Questions

The table shows how the time it takes a train to travel between two cities depends on its average speed Average Speed x mph 32 Time y hr 5 40 4 50 64 32 2 5 This rational function choose your answer hour choose your answer y 160 x 2 25 points y 6 4 x What does the numbe y x 160 y x 6 4 A models the time y in hours that it takes the train to travel between the two cities at an average speed of x miles p action that models the situation choose your answer

hombus 2 3 mZ1 21 Kite mz2 429 m21 mz2 2 mz3 m23 3 46

In 12 17 Find the indicated information for each quadrilateral 12 Parallelogram ABCD B 312 5x 8 y 61 18 D 13 Kite LMNP 3y 6 L Sy 9 X M N 9x 15 12x 3

parallelogram rectangle square trapezoid rhombus kite 26 Identify all of the terms from the following list that apply to each figure quadrilateral 24 H 25 26 H H

16 Rectangle WXYZ W Y Z X WZ 10x 7 XY 6x 19 x 17 Square DEFG D 8x y E x 10x 2x 24 y F G 7x 9

16p

Find the maximum and minimum values of the function and the values of x and y where they occur F 5x 36y subject to 6x 4y 23 4x 6y 18 X 0 y 0 a What is the maximum value of the function b What are the x and y values for the maximum Type an ordered pair c What is the minimum value of the function d What are the x and y values for the minimum Type an ordered pair Time left

Find 7A 8B 1 4 7 7 A 9 0 B 5 10 10 0 10 7 Select one O a O b 63 84 7A 8B 103 80 150 56 63 84 7A 8B 103 80 150 56 C 7A 8B 63 103 150 84 80 56 O d 7A 8B 63 103 150 84 80 56

4 Find TQ R 2x 5 14 2x 1 2 P T 18 S S

Among the following electrons which type has the highest energy Backscattered electrons Secondary electrons

2 g x 2x 4 1 f x x 1 15 h x 5 x 2 2 f x 2 2x 16 f x x 5 2 h x x 1 4

Any solid material if conductive exhibits cathodoluminescence CL True O False

Find the inverse of each function 9 f n n 5 10 f x 5x 3 11 f n 4 2 n 2 12 f x x 3 2

2 f x x 3 g x 2x 5 Find f 3 g 3 4 f t 2t 1 g t 1 2 Find 3 10 2g 10 6 f x x 1 g x x 2 Find 2f 3 5g 3 8 g x x 3 Find g g 0

Find g 6 h 6 5 f n 4n 4 g n 3n 2 Find f g 8 7 g x 3x 2 f x 2x 2 Find g 1 3 1

X rays only happen when high energy electrons bombard metals but not for nonmetals True O False

Complete the following without using Table12 1 Note Round the Total amount and Total interest to the nearest cent Time Principal Rate of compound Compounded Periods Rate Total amount Total interest years interest 1 410 8 Quarterly

Tony Ring wants to attend Northeast College He will need 50 000 5 years from today Assume Tony s bank pays 6 interest compounded semiannually What must Tony deposit today so he will have 50 000 in 5 years Use the Table 12 3 provided Note Do not round intermediate calculations Round your answer to the nearest dollar amount Amount to be deposited

Consider the area between the graphs x 4y 26 and x 6 y This area can be computed in two different ways using integrals First of all it can be computed as a sum of two integrals where a 10 b 26 c 58 and f x 24 g x n 6 Alternatively this area can be computed as a single integral where a 8 B 4 and h y 26 4y 2 6 Either way we find that the area is C f x dz 9 a de h y dy

Jazelle Momba wants to visit her family in Zimbabwe in 2028 which is 6 years from now She knows that it will cost approximately 8 300 including flight costs on the ground costs and extra spending money to stay for 4 months If she opens an account that compounds interest at 6 semiannually how much does she need to deposit today to cover the total cost of her visit Use Table 12 3 Note Round your answer to the nearest dollar Deposit

Complete the following using present value Use the Table 12 3 Note Do not round intermediate calculations Round the PV factor to 4 decimal places and final answer to the nearest cent Amount desired at end of period On PV Table 12 3 Length Rate Compounded PV factor used of time Periods used Rate used PV of amount desired at end of period

Sam Long anticipates he will need approximately 226 200 in 15 years to cover his 3 year old daughter s college bills for a 4 year degree How much would he have to invest today at an interest rate of 8 compounded semiannually Use the Table provided Note Do not round intermediate calculations Round your answer to the nearest cent Amount

Lynn Ally owner of a local Subway shop loaned 52 000 to Pete Hall to help him open a Subway franchise Pete plans to repay Lynn at the end of 10 years with 6 interest compounded semiannually How much will Lynn receive at the end of 10 years Use the Table provided Note Do not round intermediate calculations Round your answer to the nearest cent Future value

Two sides of a triangle are 5 m and 12 m in length and the angle between them is increasing at a rate of 0 06 rad s Find the rate at which the area of the triangle is increasing when the angle between the sides of length is 49 rad 3 m s

Water is leaking out of an inverted conical tank at a rate of 12 500 cm min at the same time that water is being pumped into the tan at a constant rate The tank has height 6 m and the diameter at the top is 4 m If the water level is rising at a rate of 20 cm min when the height of the water is 2 m find the rate at which water is being pumped into the tank Round your answer to the nearest integer cm min

Find the area of each regular polygon Round to the nearest tenth 1 2 8 m 10 cm

Find the area of the region bounded by the parabola y 2x the tangent line to this parabola at 3 18 and the x axis 125 6

A r 1 a sqrt a 2 x 2 The answer above is NOT correct In electromagnetic theory the magnetic potential u at a point on the axis of a circular coil is given by where A r a are constants Compute u a 8 u Ar So 172 2 3 2 da

2 1 point The Triangle Inequality states that if u and are vectors in R then This theorem merely states that the length of a side of a triangle is less than the sum of the lengths of the other two sides Verify the Inequality for the vectors 1 1 0 and 0 1 2

1 1 point The Cauchy Schwarz Inequality tells us that if we have two vectors u and in R then Note that on the left stands for absolute value and on the right denotes the length of a vector Verify the Cauchy Schwarz Inequality for 1 1 0 and 0 1 1

Find the area of the region enclosed between y 4 sin z and y 2 cos x from x 0 to 2 0 3 Hint Notice that this region consists of two parts

The boundaries of the shaded region are the y axis the line y 1 and the curve y x Find the area of this region by writing as a function of y and integrating with res y YA y 1 0 1 1 x

Sketch the region enclosed by x y 20 and x y Decide whether to integrate with respect to x or y Then find the area of the region 204 8

Determine whether the integral is divergent or convergent If it is convergent evaluate it If not state your answer as divergent 8 4t tdt

5 Verify that f and g are inverses f x x 7 g x 2x 14

Determine whether the integral is divergent or convergent If it is convergent evaluate it If not state your answer as divergen 9x2 dx 1 x6

15 A road construction company is considering the purchase of a new bulldozer They can purchase one for 380 000 if they pay in one installment Or they can pay 120 000 every quarter for one year Compute the effective annual rate of interest for the quarterly payment Use incremental IRR analysis to solve Fill in the incremental difference table below then calculate the incremental IRR Quarter Annual payment Qtrly payment Incremental diff annual qtriy 0 1 PV PMT

Determine whether the integral is divergent or convergent If it is convergent evaluate it If not state your answer as divergent 00 xe dx

2 5 2 1 1 2 N 3 7 8 6 Based on the graph above determine the amplitude midline and period of the function Amplitude Period

You have 5 000 in the bank comfortably earning 48 interest compounded monthly Your cousin needs 5 000 to buy a new car In order to get the same total return what interest rate r should you request from her if the money you lend her is to be compounded continuously Exact Interest rate without using a calculator r 48 Interest rate as a percent rounded to 2 decimal places 48

Patricia will draw 8 cards from a standard 52 card deck with replacement Which of the following are not events in this experiment Select all that apply Select all that apply drawing 8 hearts drawing 8 cards drawing 1 card

What is one reason arteries can withstand higher blood pressure than veins Arteries contain only oxygenated blood Arteries have thick walls that contain layers of muscle and connective tissue Arteries contain all types of blood cells whereas veins contain only erythrocytes Arteries have one way valves to prevent blood from flowing bacloud PL

Figure 39 1 Which area in Figure 39 1 indicates a complete sarcomere 3 2 4 5

5x List all points on the graph of y tan x on the interval 2 that have a y coordinate of 3 2

e top of a ladder slides down a vertical wall at a rate of 0 675 m s At the moment when the bottom of the ladder is 6 m from the wall it slides away from the wall at a rate of 0 9 m s How long is the lad

wo sides of a triangle have lengths 11 m and 18 m The angle between them is increasing at a rate of 2 min How fast is the length of the third side increasing when the angle between the sides of fixed length is 60 Round your answer to three decimal places m min

EXAMPLE 5 A man walks along a straight path at a speed of 5 ft s A searchlight is located on the ground 12 ft from the path and is kept focused on the man At what rate is the searchlight rotating when the man is 5 ft from the point on the path closest to the searchlight SOLUTION We draw the figure to the left and let x be the distance from the man to the point on the path closest to the searchlight We let be the angle between the beam of the searchlight and the perpendicular to the path We are given that dx dt 5 ft s and are asked to find de dt when x 5 The equation that relates x and 0 can be written from the figure X tan 0 x tan 0 Differentiating each side with respect to t we get SO dx dt de dt de dt dx dt 5 When x 5 the length of the beam is 13 so cos 0 12 and 13 de dt The searchlight is rotating at a rate of rad s

Gravel is being dumped from a conveyor belt at a rate of 15 ft3 min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal How fast is the height of the pile increasing when the pile is 13 ft high Round your answer to two decimal places x ft min

Two cars start moving from the same point One travels south at 48 mi h and the other travels west at 20 mi h At what rate is the distance between the cars increasing two hour

A baseball diamond is a square with side 90 ft A batter hits the ball and runs toward first base with a speed of 28 ft s 90 ft a At what rate is his distance from second base decreasing when he is halfway to first base Round your answer to one decimal place ft s b At what rate is his distance from third base increasing at the same moment Round your answer to one decimal place ft s