Questions

Prove that each of the following identities is true 1 cos 0 tan sin 2 sec cot csc 0 3 csc 0 tan 0 sec 0 4 tan cot 0 1 tan A 5 sin A sec A 7 sec 0 cot 0 sin 0 1 cot A 6 cos A CSC A 8 tan csc 0 cos 0 1 9 cos x csc x tan x cot x sin x 10 sin x sec x csc x tan x 1 11 csc x cot x 1 cot x csc x sec x 12 tan x cos x cot x sin x 1 13 cos x 1 tan x 1 14 sin x cot2 x 1 1

Distribution of Earthquakes Mediterranean Himalayan Belt Indonesian Belt Circum Pacific Belt Based on the earthquake distribution what can you say about the dip direction of subduction in the Indonesian Belt Shallow focus O Intermediate focus Deep focus

What causes an Earthquake a The breakdown of material in the core b When stress is less than strength of the rock c Deformation of plastic material d When stress is greater than strength of the roc e When stored elastic energy is released

Why do we study Earthquakes a to know exactly when and where an Earthquake will happen b to help determine exactly how intense an Earthquake will be c to help describe explain assess and possibly help to determine if an Earthquake is likely d because people too indifferent toward Earthquakes e because we have too much time on our hands

Whoever realizes the benefit in question 1 how much will the total benefits that the publi realizes add up to per home sold Less than 10 000 10 000

Congress is now thinking about banning TikTok or forcing its sale to a US based company likely one of the tech giants If this happens what market failure will be worse Adverse selection O Market power O Externalities O Moral hazard

JK J M G K 15 L P

need to transform the integrand first 5 x sin x dx

13 Let A 4 3 be the initial side and B 2 5 be the terminal side a Find the ordered pair for vector AB Find the horizontal and vertical components b Find the magnitude of AB Round o the nearest thousandth 0 Find the direction Round to the nearest thousandth

A rhombus is a parallelogram with four congruent sides perpendicular diagonals and the diagonals bisect a pair of opposite angles A square is a parallelogram with all the properties of a rectangle and rhombus RHOM is a rhombus Find the unknown measures Treat each problem independently 5 If OB 2x 1 and BR 3x 10 then OR 6 If RM 18 then RH OH OM 10 7 If m22 48 then mZMOH M R 4 3 B 8 5 6

Antidifferentiate using a table of integrals You may need to transform the integrand first x e4x dx

For problems 1 9 use rectangle QUAD Treat each problem independently 1 If DP 4x 1 and PA x 13 then DP 2 If m 2 12x 4 and m23 16x 12 then m23 3 If m25 12x 3 and m 6 10x 9 then mZ4 D 4 If m23 18x 8 and m 6 70 4x then mZ6 8 6 4 7 1 3 A

need to transform the integrand first dx 9 252

Find the least common multiple for the following expressions x and x 3 x 3 x x 3 Or 3 3x

Antidifferentiate using the table of integrals You may need to transform the integrand first sin 4t cos 5t dt

need to transform the integrand first 2 dz 4 x 6

need to transform the integrand first sec x dx

A kite is a quadrilateral with two pairs of adjacent congruent sides LMNP is a kite Find the unknown measures 12 If MN 4x 5 and NP 6x 1 then MN 13 If mZLMP 58 and mZLPM 7x 2 then x 14 If mZMON 8x 14 then x M

Antidifferentiate the following function using the table of integrals You may need to transform the integrand first 2 cos t dt

0 A trapezoid is a quadrilateral with exactly one pair of parallel sides In an isosceles trapezoid the legs both pairs of base angles and the diagonals are congruent TRAP is an isosceles trapezoid Find the unknown measures T O If TP 2x 3 and RA 3x 2 then TP If mZTPA 63 then mZRAP and m PTR P R

ABCD is a parallelogram Find each unknown measure 3 If DE 6 then EB DB B E C D 4 If AD 3x 6 and BC x 18 then x AD A E D

Simplify x 7x 30 823 6422 3 8 08 2 3 4 x 8 2 3 4 x 8 0 2 3 O 4 x 8 8x2 4x 40

Simplify x x 20 2 3x 15 8x 16 4 x 4 3 8 x 4 3 3 x 4 8 8 x 2

Which expression is equivalent to the complex fraction 2 7 2 1 2 2 3 0 7 2x 1 7 3 2 3 2x 1 2 2 7 3 2x 1 2 7 2 2z 3

What is the area of the figure Round to the nearest tenth 9 ft 5 ft 13 ft O 55 0 ft O 81 0 ft O 45 0 ft C 1080 2

In the vicinity of a bonfire the temperature 7 in C at a distance of x meters from the center of the fire is given by T x 500 000 x 400 At what range distances from the fire s center is the temperature less than 370 C Assume x is positive Round your values to one decimal place Enter your answer using interval nota m

Solve the inequality Enter your answer using interval notation x4 34x272 0

Find the domain of the given function Enter your answer using interval notation 4 X g x 4 x

Solve the inequality Enter your answer using interval notation x 2 X 3 X 1 X 2

Solve the inequality Enter your answer using interval notation X 1 X 11 0

Solve the inequality Enter your answer using interval notation 4 1 1 5 S X X

Suppose that antibiotics are injected into a patient to treat a sinus infection The antibiotics circulate in the blood slowly diffusing into the sinus cavity while simultaneously being blood by the liver In a future chapter we will derive a model for the concentration of the antibiotic in the sinus cavity as a function of time since the injection c t e at e t a where a 0 b At what time does the inflection point occur 2 t In d B B

After an antibiotic tablet is taken the concentration of the antibiotic in the bloodstream is modeled by the function C t 8 e 0 4t e 0 6 where the time t is measured in hours and C is measured in g mL What is the maximum concentration of the antibiotic during the first 12 hours Round your answer to four decimal place pg mL

Use logarithmic differentiation to differentiate the following functio x 1 6x 1 4x 1 f x 8x 1

College students take different course loads Many colleges determine the number of Full time equivalent students F by using the formula F students enroll for a given semester where n is the total number of credits in which 15 If students on a campus register for a total of 36075 credits how many full time equivalent students does the campus have The campus has 2405 full time equivalent students Solve the formula for n n

Determine whether 11 is a solution of the equation 7 x 1 70 Is 11 a solution Yes No

A hotel purchases a large photo for its newly renovated lobby The perimeter of the photo is 360 in The width is 5 in more than four times the height Find the dimensions of the photo The height of the photo is Simplify your answer Type an integer or a decimal The width of the photo is 4h 5

Caleb paid 27 50 including a 5 sales tax for a security wallet How much did the wallet itself cost The wallet originally cost Round to the nearest cent

Simplify the following expression Write as a single logarithm or monomial 12 In 36 12 In 36

possible Miranda s financial aid stipulates that her tuition not exceed 1200 If her college charges a 125 registration fee for the term plus 250 per course what is the greatest number of courses for whie Miranda can register Miranda can register for at most courses Your answer should be a whole number

TASK 2 Modelling a function 1 The following function h x 2 x 12 5 has undergone a horizontal transition o the right a vertical transition up by 3 and stretched by the factor of 4 What would be function 3 marks

o finance her community college education Sarah takes out a loan for 2200 After a year Sarah decides to pay off the interest which is 8 of 2200 How much will she pay Sarah will pay

Solve using the addition principle Don t forget to perform a check 5 4 2 5 x The solution is x Type an integer or a decimal

olve using the multiplication principle Don t orget to perform a check 6 7x 50 28 The solution is x Type an integer or a decimal

Translate to an algebraic expression A driver drove at a speed of 52 mph for t hours How far did the driver go The algebraic expression 52 mph at t hours is d miles

Excerpt from Why the German Republic Fell by Bruno Hellig published in Why the German Republic Fell And Other Studies of the Causes and Consequences of Economic Inequity edited by Arthur Madsen published by The Hogarth Press London UK 1941 Hellig was a journalist for newspapers in Vienna Budapest Prague and Berlin who was arrested In Austria in 1938 for being Jewish He was released from a concentration camp in 1939 emigrated to Britain and served in the British Royal Air Force during the Second World War Was there a link between the economic and the political collapse Eventually yes For as unemployment grew and with it poverty and the fear of poverty so grew the influence of the Nazi Party which was making its lavish promises to the frustrated and its violent appeal to the revenges of a populace aware of its wrongs but condemned to hear only a malignant and distorted explanation of them In the first year of the crisis the number of Nazi deputies to the Reichstag parliament rose from 8 to 107 A year later this figure was doubled In the same time the Communists captured half of the votes of the German Social Democratic Party and the representation of the middle class practically speaking disappeared In January 1933 Hitler was appointed Reichskanzler Chancellor he attained power as I said before quite legally All the forms of democracy were observed It sounds paradoxical but it was in fact absolutely logical 14 Who is the author of Source C7 15 In what way does Heilig s profession as a journalist provide value to this source for a historian studying interwar conditions in Europe 16 In what way does Heilig s profession as a journalist lead to limitations of this source for a historian studying interwar conditions in Europe

To make copies of blueprints Vantage Reprographics charges a 5 setup fee plus 3 per copy Myra can spend no more than 56 for copying her blueprints What numbers of copies will allow t stay within budget Select the correct choice below and if necessary fill in the answer box to complete your choice OA Myra can make or fewer copies

f Boris recorded the number of daylight hours on the first day of each month in a northern hemisphere town This data was plotted onto a scatter diagram The points were then joined by a smooth curve with minimum point 0 8 and maximum point 6 16 as shown in the following diagram hours of daylight each day 16 12 6 9 12 month of the year Let the curve in the diagram be y f t where t is the time measured in months since Boris first recorded these values Boris thinks that f t might be modelled by a quadratic function leng a Write down one reason why a quadratic function would not be a good model for the number of hours of daylight per day across a number of years Paula thinks that a better model is f t a cos bt d t 0 for specific values of a b and d For Paula s model use the diagram to write down b the amplitude c the period d the equation of the principal axis e Hence or otherwise find the equation of this model in the form f t a cos bt d For the first year of the model find the length of time when there 10 hours and 30 minutes of daylight per day 1

2 a Write an equation of the form y a x h k with vertex 2 10 that models the flight path for the toy rocket assuming the rocket leaves the ground at 0 0 5 marks Hint to find the value of a use the coordinates of a point where rocket leaves the groung and your knowledge of h and k values of the vertex form b What are the domain and range of the function What do they represent in this situation 3 marks

16 is what percent of 80 16 is of 80 Simplify your answer