Complex numbers Questions and Answers

Write a system of two equations in two variables to solve the problem When fully extended a ladder is 31 feet in length If the extension is 5 feet shorter than the base how long is each part of the ladder base extension ft Base ft Extension

The price p of a certain product and the quantity x sold obey the demand equation shown 1 3x 300 0 x 900 p Suppose that the cost C of producing x units is C x 150 Assuming that all items produced are sold find the cost C as a function of the price p Hint Solve for x in the demand equation and then form the composite What is the cost C as a function of the price C p Simplify your answer 400

For f x 8x 2 and g x 6x find the following composite functions and state the domain of each a fog b gof c fof d gog B The domain of g of is all real numbers c f of x 64x 18 Simplify your answer Select the correct choice below and fill in any answer boxes within your choice A OA The domain off of is x Type an inequality Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed B The domain of f of is all real numbers d gog x Simplify your answer

In Exercises 23 to 28 with P all polygons as the universe draw a Venn Diagram to represent the relationship between these sets Describe a subset relationship if one exists Are the sets described disjoint or equivalent Do the sets intersect 23 T triangles I isosceles triangles

Given its graph write the equation of the rational function Explain your reasoning Part a 3 2 1 ST 5 4 3 2 1 Y 1 2 3 4 5 2 3 4 crt 5 6 X

Use the Law of Cosines to find the angle a between the vectors Assume 0 s as 180 v 8i 4j w 4i 8j

Finally compute F 6 F 0 to get the area over the 1 2 e 12 1 2 81 376 896

Use the supply and demand curves in the graph on the right to find the equilibrium price The equilibrium price is Price in dollars 256 192 128 64 0 0 P Demand Supply 80 160 240 320 400 F

find the vector or scalar u 2i 3j v 6i j W 3i

Write the following expression as a sum and or difference of logarithms Express powers as factors loga u6v5 log a u 0 v 0 u6v5 Simplify your answer

Suppose that f x 3x 1 and g x 2x 4 a Solve f x 0 b Solve f x 0 d Solve f x g x c Solve f x g x e Graph y f x and y g x and find the point that represents the solution to the equation f x g x

Solve the equation ex e3x 4 The solution set is Type an integer or a simplified fraction Use a comma to separate answers as ne

4 Classify each of the a E C as algebraic or transcendental over the given field F If a is algebraic over F find degree a F b a ei F R

An open faced box is to be constructed by cutting squares out of the corners of a 12in by 12in sheet of tin and folding up the sides Which of the following describes the volume of such a box O The volume of the box is given by h 12 2h 2 in where h is the side length of the cut out squares O The volume of the box is given by h 12 2h in where h is the side length of the cut out squares O The volume of the box is given by 12 2h in where h is the side length of the cut out squares O The volume of the box is given by h in where h is the side length of the cut out squares I don t know

a 0 1 b 2 3 c 2 1 d 3 5 B C the system of inequalities shown in the graph determine which points are solutions to the system 10 8 N IN 321

a Suppose that u 3 2 i v 1 i and w v8 u5 Re w Number Im w Number b Let z 95535 154008 i Enter a square root of z in maple syntax in the box below

Find the amount of money in an account after t 9 years if P 4 100 is deposited into the account with an annual interest rate of r 5 compounded quarterly Use the equation where r is entered as a percentage and round your answer to the nearest cent

h x 4x x 4 2 x 3 2 If there is more than one answer separate t

Evaluate the given integral over the solid ellipsoid SSS D 5 xyz dxdydz PN XN 2 y 2 b 2 Z 1 Hint Let x au y bv and z cw Then integrate over an appropriate region in uvw space 2

3 sin 15 cos 15 tan 15 sin 1177 12 COS tan 11 12 11 12

6 pts 2 Solve the following system using a matrix and converting the matrix to reduced row echelon form without introducing any fractions 2x 5y 7 7x 4y 16

1 Imagine that you are at the origin If the waves you can see clearly are 27 miles away directly to the west of you then construct an equation describing the set of all points that you can see with the binoculars The binoculars are focused for 27 miles and the points will consist of two coordinates the distance east and the distance north

Evaluate loga a x8 y5 given that log x 7 2 and loga y 4 5

Find all zeros of the following polynomial Be sure to find the appropriate number of solutions counting multiplicity using the Linear Factors Theorem f x x 3x 23x 85 Answer

Graph 6x 5y 25 using slope intercept form

1500 is invested at an interest rate of 4 5 per year compounded continuously find the value of the investment after the given number of years Round a 2 years 1641 26 b 4 years 1795 82 c 12 years 2543 82 x X

two coupled differential equations of the first order have the following form dx t f x t with x t x t y t T f x t Solve the differential equation d d y t 5 8 ay t x t to obtain an equation relating x t

Solve the logarithmic equation Log x 4 Log x 4 Log 3 O No solutions Ox 8 O x 12 O x 10

Let U 0 1 2 3 4 5 6 7 A 1 2 3 B 2 3 4 and C 4 5 6 List the elements of the set B n AUC O 0 1 O 7 O 1 2 O 0

For the demand function q D p 461 p find the following a The elasticity b The elasticity at p 119 stating whether the demand is elastic inelastic or has unit elasticity c The value s of p for which total revenue is a maximum assume that p is in dollars a Find the equation for elasticity E p

10 3 points Solve for x log 3x 7 5

Find the difference quotient and simplify your answer f x f 27 f x x2 3 7 17 X 27

Explain how you would find the discriminant of the function f x ax bx c

10 7 points Sketch the graph of a function with the given properties x intercept is 3 0 y intercept is 0 1 5 x 2 and x 2 are vertical asymptotes y 1 is the only horizontal asymptote and passes through the points 4 0 5 2 5 1 1 5 4 1 2 1 2 1 5 4 2 5 3 3 2 4 1 5

Given the matrices A 2 A It is Select an answer Select an answer B If ad not possible possible 34 20 to add these matrices hat is A B and B 4 4 2 5

Write a polynomial f x that meets the given conditions Answers may vary Degree 3 polynomial with zeros 3 2 and 5 f x

The lower quartile for wages at a coffee shop is 9 25 and the upper quartile is 10 25 What can you conclude Choose the correct answer below OA Half the workers earn between 9 25 and 10 25 because the lower quartile has one quarter of the workers below it while the upper quartile has three quarters of the workers below it B The range is 1 00 because that is the difference between the lower quartile and the upper quartile C The median is 9 75 because that is the average of the lower quartile and the upper quartile D Half the workers earn between 9 25 and 10 25 because the lower quartile has half the workers below it while the upper quartile has half the workers above it E The median is 9 75 because that is the difference between the lower quartile and the upper quartile

Use a rectangular array to represent and solve each product a 2 3 1 5 b 3 5 4 7

in a set of y 2x 8 a t x b t 4 x repres the graph of th ular equation using answers as com separ STS OF

Using t sec 8 we can also say that 1 sec 8 V tan 8

Find the values of and at the given point ox dy z 3xy 5yz 2y 34 0 4 3 1 Ax Type an integer or a simplified fraction

Erin is writing about the history of sonnets Which is a fact Erin can include in her history O Shakespeare was the first to create poetry as a sonnet O Shakespeare was a poet who wrote only in sonnet form O Sonnets were invented in Italy before Shakespeare s time Sonnets were created by poets who wrote without rhyme patterns

Next question For the given function find the indicated function values Find the domain of the function f x 0 5x 6 f 24 f 20 f 18 f 16 f 24 Type an integer or decimal rounded to the nearest tenth as needed

Let 712 1 1 7 2 1 1 Need Help Hide Transcribed Text and T R R be a linese tansfermation fuch that T 1 1 1 4 0 1 7 0 1 2 4 4 1 T 1 0 1 0 1 1 www e Find the indicated inaje TT 2 1 1

1 Write the chemical formula for the lonic compounds made from the following elements Chemical Formula Elements potassium and iodine barium and chlorine sodium and oxygen aluminum and nitrogen lithium and sulfur magnesium and oxygen calcium and chlorine boron and chlorine beryllium and sulfur Metal ion Non metal ion Name

3 Real numbers a b c satisfy the condition a a b Find 6 a b 6 b c c b c c c a a c a

Given that f x x 6 g x evaluate h 5 A h 5 3 30 1 1 and h x x x 6

Use the difference of two squares formula to factor 1 16x y 1 16x y

n Calculus you will see the symbol y Treat y as a variable and solve the equation for y 8 x 5y 8 x 5y y 200y y 8x

Answer How to enter your answer opens in new window V x x 1 2 V x 2 Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is L O does not have an inverse function