic Map Figure 17 shows the topographic map we used in Example 8 of this section Recall that Stacey is at position S and Amy is at position A In Figure 19 Travis a third hiker is at position T 17 If the distance between A and T on the map in Figure 19 is 0 5 inch find each of the following a The horizontal distance between Amy and Travis b The difference in elevation between Amy and Travis c The angle of elevation from Travis to Amy 0001 1546 Bishop Peak 1 in 1600 ft 1200 1600 O Contour interval 40 ft FIGURE 17

17 If the distance between A and T on the map in Figure 19 is 0 5 inch find each of the following a The horizontal distance between Amy and Travis b The difference in elevation between Amy and Travis c The angle of elevation from Travis to Amy 0 1000 SO 1546 1 in 1600 ft Bishop Peak 1200 1600 Contour interval FIGURE 17 000 40 ft

What are all possible shapes of trees of height 2 with k leaf 01 02

0 1000 S 1546 1 in 1600 ft 1600 Bishop Peak 2002 Contour interval 40 ft FIGURE 17 18 If the distance between S and T on the map in Figure 17 is inch find each of the following a The horizontal distance between Stacey and Travis b The difference in elevation between Stacey and Travis c The angle of elevation from Travis to Stacey 19 Lompoc California is 18 miles due south of Nipomo Buellton California is due east of Lompoc and S 65 E from Nipomo How far is Lompoc from Buellton 20 A tree on one side of a river is due west of a rock on the other side of the

Sketch the graph of each line 19 y x 4 43 75 10

Let f x be the number in thousands of computers sold when the price is x hundred dollars per computer Interpret the statements f 25 30 and f 25 6 Then estimate the number of computers sold if the price is set at 2525 pe computer What does f 25 30 imply OA When the price per computer is 2500 for every 100 price increase the sales increase by 30 000 computers OB When the price per computer is 3000 for every 100 price increase the sales increase by 25 000 computers OC 30 000 computers are sold when the price is set at 250 OD 30 000 computers are sold when the price is set at 2500

Algebra X Slope intercept Form Find the slope of each line 1 3 SOR 2

Sketch the graph of each line 19 y x 4 21 y 4x 5 5 310 5 4 3 2 10 3 20 y 5x 1 2 10 22 y x 5 2 4 3 2 10

5 3 3 you fe 4 Algebra 13DC5 3 and 3 Name Slope intercept Form Worksheet Find the slope of each line 1 0 1 x 4 0 X 0 Y Y Y 3 1 XX 3 1 573 5 3 SOR 2 X X X2 X 3 33 4 4 3 2 1 3 3 0 ZI Elore 1 C1F 13 2 6 Name Eliya Love Date M 4 38 Us tercept form 3 1 2 Find the slon ato 2 1 2029 1 Period th X 1 1 x 3 X 1 X 3 X X 4 STOP 1 3 3 1 25 2 3 4 3 S

The point P 4 1 lies on the curve y x 3 a If Q is the point x x 3 use your calculator to find the slope of the secant line PQ correct to six decimal places for the following values of x 1 3 5 0 585786 ii 3 9 iii 3 99 iv 3 999 v 4 5 vi 4 1 vii 4 01 viii 4 001 b Using the results of part a guess the value of the slope of the tangent line to the curve at P 4 1 0 5 c Using the slope from part b find an equation of the tangent line to the curve at P 4 1 y d Sketch the curve two of the secant lines and the tangent line

Let f t be the temperature of a cup of coffee t minutes after it has been poured Interpret f 5 180 and f 5 8 Estimate the temperature of the coffee after 5 minutes and 12 seconds that is after 5 2 minutes What does f 5 180 imply OA 5 minutes after the coffee has been poured the temperature of the cup of coffee is rising at a rate of 180 degrees per minute OB 180 minutes after the coffee has been poured the temperature of the cup of coffee is 5 degrees OC 5 minutes after the coffee has been poured the temperature of the cup of coffee is 180 degrees OD 180 minutes after the coffee has been poured the temperature of the cup of coffee is rising at a rate of 5 degrees per minute

Ay 500 500 000 500 000 500 000 00 0 0 2 4 6 8 10 12 14 16 18 Years after 1980 e blue curve shows national health expenditures in billions of dollars The red curve shows its ivative C National health expenditures in billions of dollars from 1980 to 1997 are given by the function f t in the graph to the left a How much money was being spent at the beginning of 1982 billion

13 Dimensions of a Mirror A person standing 150 centimeters from a mirror notices that the angle of depression from his eyes to the bottom of the mirror is 12 while the angle of elevation to the top of the mirror is 11 Find the vertical dimension of the mirror See Figure 16 150 cm

The following figure shows the four possible configurations of a double red B 4 The following figure shows the rearrangement that fixes the Double Red violation sider this tree that was obtained by inserting J into a red black tree using the algorithm fo ary search tree and coloring the new node red We now have a double red violation C F G K J 12 H OG What is the right child of F after the rearrangement OK H OG What is the left child of J after the rearrangement OK OJ What is the left child of H after the rearrangement OK OJ OH

ecologist wishes to find the height of a redwood tree that is on the other side of a creek as shown in Figure 14 From point A he finds the angle of elevation to the top of the tree is 10 7 He then walks 24 8 feet at a right angle from point A and finds angle B is 86 6 What is the height of the tree FIGURE 14 24 8 B

15 Angle of Depression From a plane 3 000 feet in the air the angle of depression to the beginning of the runway is 3 50 What is the horizontal distance between the plane and runway That is if the plane flew at the same altitude how far would it be to the runway Give your answer to the nearest tenth of a mile 5 280 feet 1 mile

Solve each of the following problems In each case be sure to make a diagram of the situation with all the given information labeled 1 tsosceles Triangle The two equal sides of an isosceles triangle are each 42 centimeters If the base measures 30 centimeters find the height and the measure of the two equal angles Round your answer to the nearest tenth 2 Equilateral Triangle An equilateral triangle one with all sides the same length has an altitude of 4 3 inches Find the length of the sides 3 Length of an Escalator How long should an escalator be if it is to make an angle of 33 with the floor and carry people a vertical distance of 21 feet between floors Round to the nearest tenth 4 Height of a Hill A road up a hill makes an angle of 5 with the horizontal If the road from the bottom of the hill to the top of the hill is 2 5 miles long how high is the hill 5 Circus Tent A rope from the top of a circus tent pole is 72 5 feet long and is anchored to the ground 43 2 feet from the bottom of the pole What angle does the rope make with the pole Give your answer to the nearest tenth of

Solve the equation 5 q 2q 3 1 The solution set is 3 10

a b c d e f g h lim g t t 0 lim g t t 0 lim g t 2 lim g t t 2 lim g t t 2t lim g t t 2 g 2 lim 2 4 t

Use the given graph of f to state the value of each quantity if it exists If an answer does not exist enter DNE a b c d e f X 2 lim f x lim f x X 2 lim f x X 2 f 2 lim f x 4 X 4 2 f 4 0 4

Ay 000 500 3000 2500 2000 1500 1000 500 0 0 2 6 8 10 12 14 16 Years after 1980 The blue curve shows national health expenditures in billions of dollars The red curve shows its derivative Q 4 National health expenditures in billions of dollars from 1980 to 1994 are given by the function f t in the graph to the left a How much money was being spent at the beginning of 1983 700 billion b Approximately how fast was the rate of spending increasing in 1990 300 billion per year c One trillion dollars was being spent at the beginning of which year

Let f t be the temperature of a cup of coffee t minutes after it has been poured Interpret f 5 190 and f 5 8 Estimate the temperature of the coffee after 5 minutes and 36 seconds that is after 5 6 minutes What does f 5 190 imply EXOD OA 190 minutes after the coffee has been poured the temperature of the cup of coffee is rising at a rate of 5 degrees per minute OB 190 minutes after the coffee has been poured the temperature of the cup of coffee is 5 degrees C 5 minutes after the coffee has been poured the temperature of the cup of coffee is rising at a rate of 190 degrees per minute OD 5 minutes after the coffee has been poured the temperature of the cup of coffee is 190 degrees

Solve each of the following problems In each case be sure to make a diagram of the situation with all the given information labeled 1 Isosceles Triangle The two equal sides of an isosceles triangle are each 42 centimeters If the base measures 30 centimeters find the height and the measure of the two equal angles Round your answer to the nearest tenth 2 Equilateral Triangle An equilateral triangle one with all sides the same length has an altitude of 4 3 inches Find the length of the sides 3 Length of an Escalator How long should an escalator be if it is to make an angle of 33 with the floor and carry people a vertical distance of 21 feet between floors Round to the nearest tenth 4 Height of a Hill A road up a hill makes an angle of 5 with the horizontal If the road from the bottom of the hill to the top of the hill is 2 5 miles long how high is the hill 5 Circus Tent A rope from the top of a circus tent pole is 72 5 feet long and is anchored to the ground 43 2 feet from the bottom of the pole What angle does the rope make with the pole Give your answer to the nearest tenth of a degree 6 Leaning Ladder A ladder is leaning against the top of a wall that is 7 0 feet high If the bottom of the ladder is 4 5 feet from the wall what is the angle between the ladder and the wall Give your answer to the nearest tenth of a degree 7 Angle of Elevation If a flagpole that is 73 feet tall casts a shadow 51 feet long what is the angle of elevation of the sun Give your answer to the nearest

comes to playing basketball and tall people are more efficient because they can ch the basket easily allowing for more points per game as well as more rebounds and blocked shots If you watch National Basketball Association NBA games regularly you certainly notice that many players are quite tall We will explore the distribution of NBA player heights using a sample of players active in the 2019 2020 season by making a histogram of HEIGHT INCHES with bins stating at 68 inches and bin width of 2 inches We will then determine the z scores for players who are 71 inches 5 11 and b 84 inches 7 0 The dataset consists of the NBA player s name team and height measured in inches for players active in the 2019 2020 season Aaron Gordon Player Aaron Holiday Adam Mokoka Abdel Nader Admiral Schofield WAS Z Variable symmetric Numerical Variable Team Height Inches ORL Data value a x x S IND LUSE SALT OKC Import the dataset into SALT for analyzing Data value b x x CHI After you have clicked the tab for your selected topic and read the problem answer the questions below a Use SALT to summarize the data and fill in the following table rounding values to four decimal places as needed Data value a is N 80 529 73 77 77 77 b Create a histogram with Starting Point and Bin Class Width values asked for The distribution for this variable is mound shaped and is Mean 78 393 Our sample s minimum value is not Standard Deviation 3 4505 c Determine the relative standing for the two data values of interest using the z score formula appropriate for samples Round your answers to two decimal places standard deviations below Median 78 Find the data value with a z score of 3 rounded to two decimal places x 2 5 X Minimum Value standard deviations above to determine the number of standard deviations each data value is away from the mean Find the data value with a z score of 3 rounded to two decimal places X Z S X 69 the mean whereas data value b is the mean Remember to take the absolute value of the z scort maximum is histogram in SALT it can be observed that almost all A Maximum Value 89 d Most data points are within three standard deviations of the mean In other words most observations will have a score that is larger than 3 and less than 3 at least roughly further than 3 standard deviations below the mean Our sample s further than 3 standard deviations above the mean Upon further inspection of the observations would have a z score between 3 and

Solve each of the following problems In each case be sure to make a diagram of the situation with all the given information labeled 1 Isosceles Triangle The two equal sides of an isosceles triangle are each 42 centimeters If the base measures 30 centimeters find the height and the measure of the two equal angles Round your answer to the nearest tenth 2 Equilateral Triangle An equilateral triangle one with all sides the same length has an altitude of 4 3 inches Find the length of the sides 3 Length of an Escalator How long should an escalator be if it is to make an angle of 33 with the floor and carry people a vertical distance of 21 feet between floors Round to the nearest tenth 4 Height of a Hill A road up a hill makes an angle of 5 with the horizontal If the road from the bottom of the hill to the top of the hill is 2 5 miles long how high is the hill 5 Circus Tent A rope from the top of a circus tent pole is 72 5 feet long and is anchored to the ground 43 2 feet from the bottom of the pole What angle does the rope make with the pole Give your answer to the nearest tenth of a degree

3 Find exact values of the six trigonometric functions for the angle by hand Do not use a calculator 4 sin 3 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Sketch the graph of the function and compare the graph to the grap 3 f x arcsin Step 1 Recall the definition of the inverse trigonometric functions The invers sine function is defined by y arcsin x if and only if sin y x with appropriate restrictions on the domain According to this definition the equation equivalent to 6

At a restaurant If a party has eight or more people the gratuity is automatically added to the bill If x is the cost of the meal then the total bill C x with a 17 gratuity and an 8 sales tax is given by C x x 0 08x 0 1x Evaluate C 280 and interpret the meaning in the context of this problem Round to the nearest cent If the cost of the food is S then the total bill including tax and tip Is S X 3

Find an expression for a cubic function f if f 4 160 and f 4 f 0 f 5 0 Step 1 A cubic function generally has the form f x ax bx2 cx d If we know that for some x value x p we have f p 0 then it must be true that x p is a factor of f x Since we are told that f 5 0 we know that x 5 is a factor Step 2 Similarly since f 4 0 then f x has the factor x 4 I to obtain a Step 3 Since f x has the factors x x 5 and x 4 then we must have f x a x x 5 x 4 for some as yet unknown multiplier a However since it was given that f 4 160 we substitute 4 for x and 160 for f x and solve f 4 160 a 4 4 5 4 4 f x 5 Step 4 Using all the information we found we can now write the full expression x 4 and since f 0 0 then f x has the factor

Question 28 of 28 1 point 1 Question Attempt 1 of Unlimited Determine the average rate of change of the function on the given Interval Express your answer in exact simplest form f x x 1 Part 1 of 3 a on 2 0 The average rate of change of the function is Part 2 of 3 b on 2 5 The average rate of change of the function is 00

9 For a certain angle in the first quadrant it is true that sin cos 0 Which of the following statement s is guaranteed to be true 1 tan cot 0 II csc sec 0 III 0 4 A I only B II only C I and III only D I II and III

Evaluate the function f x x 6x for the given value of x Simplify your answer f x h

17 18 and 3 19 The slope of the line is 20 00 21 22 Determine the slope of the line passing through the given points Write your answer in exact simplified form 5 2 4 3 23 24

13 Find and simplify f x h Simplify your answer f x 7x 5x 6 f x h

The graph of f in the figure has vertical asymptotes at x 1 and x 5 Analyze the following limits a lim f x b lim f x X 1 X 1 e lim f x d lim f x X 5 X 5 Ay 10 c lim f x X 1 f lim f x X 5 Q Q G UA lim f x X 1 OB The limit does not exist and is neither oo nor 00 c Select the correct choice and if necessary fill in the answer box to complete your choice lim f x X 1 OB The limit does not exist and is neither oo nor co O A d Select the correct choice and if necessary fill in the answer box to complete your choice OA lim f x X 5 OB The limit does not exist and is neither o nor 00 e Select the correct choice and if necessary fill in the answer box to complete your choice OA lim f x x 5 OB The limit does not exist and is neither co nor co f Select the correct choice and if necessary fill in the answer box to complete your choice OA lim f x x 5 OR

6 17 Find two possible sets of 8 side lengths for AABC In AABC csc A A B C A B

Calculate the derivative of the following function dy dx 1 y 5x 4 11 5 3 5x 1

A student decides to finance a used car over a 6 yr 72 month period After making a down payment of 1000 the remaining cost of the car including tax and Interest is 15 192 The amount owed y A t in S is given by A t 15 192 211 t where t is the number of months after purchase and Ost 72 Determine the t intercept and y intercept and interpret their meanings in context Amount Owed on Vehicle after r Months Amount Owed Part 0 4 Part 1 of 4 12000 4000 2000 O A 15 192 211 Number of Months t

11 Find csc if cot 0 7 co 3

Evaluate the function f x x 6x for the given value of x Simplify your answer f x h

3 Explain why sec is always greater than or equal to 1 or less than or equal to 1

Find the exact values of the six trigonometric functions of the angle 1560 sin 1560 cos 1560 tan 1560 Simplify your answers Type exact answers using radicals as needed Use integers or fractions for any numbers in the expression Rationalize any denominators

Use a calculator to find the trigonometric value tan 37 tan 37 Type an integer or decimal rounded to four decimal places as needed

Use a calculator to find the decimal approximation for the following value tan 9 tan 9 Round to seven decimal places as needed

nd exact values of the six trigonometric functions by hand for the following angle Do not use a T 4 e exact values of the six trigonometric functions for the given angle are below sin 4 T COS tan T CSC sec cot T 4 T 4 I II Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Question Use the washer method to calculate the volume of the solid formed when the region bounded by y 2x and y 2 5 revolved around the the line y 3 Provide your answer below