Math - Others Questions

10 Let z 8i and z2 2 3 2i Find the trigonometric form of each complex number a Find the product of z and 22 b Raise zi to the power of 3

Use your calculator to evaluate cos 0 84 to at least 3 decimal places Give the answer in radians

Question 9 1 point XOH 0 2 345 3 linear 6 O quadratic 11 15 What type of relation does the table represent exponential Y Qother 95437H 9 5

3 2 7 T 2 3 2 1 1 2 The graph above is a graph of what function Oy cos x Oy tan x Oy sin x Oy csc x Oy sec x Oy cot x 2 3 2

cos 7 Evaluate the expression sin 1

5 5 0 5 5 edit graph on desmos Determine an equation in factored form for this parabola

6 5 4 3 2 1 8 7 6 5 4 3 2 7 2 3 4 15 60 8 1 2 3 4 5 Write an equation for the graph above f x 6

6 y 5 11 4 3 2 6 5 4 3 2 1 1 I 2 3 4 5 I P B S 4 Write an equation for the function graphed above 6

Follow the instructions below a Rewrite the percentage in the sentence below as a decimal The model was 5 of the size that the original was b Rewrite the decimal in the sentence below as a percentage In a recent poll 0 234 of the people surveyed were in favor of the new law Decimal Percent

6 5 2 3 2 1 1 2 The graph above is a graph of what function O y cos x Oy sec x Oy sin x Oy csc x Oy cot x

6 8 7 6 4 3 2 1 5 4 3 2 1 1 2 1 2 3 4 5 6 O Write an equation in the form y c a sec b x d or y c a csc b x d for the func graphed above

V Answer each part If necessary round your answers to the nearest hundredth a Austin runs 6 miles in 45 minutes How many minutes does he take per mile minutes per mile b Diane bought 20 pounds of sugar for 8 How many dollars did she pay per pound of sugar dollars per pound X

St 23 to y sin x Oy cot x 0 The graph above is a graph of what function Oy csc x Oy tan x Oy sec x O y cos x

a b The voltage V in a circuit is given by V 3R 135R 1800R 200 where R is the resistance in ko 1 Compute dV dR Compute R values of turning point Compute whether R makes a maximum voltage or minimum voltage If y x show that logarithmic differentiation dy dx 2x 1 x 3 marks 3 marks 4 marks 1 by 6x In x 3 at the point x x 3 10 marks

TU 2 2 1 1 TX2 R The graph above is a graph of what function Oy cot x y sin x Oy tan x Oy csc x Oy cos x 37 2 27 Q

Match the function with its features V Spe N The function has a vertical asymptote at x 0 and is increasing for x 0 The domain is R and the function is increasing for ER The function has no y intercept an x intercept at 1 0 and a point at 2 1 The range is y ER y 0 and the function is decreasing for ER 1 y 52 2 y log 3 y log x 4

Where is the vertical asymptote of g x 3 log x 2 5 a x 1 b x 0 O c x 2 d x 2

When f x log x is transformed to g x 3 log x 4 which transformations do not occur Check all that apply a Reflection over the y axis b Vertical shift down 5 units c Horizontal compression by a factor of d Vertical stretch by a factor of 3 c Horizontal shift left 4 units

Determine the equation of the inverse of y log x 1 log7 b y log 7 a y Ocy 7 C y log r

How do you find the function values for f x log5 if your calculator does not allow you to directly evaluate logarithms with a base of 5 Write an equivale expression for log5 x

What is the domain of the function shown 0 15 Oa x R Ob x ER x 0 Oc x R x 0 Od x R x 0 15 20 25 30 35 4

Where is the vertical a x 1 b x 0 O c x 2 d x 2 asymptote of g x 3 log x 2 5

Given the Boolean matrices M and N as shown here select the matrix that equals M v N M 010 111 N 110 000

What is true about the function shown below Check all that apply 10 a The y intercept is at 0 1 b The x intercept is at 1 0 c The vertical asymptote is at x 0 d The horizontal asymptote is at y 0 e It is an exponential function of the form f x ab where 0 b 1 G K

Give a pair of alternate interior angles a pair of corresponding angles and a pair of alternate exterior angles a b 12 3 4 5 6 7 8 h a Alternate interior angles b Corresponding angles c Alternate exterior angles X and Z 0 2 and 2 and 0

Determine the equation of the inverse of y a y x log b y log Oc y log Od y P 3

A rectangular region is removed from another rectangular region to create the shaded region shown below Find the area of the shaded region Cm 4 cm 15 cm 9 cm

Questions 1 3 relate to two objects that start at x 0 at t 0 and move in one dimension independently of one another Graphs of the velocity of each object versus time are shown below Object A 2 v m mc 1 04 4 of 1 0 2 01 10 i Which object is farthest from the origin at t 2 seconds A A B B C they are in the same location at t 2 seconds D They are the same distance from the origin but in opposite directions 3 Which object is in its initial position A A B B C both A and B t sec Which object moves with constant non zero acceleration A A B B C both A and B D neither A nor B Velocity m s Object B v m ec 10 A 1 0 2 0 101 at t 2 seconds D neither A nor B 14 0 t sec Time s The graph above shows the velocity versus time for an object moving in a straight line At what time after t 0 does the object again pass through its initial position A 1 s B Between 1 and 2 s C 2 s D Be veen 2 and 3 s 5 A body moving in the positive x direction passes the origin at time t 0 Between t 0 and t 1 second the body has a constant speed of 24 meters per second At t 1 second the body is given a constant acceleration of 6 meters per second squared in the negative x direction The position x of the body at t 11 seconds is A 99m B 36m C 36 m E 99 m 6 A diver initially moving horizontally with speed v dives off the edge of a vertical cliff and lands in the water a distance d from the base of the cliff How far from the base of the cliff would the diver have landed if the diver initially had been moving horizontally with speed 2v A d B 2d C 2d D 4d

A kite flying in the air has a 12 ft line attached to it Its line is pulled taut and casts an 11 ft shadow Find the height of the kite If necessary round your answer to the nearest tenth 12 11 1 2 P

A point P x y is shown on the unit circle corresponding to a real number t Find the values of the trigonometric functions at t The point 5 245 5 2 5 P is sint cost tant csct sect cott P point s possible Q Q 1 0 C Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

Answer the questions about the polygons below Figure A Figure B Figure C Figure CO None Figure CO None Figure B O Figure CO None Figure A Figure B Which figure is a triangle Which figure is a heptagon O Figure A O Figure B Which figure is a quadrilateral O Figure A

Write the expression in terms of sine and cosine and then simplify so that no quotients appear in the final expression and all functions are of 8 onl 1 sec 8 sec 0 1 sec 8 sec 8

Question In APQR sin P sin Q 2 and p 15 Find the side length q H Select the correct answer below 09 1 O q 75 Oq 6 Oq 31 09 4 q 30

2 A function f x has the following properties a There is a hole at x b There are two zeroes One zero occurs when x c The equation of the horizontal asymptote is y d The equation of the vertical asymptote is x e The function passes through the point 0 2 Determine the equation of the rational function and state the 2nd zero 5 marks

A ladder leans against the side of a house The top of the ladder is 24 ft from the ground The bottom of the ladder is 10 ft from the side of the house Find the ength of the ladder If necessary round your answer to the nearest tenth 24 10 0f

Sive a pair of corresponding angles a pair of alternate exterior angles and a pair of alternate interior angles 8 6 4 2 57 13 M a Corresponding angles b Alternate exterior angles c Alternate interior angles X and 0 and 20 20 and 20 N S

Give a pair of alternate exterior angles a pair of corresponding angles and a pair of alternate interior angles 18 7 3 4 1 2 S 9 h m a Alternate exterior angles b Corresponding angles c Alternate interior angles X 20 and 20 and 2 0 0 and 2

16 If a b which of the following must be true 1 a b II 2a 2b III b a A II only B I and II only C II and III only D I II and III

The table below shows some input output pairs of two functions f and g that agree for the values that are given but some of their output values are missing t f t g t 0 0 0 15 0 5 0 5 30 45 1 3 1 3 60 2 2 75 2 7 2 7 90 105 4 4 Graph both functions and explain from the graph why f is invertible and g is not Come up with two real life situations that f and g could be representing Find and interpret the value f 4 in terms of these contexts 120 Complete the table in a way so that f could be invertible and so that g is definitely not invertible

Given the following two functions shown below The graph in green is y f x and the graph in blue is y g x 15 14 13 12 11 10987 2 5 0 556 7 6 marks 6 5 3 2 3 4 5 6 Determine the intervals on x where f x g x Your solution must be entirely algebraic Simply reading the intervals off of the graph will result in a mark of zero Note The horizontal asymptote for y f x is y 1 and the vertical asymptote is x 7 The horizontal asymptote for y g x is y 1 and the vertical asymptote for y g x is x 2

LC Exercise Apply the BFGS method to the following functions with x a and H I Show that H 3 G a f x x 22 x 8 4 x b f x x 5323 x 0 1 x

Find the missing side length Assume that all intersecting sides meet at right angles Be sure to include the correct unit in your answer 8 ft 13 ft 6 ft 5 ft 10 ft 00

In the figure below I m Find x 55 60

Give a pair of alternate interior angles a pair of alternate exterior angles and a pair of corresponding angles m 4 3 2 18 1 5 6 7 a b a Alternate interior angles and 0 b Alternate exterior angles and 20 20 and 20 c Corresponding angles X

Pea plant reproduction can be simulated with coin tossing The equally likely outcomes of heads and tails are used to simulate the transfer of equally likely genes R and r from two Rr pea plants red flowered because R is dominant bu carrying both red and white genes Two coins heads representing R and tails have been tossed 50 times for the simulation Using the color interpretation hh red ht th red and tt white gives the sequence of flower colors in offspring shown below red red red white red red red red red red red red white red red red red red red red red red red white red white red red red red red white white red white white red red red red red white red red white red red white white white Use the given sequence of flower colors to approximate the probability that five successive offspring all will have red flowers

A kite flying in the air has an 11 ft line attached to it Its line is pulled taut and casts a 9 ft shadow Find the height of the kite If necessary round your answer to the nearest tenth 11 5 X S

5 5 15 feet Part I State the equation that relates arc length to central angle 2 points Part II Find the angle 0 in radians 2 points Part III Convert your answer from Part II to degrees and write it to the neare hundredth of a degree 2 points

For the following right triangle find the side length x 35 12 X

ans wants to measure the height of a tree He sights the top of the tree using a mirror that is lying flat on the ground The mirror is 37 ft from the tree and ans is standing 10 6 ft from the mirror as shown in the figure His eyes are 5 ft above the ground How tall is the tree Round your answer to the nearest foot The figure is not drawn to scale 5 ft 10 6 ft 37 ft 0 ft X

The quadrilaterals JKLM and PQRS are similar Find the length x of RS M xXx 11 3 L J 5 6 K S 5 4 x R 5 P 9 10 8 Q