Inverse Trigonometric functions Questions and Answers

Solve the given equation Enter your answers as a comma separated list Let k be any integer Round terms to two decimal places where appropriate cos 0 0 24 0 rad List six specific solutions 0 rad

Macmillan Learning The value of a trigonometric function of an acute angle and the length of one side of a right triangle with that angle is given Use this information to calculate the lengths of the remaining sides of the triangle You may find it helpful to draw a picture of the right triangle Let z be the hypotenuse and x be the length of the unknown side The cotangent of an acute angle t in a right triangle is The length of the opposite side is 9 Use decimal notation Give your answers to two decimal places x

4 10 Give the general solution to the differential equation y 2y 5y 0

Last year Jarod left a job that pays 80 000 to run his own bike repair shop Jarod s shop charges 65 for a repair and last year the shop performed 5 000 repairs Jarod s production costs for the year included rent wages and equipment Jarod spent 60 000 on rent and 100 000 on wages for his employees Jarod keeps whatever profit the shop earns but does not pay himself an official wage Jarod used 30 000 of his savings to buy a machine for the business His savings were earning an annual interest rate of 4 percent Instructions Enter your answers as a whole number If you are entering any negative numbers be sure to include a negative sign in front of those numbers a What is Jarod s annual accounting profit 135000 b What is Jarod s annual economic profit 92900

Find an equation of the line tangent to the graph of G x 7e 6x at the point 0 7 The equation of the line is y

5 Emma hll Teight of the ball is given by y 0 01x 0 5x 0 2 where y is the vertical height in yards above the ground and x is the horizontal distance from the tee in yards Round all answers to one decimal place a How far does Emma hit the golf ball

Find a particular solution to the differential equation 1 y 3y 9 2 y y y 2 sin 3t

O A producer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season The first variety is milk chocolate while the second is milk chocolate filled with mint It is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances Two independent samples of 18 observations each are collected for the holiday period A sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2 5 million A sample mean of 13 5 million truffles filled with mint sold with a sample standard deviation of 2 3 million Use milk chocolate as population 1 and mint chocolate as population 2 Assuming the population variances are equal which of the following is the value of the appropriate test statistic 3 41 18 Multiple Choice z 1 8734 Z 1 8734 t34 1 8734

B A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield He subdivides his six lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half The following table shows the results Lot 1 2 3 4 5 6 Crop Yield Using Old Fertilizer 12 9 10 12 8 9 Assume the crop yields are normally distributed Which of the following is the correct value of test statistic Multiple Choice t5 1 22 2 1 22 2 1 22 Crop Yield Using New Fertilizer 14 9 11 10 12 10 t5 1 22

Write the equation of a sine or cosine function to describe the graph 2x 2x 4x 2x K 8x 3 10x 3

Let p x q r be propositions over Z p x x 10 q x x 2 6 a Translate the following statement into English 3x z p a q x O A 10 and 2 2 6 for some integer a OB There exists a rational number a so that x2 10 and x 2 6 OC For all integersa a 2 10 and x 2 6 OD For all rational numbers a x 2 10 and x 2 6 OE None of the above b Translate the following statement into English Va z p x q x OA For all rational numbers x x 10 or x 2 6 OB 10 or x 2 6 for some integer a OC For all integers x x 10 or x 2 6 OD Every integer x satisfies x 10 and x 2 6 OE None of the above

Consider the following propositions over R Which of these propositions are contradictions Select all that apply OA q x 10 x 100 OB q z x 0 OC g x x 6 x 6 x 36 OD q z 10 6 Be able to justify your answers using truth sets

14 1 point A mobile phone company offers a phone plan that allows 600 min of airtime per month The revenue generated from this plan depends on the price of the plan according to the data in the table 10 30 35 Monthly Plan Price Revenue 1000s 15 20 1560 1740 1180 1500 1080 25 1720 The first differences for this data imply a rate of change of revenue with respect to monthly plan price that is constant increasing or decreasing ARESIO

1 point A relation can be modelled using a quadratic relation when the differences are constant

37 Hugo Ch vez is the president of Venezuela Venezuela is a major producer of oil products which remain the keystone of Venezuela s economy Suppose President Ch vez wants to increase his popularity with the citizens of Venezuela and enacts a government policy that reduces the customer price of gasoline sold at state owned gas stations to 50 of the previous price This policy is called a A price control B price floor C price ceiling D quota

A ski resort is building two parallel straight ski slopes for children One of them has a 1 gradient of The other ski slope will pass 3 through points 2 3 and s 5 Find the value of s

Exercise 8 5 5 Use the following steps to prove that det AT det A 1 First write PA LU as I did in definition 8 3 1 Then take the transpose of both sides 2 Now take the determinant of your equation with four terms Analyze which determinants you know which are simpl and which remain to be thought about 3 At the end lots of things should cancel and you should get det A det U det AT

O Macmillan Learning Find the coordinates of the trigonometric point associated with an angle of the special values Give your answer in the form Express numbers in exact form Use symbolic notation and fractions where needed P 3 12 2 T radian The appropriate reference angle is one o 3

Price 16 14 12 10 8 006 4 2 Sd 0 10 20 30 40 50 60 70 80 90 Quantity Dd Refer to the accompanying graph where Sa and D are the domestic supply and demand curves for a product The world pri of the product is 6 If an import quota of 40 units were imposed on the product then the equilibrium price would be 8 and the quantity consumed 70 units O 12 and the quantity consumed 50 units O 6 and the quantity consumed 80 units O 10 and the quantity consumed 60 units

ship A is 170 km west of ship B Ship A is sailing east at 40 km h and ship B is sailing north at 20 km h How fast in km hr is the distance between the ships changing at 4 00 p m Round your answer to three decimal places km h

One of your customers is delinquent on his accounts payable balance You ve mutually agreed to a repayment schedule of 450 per month You will charge 1 3 percent per month interest on the overdue balance If the current balance is 18 000 how long will it take for the account to be paid off

6 Assume te a b and f n t y M show Taylor s method of order n has a local truncation error of O h 7 Computational exercise Write a script to use Euler s method to compute the approximate solution

105 000 m to kilometers km

How many units of each product is to be made so as to utilise the full available raw material Solution Step 1 The situation is easily identifiable y fitne Step 2 Suppose the firm produces x units of P y units of P and z units of P Since product P requires 3 units of R P requires 7 units of R and P requires 5 units of R observe matrix B and the total number of units of R available is 330 we have 3x 7y 5z 330 for raw material R Similarly we have and 4x 9y 12z 455 for raw material R 3y 72 140 for raw material R This system of equations can be expressed in matrix form as 202 MATHEMATICS 375 4 9 12 037 330 y 455 140 X Rationalised 2023 24 Step 3 Using elementary row operations we obtain 100 X 010 00 Z This gives x 20 y 35 and z 5 Thus the firm can produce 20 units of P 35 units of P and 5 units of P to make full use of its available raw material 20 35 Remark One may observe that if the manufacturer decides to manufacture according to the available raw material and not according to the purchase orders of the two clients F and F as in Example 3 he she is unable to meet these purchase orders as F demanded 6 units of P where as the manufacturer can make only 5 units of P3 Example 5 A manufacturer of medicines is preparing a production plan of medicines M and M There are sufficient raw materials available to make 20000 bottles of M and 40000 bottles of M but there are only 45000 bottles into which either of the medicines can be put Further it takes 3 hours to prepare enough material to fill 1000 bottles of M it takes 1 hour to prepare enough material to fill 1000 bottles of M and there are 66 hours available for this operation The profit is Rs 8 per bottle for M and Rs 7 per bottle for M How should the manufacturer schedule his her production in order to maximise profit Solution Step 1 To find the number of bottles profit under the given hypotheses bed the and M in order to maximise the Step 2 Let x be the number of bottles of type M medicine and y be the number of bottles of type M medicine Since profit is Rs 8 per bottle for M and Rs 7 per bottle for M therefore the objective function which is to be maximised is given by Z Z x y 8x 7y The objective function is to be maximised subject to the constraints Refer Chapter 12 on I inear Programming

7 Computational exercise Write a script to use Euler s method to compute the approximate solution to y cos 2t sin 3t for 0 t 1 y 0 1 and h 0 1 Please give the approximate solution w at t 0 h 2h Nh 1

Find the domain of the following rational expression x 3 x 7x 30

Name the property of real numbers illustrated by the equations 5 6 65 Associative Property O Multiplicative Inverse O Commutative Property

A car rental agency rents compact midsize and luxury cars Its goal is to purchase 70 cars with a total of 1 200 000 and to earn a daily rental of 3200 from all the cars The compact cars cost 10 000 and earn 40 per day in rental the midsize cars cost 20 000 and earn 50 per day and the luxury cars cost 40 000 and earn 60 per day To find the number of each type of car the agency should purchase solve the system of equations below where x y and z are the numbers of compact cars midsize cars and luxury cars respectively y 70 X 1 10 000x20 000y 40 000z 1 200 000 2 40x 50y 60z 3200 3 2 Select the correct choice below and fill in any answer boxes within your choice OA There is one solution The agency should purchase compact cars Simplify your answers OC There is no solution midsize cars and luxury cars OB There are infinitely many solutions If the agency purchases z luxury cars then the agency should purchase Type expressions using z as the variable compact cars and midsize cars

Use the following table of exchange rates to solve the problem Round your answer when appropriate Dollars per Foreign Foreign per Dollar 1 624 0 6158 Currency British pound Canadian dollar European euro Japanese yen Mexican peso 1 005 1 320 0 0120 0 07855 0 9950 0 7576 83 33 12 73 16 How many Mexican pesos can you buy for 180 A 2 16 pesos B 14 999 4 pesos C 2291 4 pesos D 14 139 pesos 17 You return from a trip with 3400 Japanese yen How much are your yen worth in dollars A 40 80 B 2575 84 C 267 07 D 283 322 18 A fresh juice stand in Montreal sells a large glass of orange juice for 4 40 Canadian dollars If you buy 5 glasses how much have you spent in U S dollars A 16 67 B 22 11 C 29 04 D 21 89 16 17 18

For a dosage of x cubic centimeters cc of a certain drug the resulting blood pressure B is approximated by the function below Find the maximum blood pressure and the dosage at which it occurs B x 330x 1320x 0 x 0 25 The maximum is obtained for a dosage of Round to two decimal places as needed

Find the point P such that v PQ has the components 9 9 25 13 Q 3 4 25 5 P help points

Let A 4 1 0 4 7 8 5 3 2 9 8 9 10 7 8 10 K Then tr A and A 1 2

annual payments be repay in five equal annual end of year payments of 10 000 with the first payment to 5 29 Solving for r of an annuity You lend a friend 30 000 which your friend will be received 1 year from now What rate of return does your loan earn

5 complete statement of cash flows using a spreadsheet under the indirect method Note Enter all amounts as positive values Balance sheet debit balance accounts Cash Accounts receivable Inventory Equipment Balance sheet credit balance accounts Accumulated depreciation Equipment Accounts payable Income taxes payable Common stock 2 par value 11116 GOLDEN CORPORATION Spreadsheet for Statement of Cash Flows For Current Year Ended December 31 December 31 Prior Year 115 800 79 000 534 000 307 000 1 035 800 108 000 79 000 29 100 576 000 170 000 Analysis of Changes Debit Credit December 31 Current Year 172 000 172 000

es Required information Cash flows from operating activities FORTEN COMPANY Statement of Cash Flows For Current Year Ended December 31 Adjustments to reconcile net income to net cash provided by operations Income statement items not affecting cash Changes in current assets and current liabilities Cash flows from investing activities 0

Assignment4 Problem 6 1 point Assume that A is a matrix with three rows Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed R R 1888 E 00

Find the area of the figure Sides meet at right angles 8 yd 10 yd 4 yd A s yd 5 yd 3 yd 3 yd 8 yd 0yd

A rectangular piece of paper with length 28 cm and width 12 cm has two semicircles cut out of it as shown below Find the area of the paper that remains Do not round any intermediate steps Round your final answer to the nearest hundredth and be sure to include th correct unit If necessary refer to the list of geometry formulas 28 cm 0 112 cm 11 petsee 0 0 cm 08 X cm cm

A company makes wax candles in the shape of a rectangular prism Each candle is 5 inches long 4 inches wide and 6 ches tall How much wax will they need to make 360 candles 3 peosed

a 1 pt If possible find a rational number that is between 1 41 and 1 414414441 If not possible just say so Show work as needed

12 Can a police officer search a motor vehicle for a radar warning device 1 marks Ref 13 Can a police officer search the driver of a motor vehicle for a radar warning device 1 marks Ref 14 Can a driver possess more than one driver s licence 1 marks Ref 15 Can a police officer seize a second licence found a driver 1 marks Ref 16 Can a police officer order the removal of vehicle blocking a live lane of traffic 1 marks Ref

Current Attempt in Progress In May 1991 Car and Driver described a Jaguar that sold for 980 000 At that price only 50 have been sold It is estimated that 350 could have been sold if the price had been 560 000 Assuming that the demand curve is a straight line and that 560 000 and 350 are the equilibrium price and quantity find the consumer surplus at the equilibrium price dollars Consumer surplus i

For a product the supply curve is given by q p 10p60 and the demand curve by q p 2p 60 where p is in dollars and q is in millions a What is the equilibrium price and quantity p 10 40 Consumer surplus dollars b Find the consumer and producer surplus using the Fundamental Theorem of Calculus Producer surplus million million dollars million dollars

Prof Ciancia Andrew Homework 9 Distribution Date 10 05 2023 Due Date 10 09 2023 1 The following are the results of a compaction test Mass of mold 2850 wet soil g Water content 10 1 2990 12 1 Volume of mold 1000 ml mass of mold 1000g Specific gravity Of solids 2 69 3090 15 2 3030 17 5 2890 NOTE Show all the calculation steps 20 2 Fall 2023 1 Find the compaction curve showing the optimum moisture content and maximum dry density please use excel 2 Plot the zero air void line 3 Determine the degree of saturation at the maximum dry density

11 WRITE Math Draw a model and write an equation to represent 4 times as many as 3 is 12 Explain your work

5 1 point Evaluate 42 2 3 2 Express your answer using only positive exponents C d 65 144 72 144 97 144

point Express 3 5 1 as a power with a negative exponent b 3 C 7 d 74

3 A hot air balloon is on the ground 300 feet from Mercedes She watches the balloon as it fires its burner and begins to ascend straight up into the air Write a function that models the height h in feet of the balloon as a function of the angle of inclination from Mercedes

4 Using a two way radio Melissa can talk to anyone within an 8 mile radius of her location Oscar is 30 west of south from Melissa s location What is Oscar s exact location relative to Melissa s location at the greatest distance where they can talk using two way radios West 8 30 8 North South Wo East

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