Complex numbers Questions and Answers

Use the diagram below to find the missing values Note triangle not to scale a 0 a Given a 5 and 0 find b 0 0914 b Given b 4 8 and 0 1 find a 0 4031

A cannon ball is launched into the air with an upward velocity of 380 feet per second from a 9 foot tall cannon The height h of the cannon ball after t seconds can be found using the equation h 16t 380t 9 Approximately how long will it take for the cannon ball to be 1846 feet high Round answers to the nearest tenth if necessary units How long long will it take to hit the ground units Question Help Message instructor

The flow rate of a safety discharge p asked if this flow rate could have ha measured as 509 pints per second d2

1 Use the limit of a Riemann sum to find the area under f x 1 3x from x 1 to x 2 2 Use the limit of a Riemann sum to find the area under f x x from x 0 to x 2

f x 2x 5x 3 x h f x h Simplify you

Iff S Tis onto and g T U and h T U are such that gf h f prove that g h If g ST h S T and if f T U is 1 1 show that if f g f h then g h 6 Let S be the set of all real numbers and T the set of all positive reals Find a 1 1 mapping of S onto T such that f s1 s2 f s1 f s2 for all s1 s2 E S

onsider the space curve F t t 4 2t 3 3t 4 a Find the arc length function for r t s t b Find the arc length parameterization for r t T S 30

Let r t ti j tk Then r t Oix j tk ti k Oix k Oix j tk ti k tla 1 ta x itk

Cooper 11 0 26 A lake has a volume of 10 8m 3 A river flows into the lake at the rate of 4 X 10 5m 3 day The same amount of pure water evaporates from the lake each day so the volume of the lake does not change The river contains 5 pollution The lake is initially unpolluted a What is the percentage pollution in the lake after t days b When does the pollution in the lake reach 1 after days

5 3x y 7 2x 4y 0

15 In a right triangle the measure of one acute angle is 12 more than twice the measure of the other acute angle Find the measures of the 2 acute angles of the triangle

Directions Identify the key components create a compound interest equation and answer the questions You invest 4000 into an account that compounds interest on a quarterly basis at 3 How much money will you have after 5 years Compound Interest formula A P 1 17 a P b r c n d t e Value after 5 years round to two decimal places

Use the shortcut for the linear approximation for roots and powers to find an approximation for the function f x for values of x near zero

Let V R For u v E V and a ER define vector addition by u v u v 2 and scalar multiplication by au au 2a 2 It can be shown that V is a vector space under the operations and over the scalar field R Find the following a 7 5 b 67 c the zero vector 0 d the additive inverse X

If the 8 men on a construction crew make up 40 of the entire crew how many people are in the crew

You bought a bottle of juice at apewer be

her team is independent of the axioms due Wed Feb 8th Stahl 1 2 2 make precise statements of Euclid s propositions 5 to 9 using modern terminology and notation Stahl 1 2 10 prove that the angle bisectors of a triangle are concurrent meet in a single point Does this hold in neutral geometry as well

17 19 21 23 25 18 4 g mL x 5 5 mL 1 0058 t x 1000 kg t 358 6 g 2 02 mol 56 9 g 2 000453 g mol 456 7 L x 7 8 mol L 18 20 22 24 26 21 4 g x 1 kg 1000 g 6 0 g 24 3 g mol 2 64 g 5 38 g mL 3 004 mol x 4 3 g mol 7 9 g 3 456 g mol

Complete the following tables Measured Value s d 18 58 1500 C 0 5306 m 0 0062 L 10128 km 4 2 bd 2 Calculated Value 6 249 mm 10 98 g 0 0573 mol 69 95 km h 296 038 cm Rounded off 6 2 11 0 0 07 70 0 296 0 s d 2 3 2 3 4

Use the figure to evaluate the following function given that f x sin x f 20 a 2 x www 3 Q f 20 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any nu

Question 1 15 marks Let g x y In x 2 y 2 4 e x y 3 a Find and draw the domain of g x y b Find gx gy gxx gyy gxy and gyx

Solve 6 6x 3x Choose 1 answer A x 3 1 B CO C D H H 1 17 4 4 34 3 7 193 12

Find an equation of variation where y varies jointly as x and the square of z and where y 385 when x 15 and z 11 The equation of variation is y Simplify your answer

Find an equation of variation in which y varies jointly as x and z and y 18 when x 3 and z 6 www The equation of variation is y Simplify your answer

2 The Intensity of light at a depth of x meter below the surface of lake satisfies the 10 Hint apply variable separable method 10 ii What is the intensity at a depth of 10m

Use the given zero to find all the zeros P x x 5 8x 4 3x 3 82x 2 78x

Problem 4 Sketch the following sets and determine which sets are of a z 2 i 1 b Re 1 2 1 2

f x x 6x 5 Question 4 25 points Which of the below could be a correct polynomial function for the graph shown at the right based on it zeros assume all coefficients must be real 3 2 1 x x 1 x 4 x 4 f x x 1 x 1 x 4 x x 1 x 1 x 4 x x 1 x 4 x 4 5 3 2 1 T 3 31 4 2 3 55

2x 30 4x 60 Solve for x Justify each step in a proof

Use the Euclidean Algorithm to compute the GCD of a 1856316 and b 246840 a gcd 1856316 246840 132 b lcm 1856316 246840 3471310920 Use backward substitution to find u and v in the equation 1856316u 246840v gcd a b So 1856316 246840 gcd a b

of what to study the followin n the actual assessment the ques ch skills are helpful for which prok nctions f x 1 1 x 1 1 x

An item selling for 330 is marked down 25 for a special promotion It is later marked down 20 of the sale price What is the final selling price of the item

Hint What is the surface area of a square pyramid that has an 8cm base length and triangular faces that are 14cm tall Surface Area cm 2

1 EXPLORATTON Adding and Subt Work with a partner Find the sum or diff match the sum or difference with its domai Sum or Difference a 1 x 1 3 x 1

Let p and q be distinct prime numbers Determine the total number of elements of order pq in Z pq x Z pq You should justify your answer

a city has cone shape buildings for storing salt and sand prices each building has a radius of 30 ft and a height of 20 ft what find the volume of the building use 3 14

11 10 8 7 6 5 4 3 2 1 Find an equation for the graph above 6 g c 5 4 3 2 1 2 3 6 2 3 4 5 6 7 8 9

Solve the general triangle shown A b Question 5 Solve the triangle shown b 60 ft C 150 ft C 120 C 83 a 61 50 ft a E

Determine a the slope of the line parallel to the line whose slope is 9 a What is the slope of a line parallel to the line whose slope is Select the correct choice below and fill in any answer boxes within your choice 5 A m OB The slope is undefined Type an integer or a simplified fraction and b the slope of the line perpendicular to the line whose slope is 5 5 9 b What is the slope of a line perpendicular to the line whose slope is Select the correct choice below and fill in any answer boxes within your choice 5 OA m OB The slope is undefined Type an integer or a simplified fraction

7 f x x 2 10 f x x 3 4 8 f x x 1 3 11 f x x 4 3 9 f x x 1 2 12 f x x 1 1

Write an equation for the function graphed below The y intercept is at 0 0 2 7 6 5 y 321 4 1 a

2 An apple tree casts a 24 foot shadow If the angle of depression is 61 how tall is the tree

Quadrilateral PQRS is inscribed in the circle shown and PQR is a semicir S P R Q anks to correctly complete the sentences

10 3x 75 12 4x 24

A SPAR 13 5 12 C Sin A Tan B Cos B Cos A Sin B

A sin B cos B tan B 15 B 8 C sin A cos A tan A

5 the sum of w and 3 4 is greater than or equal to 10 5

The equation for compound interest is A P invested r is the interest rate as a decimal n is the number of times compounded annually and this the number of years where P is the initial amount Determine the value of the account if the initial investment is 8 000 compounded monthly at a rate of 6 after 10 years 8409 12 8480 00 14 326 78 14 555 17

Which of the following is equivalent to log a log b log a b log ab 2 0 0212 03 Question 16 2 points Expand the logarithm

Consider the first six terms of this sequence 3 6 12 24 48 96 What would be the 19th term of this sequence 393 216 786 432 1 572 864