Complex numbers Questions and Answers

40 Write an equation of the circle satisfying each of the following conditions legg cen a Center 3 4 and passing through 2 6 b Center 2 5 and radius 7 int istotaliups li c Endpoints of a diameter at 4 5 and 12 7

5 For the following equation Decide how many different real number roots the equation has x 4x 8 different real number root s

Show that a triangle with vertices at A 2 2 B 2 1 and C 3 5 is isosceles Distance from point A to point B Distance from point B to point C Distance from point A to point C Since Select have the same length the triangle is isosceles

125 1 Note there are five images to evelnate O

3 5 pts Find a formula for the general term an of the sequence assuming the pattern of the first few terms continues 63 89 1027 1281 14243

31 Maximize P 2x 6y given the following constraints 4x 8y40 10x 10y 80 x 0 y 0 The maximum is at

ind the volume of the sphere shown to the right Give an answer in terms of and rounded to the nearest cubic unit he exact volume is in Simplify your answer Type an exact answer in terms of t C

5 Find all of the fourth roots of 3 3i in polar form gop 5444 keep Keep in radians 324cis 360 18cis45

2 Rewrite in polar form for oce 360 Then write two other possible polar forms for the number 1 2 round to nearest tenth of a degree

ABCDE what is the scale factor E N DO 2 E B 20 D TO

When an object is translated the resulting image is congruent to the pre image O True False

If point x y is rotated 180 degrees about the origin the resulting point is x y True False

The transformation shown is a translation True False

Which of the following is the appropriate way to name the line connecting points A and D

If point x y is reflected over the x axis the resulting point is x y True False

1 point Which image below shows an angle O

73 On July 21 2016 the water level in Puget Sound WA reached a high of 10 1 ft at 6 a m and a low of 2 ft at 12 30 p m Across the country in Long Island NY Shinnecock Bay s water level reached a high of 2 5 ft at 10 42 p m and a low of 0 1 ft at 5 31 a m The water levels of both locations are affected by the tides and can be modeled by sinusoidal functions Determine the difference in amplitudes in feet for these two locations

457 The function f x a cos bx c is plotted on the graph shown below f x 1 2 3 4 M 3 What are the values of a b and c a 2 b 6 c 3 a 2 b 3 c 1 a 4 b 6 c 5 T a 4 b c 3 27 X

455 Which equation is represented by the graph shown below 1 2 3 4 Inf 37 0 5 0 5 2 y cos 2x y cos x y y 1 20 cos x 1 y 2 cos x 122

1 a Show the given information in the diagram using tick marks to show congruent sides and arcs to show congruent angles b Show any other congruent parts you notice from vertical angles sides shared in common or alternate interior angles with parallel lines c Give the postulate or theorem that proves the triangles congruent SSS SAS ASA AAS HL Finally fill in the blanks to complete the proof d Statements 1 2 Given BC DC AC EC Prove ABCA ADCE 3 ABCA ADCE Reasons 1 Given 2 Vertical Zs Theorem 3 B E

Find the volume of each cone Round to the nearest tenth 12 cm 2 e T 9 cm

13 Find the sum of the geometric series 6 4 1 2 1354 1333 1364 O1349 O None of these are correct

7 Find the sum of the geometric series a1 27 a3 243 r 3 S3 x

53 153 Find the value of x 1 To X 4 19 50 180 7 X 55 X 16 18 47 5 6 to 3x 2 G 50 18 x 155 180 4x 6 24 4X 4 X 5 4 X 5 2015 60 55 36 55s 8 2x 60 76 X X X 3 132 152 T26 194 94 X x 5 43 9 ZBR x 45 2 2 4 40 965 40 20 45 xo 2 6 Same X 4x 76 180 18212 76 1801020 76 1 04 70 1647 40 X t 40 45 11000 7 0 170 770 4 45

1 For the geometric sequence find the two missing terms between 96 and 96 12 12

Consider the following polynomial q x x4 7x 11x 7x 12 Step 2 of 2 Use polynomial division and the quadratic formula if necessary to identify the actual zeros Answer Separate multiple answers with commas Keyb Previou

find the perimeter of a regular hexagon joined with a regular pentagon Each side of the hexagon is 1 25 times larger than each side of the pentagon The Pentagon radius is 55

7 Find the sum of the arithmetic series if a 1 n 10 and d 4 S10

6 Find the sum of the arithmetic series if an 46 n 15 and d 4 S15 E O S15 1120 O S15 1110 S15 1109 1099 O 15 S15 O None of these are correct

5 Find the sum of the arithmetic series if a 84 n 15 and d 10 S15

Look at ALMN on the coordinate plane N 3 4 3 2 19 2345 2 M Which coordinate plane shows ALMN after a 90 counterclockwise rotation al the origin

On your birthday your grandmother gave you 18000 You would like to invest at least 7500 of the money in municipal bonds yielding 3 and no more than 4000 in Treasury bills yielding 5 How much should be placed in each investment in order to maximize the interest earned in one year Assume simple interest applies Let x represent the amount of money in municipal bonds and y represent the amount of money in Treasury bills Answer Enter the value in the first box and the ordered pair in the second box Maximum income of Maximum income at Keypad Keyboard Shortcuts

Simplify the following expression 4 2i 1 i

5 Calculate the net outward flux of the vector field F x y z xi yj 5k across the surface of the solid enclosed by the cylinder z 1 and the pla y 0 and y 2

Z 1 i 2 1 and b Write the vector z Z 2 a Show that z z is an orthonormal set in C 2 4i 2i combination of z and 2 S 2 as a linear

prove cos x y cos x y cos 2x cos 2y 1

Which equation describes this graph 6 5 4 3 2 Select the correct answer below 8 7 5 4 3 2 3 4

c A tower 48 7 m high is located at the top of a hill Point A at the foot of the hill is 305 m measured along the hillside from the tower the angle between the surface of the hill and the line of sight to the top of the tower is 8 90 Find the angle of elevation of the hill to the horizontal plane at point A The angle 5 4 0

T D 2 E C DIRECTIONS Choose the best answer for each question below Remember you can only draw logica geometric conclusions based on information that is given to you You cannot assume from the diagram 1 In the figure below D is the midpoint of AC and DC EC Which of the following is always true BE EC AD BE AD EC AC BC

Find the distance d P1 P between the given points P and P2 P 0 0 P 3 1 www d P1 P Simplify your answer Type an exact answer using radicals as needed 10 at TH k

2 For each of the following quadratic functions complete the table below a f x 21 21 3 Function b g x c d 1 3 20 3x 2 f x 1 3 h t 3x Show work to b 1 2 2a find Show work to b find 2 2a Vertex Axis of Symmetry Equation

Find all points having an x coordinate of 1 whose distance from the point 3 2 is 5 The point s is are Type an ordered pair Use a comma to separate answers ar nodod

5 Give the domain and range in interval notation for each of the graphs shown below n b c Lev 2 2 4 6 10 3 2 1 3 2 1 1 2 3 Domain Range Domain Range Domain Range

Find the distance d P1 P2 between the points P and P2 P 4 2 P 5 5 d P1 P 0 Simplify your answer Tynn on

the co nates of two points on the real number line the distance between these points is www If 3 and 5 are the coordinates of two points on the real number line the distance between these points is Type an integer or a decimal

9 A movie earned 80 million in its first week of release with the sales decreasing by 30 each week a How much will it earn in the 4th week hat will be the total sales for 8 weeks if it continues at this rate

7 For angle in the second quadrant tan 0 a sin 0 314 b cos

5 Rewrite the general form of the circle below into graphing form Identify the center and radius of the circle and sketch the graph x y 8x 6y 11 0 Center

Parabolas Write the equations in the proper form Name the vertex and focus the equations of the axis of symmetry and directrix and the direction of opening of the parabola Then find the length of the L R latus rectum y 2x 5x 10 Vertex Axis Focus Directrix

For the following equation a give a table with at least three ordered pairs that are solutions and b graph the equation y x 9 a Complete the following table X 4 y