Complex numbers Questions and Answers

A ladder is 27 8 feet long It leans against the wall with one end on the ground is 13 2 feet from the wall The other end just reaches a windowsill Use the Pythagorean formula to calculate the height of the windowsill above the ground 27 8 ft 13 2ft h

Type an equation for the following pattern X 1 2 3 4 5 1 2 1 3 2 2 5 2 1 y x

dd and simplify 7 3i 6 2i 7 3i 6 2i Simplify your answer Type y answer in the form a bi

Divide 700 100 700 100 Simplify your answer Type your answer in the form a bi Type an exact answer L radicals as needed

12 3 12 3 Simplify your answer Type an exact answer using radicals as needed Type your ans in the form a bi

1 Given the functions f x 3 with the domain 3 and 0 and x x x g x with the domain x x 0 what is the domain of o g x I a xx 0 x R b x x 0 x R c xx 3 or 0 x x R d xx 3 x R

For the functions f x sin x and g x cos x a 4 x t Ob c d tan x x sin x 4 x cos x 4 x sin X COS X 2 would be equal to

10 11 17 14 15 16 20 age 3 1 4 10 12 13 age 4 1 ww 18 19 25 MA 22 23 7 28 29 26 32 33 4 35 36 1 38 39 An example of a relation that is not a function but is odd is Ob d 7 5 7 6 5 6 3 5 3 2 5 2 L 5 1 0 5 113 12 S 2 1 5 1 0 5 I Y 3 X 5 1 0 5 0 5 1 1 5 2 2 5 0 5 2 2 5 3 3 5 4 4 5 5 X 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 N 451A3252 45 103 10 951 15 05 23 3 354453

J Page 2 11 12 14 17 18 20 Page 3 21 24 30 Page 4 34 15 16 13 22 40 23 31 32 33 a 25 26 28 29 137 38 39 135 36 If f z cos 2 and 9 2 x 2 which graph is fog b Od Od T 2 B 1 1 5 0 5 1 0 5 4 1 54 2 5 1 5 D S 0 5 1 0 5 Y R

fog x and gof x are the same function This statement is a always true b true for most functions f x and g x c false for most functions f x and g x d always false

13 16 19 23 26 29 3 33 36 39 Question 33 1 point Listen Which graph represents f g x for the given graphs of f x and g x a Ob Oc 5 16 SE f g x 16 5 4 4 3 4 3 8 x 1 8 x Y g x 2 3 4 Y 6 X 3 A S 6 3 4

The function f x sin x can be transformed to a function equivalent to g x cos x by a phase shift of a un to the left b units to the right c units to the left d units to the right

One cycle of a sine function begins at x and ends at x 3 What is the phase shift of the function a right b left c There is no phase shift d left 2

Write the equation in exponential form Assume that all constants are positive and not equal to log y C

Find the exact value without using a calculator Joga 4 log4

Which of the following is the equivalent statement to 1 2 cos 0 Oa 2 tan 0 b sec 0 2 sec 6 Oc 1 2 tan 0 d sec 0 2

Solve 2 sec x 5 sec x 2 0 for 0 x 2 O 57 a 3 Ob and 5 3 7 c 3

Which of the following is an equivalent expression to 1 tan 0 sin 0 a 1 a sin 0 b cos 0 sin 0 sin 0 c cos 0 sin 0 sin 0 d cos 0 sin 0 sin 8

Which graph is defined by the function given below y x 2 x 7 10 10 10 A CO 10 10 OA Graph A OB Graph B C Graph C 10 D Graph D 10 10 10 10 10 B C Click here for long description 10 10 10 10 D 10

10 0 6x The population of wolves in a wildlife reserve can be modelled by the function f x 1000 600 where f x is the population of wolves and x is the number of years since the population was introduced In the context of this model what does the vertical asymptote represent a The time at which the wolves began living in the reserve b Nothing the vertical asymptote is outside the domain COMPE WO S uover c The maximum number of wolves that can survive in the reserve at any given time CO d Nothing the vertical asymptotes are irrelevant in all contexts

1000 600x 10 0 6x The population of wolves in a wildlife reserve can be modelled by the function f x where f x is the population of wolves and x is the number a years since the population was introduced According to this model What is the maximum number of wolves that can survive in this reserve a 600 b 1000 O c 10 d 100

The concentration C of a drug in the blood after thours is given by C t 2 6 where C is measured in mg L In the context of this model what is the domain of the function a Domain tt 0 t R b Domain tt E R c Domain tt 0 t R d Domain t 0 7217 t 0 7217 t R

Listen Which of the following has no vertical asymptotes a f x 2x 3 x 3 O b f x 2 3 x 3 c f x 2x 3x x2

3 2 S R R Q X A rotation 180 about the origin B reflection across the y axis C translation 2 units right and 6 units up D reflection across y x

1 Here is a circle with a radius of 15 units whose center is at 0 0 a If the y coordinate of point C is 12 what is the x coordinate Explain or show your reasoning x 9 b Name 2 other points that must be on the circle 1 12 9 12 3 Find the measure of 6 to the nearest hundredth cos8 1 8 21 2 11 11 8 2 Solve the following triangle 4 6 tan 42 x 5 mi 4 5 mi A 4 Find the missing values for the following right triangle cos30 3 tan 30 1 24 xo 27 7 13 9

Level 4 Mastered The sun shines on a flagpole causing a shadow to be cast on the ground The distance from the base of the pole to the tip of the shadow is 49 feet At that time of day the sun s rays make an angle of 38 with the ground How tall is the Flagpole Draw a picture

11 What is the solution for2 cosx 3 0 for 0 x 2m

Which function has the graph shown A y sinx B y secx C y tanx D y cotx 72x 2 1 2 3

valuate the integral Remember to use absolute values where appropriate Use C for the constant of integration S 25 x X dx

Find the mean X of the data 3 4 5 7 10 12 15 x Mean

Find the mean X of the data 56 52 46 49 57 64 x

Find the standard deviation of the given data Now find the variance or the average of the squares of the differences Data 5 6 8 Data x 3 2 0 Data x 9 4 0 13 5 25 Variance 0 9 4 0 25 4 Variance

Find the slope of the tangent to the f x 3x 7x 11 at x 2 a 5 b 19 c 12 d 7

Question 19 1 point E Listen Which general form of the following equations would represent the graph below 2 1 30 y 20 10 Oc f x ax b 10 20 30 a f x ax bx c b f x ax bx cx d d f x ax b cx dx e

a Find f g x f g x 10x 5 5x 2 Simplify your answer What is the domain off g Select the correct choice below and if necessary fill in th your choice

Question 35 2 points Listen The displacement s in meters of an object moving back and forth in a straight line can be modeled by a function s t 3 t 5 2 3 The instantaneous rate of change 5 seconds is a zero b positive c negative d undefined

Use the like bases property and exponents to solve the equation 2 10 2000 x

Find the Product 30 x 10 900 x 10 8 000 x 10 450 x 10 3 400 x 10

Simplify completely 6 8 2x 7 1 9 2m X 3m

Simplify Express answers using POSITIVE exponents 4 2 3 5 7x 12

How many students in Honor Roll How many have perfect attendance honor roll not taking adu class Honor G 3 5 2 Denfert Adu

3 Ten cars were recently assembled at a factory Of these cars 3 will be picked at random for inspection Of the 10 cars 5 are blue and 5 are grey What is the probability that all 3 cars picked for inspection will be blue

If you invested 1 000 in Netflix stock ten years ago what would it be worth now

6 SIA 20 20 Write the factored form of the equation of the most appropriate polynomia f x a 10 10 K sin a

12 Write a quadratic equation in standard form that has roots of 3 and 7

A correct numerical answer with ho 10 A quadratic function is graphed on the set of axes below Find the axis of symmetry vertex domain and range Axis of Symmetry Vertex Domain Range X 4 pts

8 The graph of the equation y ax is shown to the right If a is multiplied by 1 the graph of the new equation is 1 wider and opens downward wider and opens upward 2 3 narrower and opens downward narrower and opens upward 4

blems 11 You have a piggy bank that has 275 dimes and quarters that total 51 50 How many of each type of coin do you have in the piggy bank

2 3 1 1 0 4 E 2 y 1 A 7 6 5 4 Does the function above show exponential GROWTH or DECAY 2 44 S 6 6 S

Jse the graph of f x x to write a formula for the function whose graph shown be 12 8 16 12 8 00 4 12