Basic Math Questions and Answers

Verify the identity csct 1 cott B Choose the sequence of steps below that verifies the identity OA O C O D cott csct 1 csct 1 csct 1 csct 1 cott cott csct 1 csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 csct 1 csct 1 sc t 1 csct 1 cott csct 1 csc t 1 cott csct 1 CSC csc t 1 cott csct 1 csct 1 csct 1 csc t 1 cott csct 1 cott csct 1 cott cot t cott csct 1 csct 1 cot t cott csct 1 cot t cott csct 1 cott cott csct 1 cott csct 1 cott csct 1 cott csct 1

cies Prove the given identity sin xsec x cos x csc x sec xcsc x Choose the correct proof below A sin xsec x cos xcsc x 1 sin x cOS X sin x cos x 2 x cos X 2 sin sin x cos x 1 sec x csc x OC sin xsec x cos xcsc x sin x 1 cos x COS X sin x cos x 2 sin x cos sin x cos x 1 sec x csc X X sin x Question 7 of 10 OB sin xsec x cos xcsc x 1 sin x cOS X sin x cos 2 sin x cos x 1 sin x cos x sec x csc X This quiz 20 poin This question 2 OD sin xsec x cos xcsc x 1 sin x COS X X cos X sin x cos x sin x cos x 1 sin x cos x sec x csc X 1 sin

K Prove the given identity cos 8 cot 8 csc 8 sin 8 Choose the correct proof below OA cos 8 cot 8 csc 8 cos 8 OC cos 8 cot 8 csc 8 cos 8 cos 8 sin 8 OD cos 8 cot 8 csc 8 cos 8 sin 8 sec8 OB cos 8 cot 8 csc 8 cos 8 cos 8 sin 8 cos 8 sin 8 cos 8 sin 8 1 sin 8 1 sin 8 1 sin 8 Question 4 of 10 cos 8 1 sin 8 cos 8 1 sin 8 sin 8 cos2 8 1 cos 8 1 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8

Establish the identity cos x sin x 1 2 sin x Using the identity sin x cos x 1 make the appropriate substitution Which of the followin O A 1 cos sin 1 2 sin x OB 1 sin sin 1 2 sin O C 1 sin sin 1 2 sin x 1 2 sin 1 2 sin a 2 1 2 sin 2 1 2 sin a 1 2 sin 1 2 sin x OD 1 cos sin 1 2 sin x 2 1 2 sin 1 2 sin x

tities Prove the given identity cot x sec xcsc x tan x Choose the correct proof below OA cot x sec xcsc X 1 1 sin x cos x sin x sin x cos x 2 1 cos X COS X sin x cos x sin 2 tan x OC cot x sec xcsc x cOS X 1 1 sin x sin x X cos x 2 1 cos X tan x sin x cos x sin x sin x cos x Question 2 of 10 OB cot x sec xcsc x cOS X sin x sin x cos x This quiz This ques 2 cos X 1 tan x sin x cos x sin x OD cot x sec xcsc x cos x sin x 1 cos x sin x cos x Sin sin x cos x tan x

Verify the following identity 1 tan 0 2 cos 20 1 tan 0 Which of the following four statements establishes the identity 2 1 tan 0 1 tan 0 2 1 tan 0 O A cos 20 2 sin 0 cos 0 OB cos 20 cos 0 sin 0 OC cos 20 cos 0 sin 0 O D cos 20 2 sin 0 cos 0 2 csc 0 2 1 tan 0 2 sec 0 2 1 tan 0 csc 0 2 1 tan 0 sec 0 2 1 tan 0 1 tan 2 2 1 tan 0 1 tan 0 2 1 tan 0 2 1 tan 0 2 0

Five lbm of R 134a is expanded isentropically in a closed system from 100 psia and 100 F to 10 psia Determine the total heat transfer and the work production for this process Use the tables for R 134a The total heat transfer is Btu The work production for this process is Btu

Problem 07 027E Isothermal heat rejection process of Carnot cycle During the isothermal heat rejection process of a Carnot cycle the working fluid experiences an entropy change of 0 760 Btu R The temperature of the heat sink is 95 F Sink 95 F Heat 95 F Carnot heat engine roblem 07 027E a Heat transfer to working fluid in a heat rejection process he amount of heat transfor is etermine the amount of heat transfer

A radioactive material decays according to the function A t Age 0 0244t where Ao is the initial amount present and A is the amount present at time t in years Assume that a scientist has a sample of 400 g of the radioactive material a What is the decay rate of the radioactive material b Graph the function using a graphing utility c How much radioactive material is left after 30 years d When will only 300 grams of the radioactive material be left e What is the half life of the radioactive material a The decay rate of the radioactive material is 2 44 Type an integer or a decimal b Graph the function Choose the correct graph below The graphing window is 0 800 100 by 0 1 0 25 A Q B O c There will be about gram s of the radioactive material left after 30 years Do not round until the final answer Then round to the nearest tenth as needed O C 20 Q OD Sa Q

A plane has an airspeed of 127 km h It is flying on a bearing of 85 while there is a 27 km h wind out of the northeast bearing 225 What are the ground speed and the bearing of the plane The ground speed is km h Round to the nearest tenth as needed

Let A 3 6 8 Which of the following relations on A are antisymmetric Select all that apply A 3 3 6 8 8 3 8 8 B 3 6 3 8 6 8 8 3 OC 3 6 3 8 6 8 8 6 OD 3 3 6 6 8 8

Find the adjacency matrix for the relation r 3 9 6 5 8 5 6 9 from the set A 3 6 8 to the set B 3 5 9

Let A 3 4 8 Which of the following relations on A are symmetric Select all that appl DA 3 8 4 8 8 3 8 4 8 8 B 3 3 3 4 4 3 4 8 8 8 OC 3 3 4 4 OD 3 4 3 8 4 3 4 8 8 3

The link below gives the Hasse diagram for a poset with partial ordering Click this link to view the Hasse diagram Which of the statements below are true Select all that apply DA bza OB a a OC c f OD d b DE b d OEde e a b C

4 1 4 relation r relation 3 2 3 4 relation relation r 3 2 3 4 attempts remaining The link below gives the digraphs for four different relations r1 12 13 14 on the set A 1 2 3 4 Click this link to view the digraphs Which of these relations are antisymmetric Select all that apply Be able to explain your answers OA TA OB rs DC n OD 12

Problem 07 021 Heat transferred between two reservoirs Heat is transferred at a rate of 2 kW from a hot reservoir at 900 K to a cold reservoir at 300 K Calculate the rate at which the entropy of the two reservoirs changes Round the final answer to three decimal places The rate at which the entropy of the two reservoirs changes is Is the second law satisfied Click to select Click to select Yes No kW K

11 az a 160 B 7 Use decimal notation Give your answers to three decimal places Include the degree symbol in your answers where nee

Macmillan Learning Solve the given triangle Use degree measure B A 55 A 5 Use decimal notation Give your answers to three decimal places Include the degree symbol in your answers where n C A

Macmillan Learning Find the area of the triangle in the figure 5 area 3 Macmillan Learning Crauder et al Preparation for Calculus le 2022 Give an exact answer Use symbolic notation and fractions where needed

oblem 1 Use the Law of Sines of the Law of Cosines when it applies Solve each triangle and assume standard labeling a b 3 4 c 2 8 A 82 b A 30 a 20 B 45 c A 30 a 5 b 5 2 d a 19 b 2 c 3 e a 40 2 A 135 B 30 f A 63 C 55 a 8 3

ne opens an account at the local bank by depositing 50 of his birthday money He continues to deposit 50 each month for 5 years If the account 3 25 interest compounded monthly how much is in the account after 5 years 0 10000 Word Limit

Let A 3 6 8 Which of the following relations on A are antisymmetric Select all that apply OA 3 3 6 8 8 3 8 8 B 3 6 3 8 6 8 8 3 OC 3 6 3 8 6 8 8 6 P 3 3 6 6 88

Problem 3 A pole tilts towards the sun at an 8 angle from the vertical and it casts a 22 foot shadow The angle of elevation from the tip of the shadow to the top of the pole is 43 How tall is the pole Include a diagram

A service ramp is 20 feet long and makes an angle of 10 with the horizontal See the figure It is found to be out of compliance with regulations of the Americans with Disabilities Act ADA and must be replaced with a new ramp that makes an angle of 5 with the horizontal New ramp length 20 50 10 How long is the new ramp Give your answer to the nearest whole number feet

4 4 attempts remaining The link below gives the diagraph for a relation r on t set A 1 2 3 4 Click this link to view the graph Find all the elements in r Enter your answer below a list of ordered pairs separated by commas Answer r

The strength of a beam is directly proportional to its width and the square of its depth but inversely proportional to its length A beam that is 4 inches wide 8 inches deep and 8 feet long can support a weight of 1920 pounds If the same type of beam that is 7 inches wide and 4 inches deep can support 480 pounds how long is the beam The beam is feet long Type a whole number

Assume that the amount of water that Mario uses for irrigation at his vineyard is inversely proportional to the amount of rainfall If he uses 80 000 gallons during a month in which there is 3 inches of rain how much water would he use in a month that has 6 inches of rain gallons Round to the nearest integer as needed

To determine the number of trout in a lake a conservationist catches 131 trout tags them and throws them back into the lake Later 56 trout are caught 14 of them are tagged How many trout would the conservationist expect to be in the lake The conservationist would expect that there are trout in the lake

Assume that r varies jointly as s and b2 If r 525 when s 6 and b 5 what is the value of b when s 4 and r 1134 Points 0 of

Solve the following variation problem by first writing the variation as an equation and finding the constant of variation Then answer the question Assume that r varies inversely as s If r 8 when s 1 2 find r when s 1 Which of the following is the appropriate problem solving method OA Try a simpler version of the problem B The splitting hairs principle C Choose good names for unknowns OD Draw pictures C

K 3 If D varies inversely as C and D when C5 find D when C 24 D Type an integer or a simplified fraction

Assume that y varies jointly as x and w and inversely as z If y 15 when x 2 5 w 8 and z 20 what is the value of y when x 7 w 7 and z 14 y Type an integer or a simplified fraction TEE

K Find the missing number in the proportion 12 3 x w 8 x

K Solve for x in the following proportion 2 x 6 21

A country s population in millions in 2002 and 2010 are given below Use this information and the exponential model A P 1 r to find the growth rater for the country over this period population in 2002 137 million population in 2010 134 million The country s growth rate over this period was Round to the nearest hundredth as needed

When a drug such as a pain killer or an antibiotic is introduced into the body the kidneys work to eliminate the drug Assume that after an hour 20 percent of the drug in the body is eliminated After another hour 20 percent of the remaining drug is eliminated and so on If a person receives an injection of 300 mg of pain killer how much of the drug will remain in the person s body after two hours mg Round to the nearest whole number as needed CE

A country s populations in 2002 and 2010 are given below Use this information and the exponential model A P 1 r to find the growth rate for the country over this period population 2002 77 million population 2010 115 million The country s growth rate was approximately Round to two decimal places as needed C

A bank account has an initial deposit of 16 000 After 7 years the bank account has 21 000 Assuming that compounding interest is done annually and that no withdrawals are taken find the annual interest rate on the investment Points 0 of 1 If interest is compounded annually what is the approximate interest rate on the investment Do not round until the final answer Then round to the nearest hundredth Saw

You are given the principal in a bank at the beginning of a year and a rate of interest that is compounded annually Calculate the amount in the account at the end of the year 9000 9 percent If interest is compounded annually what is the amount of money after t 1 years Round to the nearest cent

7 2 The chart to the right indicates projected demand for nurses a Write a linear equation in slope intercept form that models the data b Use the equation from part a to project the demand for nurses in 2022 c Project the year when the demand for nurses will reach 5 million Part 2 of 3 a Which linear equation best models the projected demand for nurses OA y 0 04x 2 8 B y 0 04x 2 4 C y 0 04x 2 8 OD y 0 04x 2 4 b The projected demand for nurses in 2022 is million Type an integer or a decimal II Projected Demand for Nurses 2018 2008 Points 0 of 1 0 2 8 2 4 In Millions

Part 2 of 2 Points 0 of 1 Save In a certain year expenses at a four year public college averaged 10 900 and were increasing at a rate 680 per year Model this information with a linear equation and use the model to predic the average cost of attending a four year public college Let x be the number of years since a certain year and let y be the cost of attending a four year public college Choose the equation of a line that models the information A y 680x 10 900 OB y 680x 10 900 OC y 680x 10 900 D y 680x 10 900 The cost of attending a four year public college 11 years later is predicted to be

K Find the linear equation whose graph passes through the given points Write the equation in slope intercept form 13 3 and 6 3 TE y 0 Simplify your answer Type an expression using x as the variable Use integers or fractions for any numbers in the expression

K Find a linear equation whose graph has the indicated slope and passes through the given point slope 3 point 3 2 The equation of the line is Simplify your answer Type your answer in slope intercept form COLOA

According to a census there were 68 people per square mile this is called the population density in a certain country in 1980 By 2000 the number of people per square mile had grown to 78 This information was used to develop a linear equation in slope intercept form given below where x is the time in years and y is the population density Think of 1980 as year zero What is the population density expected to be in 2014 1 y x 68 In 2014 the population density is expected to be people per square mile ww

K Graph the equation by first finding the x and y intercepts 1 Use the graphing tool to graph the line Use the intercepts when drawing the line If only one intercept exists use it and another point to draw the line Click to enlarge graph Points 0 of 1 Ay 10 8 2

4 ces Direct materials 61 000 pounds 5 10 per pound Direct labor 23 000 hours 12 30 per hour Overhead costs Indirect materials Indirect labor Power Maintenance Depreciation Building Depreciation Machinery Taxes and insurance Supervisory salaries Total costs Actual Cost 0 2 Compute the direct materials variance including its price and quantity variances Note Indicate the effect of each variance by selecting favorable unfavorable or no variance 0 41 650 176 150 17 250 34 500 24 000 94 500 16 200 293 000 311 100 282 900 0 697 250 1 291 250 0

13 points eBook Hint Print References Mia Wiz sells computers During May it sold 600 computers at a 800 per unit price The fixed budget for May predicted sales of 650 computers at an per unit price of 780 AQ Actual Quantity SQ Standard Quantity AP Actual Price SP Standard Price 182 Compute the sales price variance and the sales volume variance for May Identify it as favorable or unfavorable Note Indicate the effect of each variance by selecting favorable unfavorable or no variance Actual Sales 0 Check my work Flexible Budget 0 Budgeted Sales 2021 marks

Solve the formula for the specified variable V 1 X vd for v

UNIT III The 30 students in MAT101 just completed the final exam The results are as follows 85 90 58 68 79 85 90 64 score 88 81 85 90 64 88 81 85 72 64 74 81 90 72 64 74 81 6 Complete a frequency chart for the test scores no work to show 90 72 68 74 81 frequency

K Solve the formula for the specified variable 9 0 q 1 qz for q