Quadratic equations Questions and Answers

et P be the point given in polar coordinates by 4 5 a Plot P on the polar axes below 61 6 7 6 21 3 4T 3 T 2 31 2 11 3 or the point P 51 3 77 6 1110 Express the point P in polar coordinates with a positive r value and a positive 9 valu

For which values of x is the following matrix invertible x 2 2 4 2 4 1 4 2 x

2 Like terms Combine the like terms a 2ab 5ab 3a b x y 5xy 3x y c 4xz 2yz 7xy

Question 1 2 points 4 Listen Factor the expression 9x x 1 7 x 1 Do include any spaces in your answer Type exponents using caret key For example t

Solve for x rounding to the nearest hundredth 550 2 55

1 Graph the function g given by g x f x 2 Graph the function h given by h x x Draw each graph in a different color and label each graph with the name of the function YA f 2 1 4 8 4 2 0 2 0 7 1 6 N

Which of the contexts below represents exponential decline or decay A population of 350 bacteria doubles every day The amount of a certain medication in a person s bloodstream decreases by every week A coin collection appreciates at a rate of 19 4 per year An elevator descends at a rate of 26 feet per second

Which of the contexts below could not be modeled by an exponential function A car depreciates at a rate of 3 7 per year A sunflower was growing at a rate of 2 75 inches per week A certain population of 25 aggressive zombies quadruples every week Money invested in a savings account grows at an annual rate of 2 2

What are the domain and range of the function f x 2482477 41

NASA launches a rocket at t 0 seconds Its height in meters above sea level as a function of time is given by h t 4 9t 256t 150 A Assuming that the rocket will splash down into the ocean at what time does splashdown occur Round answer to 2 decimal places The rocket splashes down after B How high above sea level does the rocket get at its peak Round answer to 2 decimal places The rocket peaks at seconds meters above sea level

2 36 27 18 a 9 18 27 2 4 6 8 36 q Which of the following is the equation of the graph shown Oy x 9x 10 Oy x 9x 10 Oy x 9x 10 Oy x 9x 10 Oy x 9x 10 Oy x 9x 10 10 12

Find the equation 1 KIN 2 A y 2 sin x B y 2 sinx C y 2 sin x D y 2 sin x

432 1 1 2 3 4 Determine the period N O CO 181 Enter

d p 8p 16 Write each function in vertex form and state the vertex f x x 6x 16 a Vertex form h 0 6x 16 6x x 161911 Explain how you know the vertex is a maximum or minimum 2 f x 2 20 Vertex dola x 3

Exer nd x intercepts Describe the domain and range of the function 3 m x x 5 x 1 4 y 4 x 3 x 1

ollowing identities If it is a one step problem please state the formula used a b O c sin x cos x sin x cot x cos x cot2 x sec x tan x csc x d sin x sin y sin x y sin x y

12 Write a quadratic function in standard form whose graph passes through 0 0 2 0 and 2 4

Solve for all values of x in the given intervals 0 a 2 cos x 1 0 for 0 x 2 b sin x tan x for CER c 3 cot2 x 1 for

Express the answer in simplest radical form 3 10 7

3 Rewrite j26 in simplest form

In a particular factory the ambient noise has a loudness of 100 dB If prolonged exposure to a loudness of 85 dB can cause permanent damage how much more intense is the factory than the damage threshold

A diving pool that is 6 5 m deep and full of water has a viewing window on one of its vertical walls Find the force on a window that is a square 1 m on a side with the lower edge of the window on the bottom of the pool Use 1000 kg m for the density of water and 9 8 m s for the acceleration due to gravity Find the width function w y for each value of y on the face of the window w y Use integers or decimals for any numbers in the equation

Solve for all possible values of x within the domain of the following logarithmic expressions a log4 log x 1 b 3 log 9

Solve each system of equations algebraically 1 4x y 25 1 2x y 2 3 4 5 6 7 y 1 4 x x y 1 x 3x 4y 2 y 2x 1 x y 2 x 100 y x y 10 x 2y 5 x y 16 y x 4 3x 5 y x 2y 10

14 Tony wants to have 4000 in 5 years a How much does he need to invest now at 3 8 annual interest compounded semi annually Round your answer to the nearest dollar

15 Andrea wants to borrow 2400 She is considering the following two loans A 2400 at 5 per year compounded semi annually for 4 years B 2400 at 4 7 per year compounded quarterly for 4 years a Draw a time line to illustrate each loan b Which loan should Andrea take Justify your response

Given a rectangular box with dimensions I w and h Determine l w and h in order to maximize the volume under the following condition the sum of the lengths of all its edges is 60cm

Consider the following functions Step 1 of 4 Find f g 1 f 1 5 4 1 1 1 and g 1 3 1 4 Answer How to enter your answer opens in new window f g 1

Find the Area of the figure below composed of a rectangle with two semicircles removed Round to the nearest tenths place 6 D

The total cost in dollars of producing a product is given by C x 500x 0 1x 1400 where x represents the number of units produced a Give the total cost of producing 10 units b Give the value of C 100 C 100 c Give the meaning of C 100 For every additional 100 units created the cost in dollars decreases by this much For every 100 increase in cost this many more units can be produced This is the total cost in dollars of producing 100 units It costs 100 to produce this many units

For f x x 1 2 and g x 1 3x we have fog x f g x f 1 3x Step 3 Find f 1 3x by substituting 1 3x for the input and simplify x 1 f 1 3x 11 1 3r X X

f f x Step 1 To compose a function f with itself substitute f x for x in the formula for f f f x f I

f x f f x Step 1 Here we are multiplying a function by itself For f x x 1 2 we have the followin f f x x 1

Step 1 To compose two functions we use the definition that fog x f g x Step 2 For f x x 1 2 and g x 1 3x we have fog x f g x g x

Solve this equation to find x 4 86x 164 500 X 4 86 x 164 500 Enter an exact number to the nearest 100

Solve the equation e3z 5 14 Fill in blanks to express the answer in the form The value of a is 1 Type an integer or a simplified fraction The value of b is AV Type an integer or a simplified fraction The value of Cis A Type an integer or a simplified fraction Ina b C

Express the following inequality in interval notation X29 The inequality in interval notation is Type your answer in interval notation

c Given two sequences fn neN gn neN C C 0 1 of continuous functions on the closed unit interval 0 1 defined by fn z and 9n 1 Find the limit f and g respectively of each sequence if it exists Which of these sequences converge uniformly on 0 1 That is do f and g belong to C 0 1 or not nx 1 nx nx 1 n x

f x x 1 x 2 x 1 and g x x 2 x 3 x 3 For what values of x are both f x and g x decreasing

Plot the points x y and x2 Y on a coordinate system if x 4 y 1 X 7 and y 3 Plot the point x 4 1 08 6 10 2 Ay 6 10 17

Simplify the expression 5x 2y4 4x y4 137 6x 4y 5y 105 4 5x 2y4 4x y4 137 6x 4y 5y 105 Simplify your answer

Michael was sketching the graph of f x He lost part of his notes including the equation for the function Giv the partial information below sketch a possible graph of f x The domain of f x is R lim f x o and lim f x 0 X 8 X118 The y intercept is 2 The x intercepts are at 1 3 and 5 There are local extrema at x 2 3 and 4

x 1 4x 9 Sketch the function f x Be sure to include everything we have talked about intercepts restrictions behaviour around asymptotes local extreme maxima minima points of inflection all intervals of everything etc Complete all calculations on a separate page and graph the function below Make sure you hand in all your calculations

Suppose that you have 5500 to invest and you invest x dollars at 15 and the remainder at 6 Write expressions in x that represent the follor values a the amount invested at 6 b the interest earned on the x dollars at 15 c the interest earned on the money invested at 6 d the total interest earned

Find the value of x 116 144 A 117

Solve log 7x log 5x 14 Select the correct answer below 02 O 14 07

Convert each equation from Polar to Rectangular Identify the shape if possible 0 57 4 Rectangular equation The shape is a n Question Help Select an answer Select an answer line circle Submit Question parabola

Solve 72 Round to the nearest thousandth as needed Provide your answer below

The table shows the sight distance y in feet for a car traveling at x miles per hour x in mph 20 60 65 40 50 1485 1840 2140 2315 y in feet 815 OA 2500 a Make a scatter diagram of the data Choose the correct graph below OB OC 80044 OA 2500 100 000 P 0 30 1090 100 Q Av E 2500 800 B 2500 100 800 CODE Q 100 70 2490 b Use the regression feature of a calculator to find the best fitting linear function for the data Give the coefficient before x to the nearest hundredth and the constant to the nearest tenth y Type your answer in slope intercept form Graph the function with the data Choose the correct graph below 2500 800 14 100 OC 2500 17 800 O D 100 2500 800 0 COD 2500 100 800 14 100

Tutorial Exercise Consumers Surplus The demand function for a certain brand of CD is given by p 0 01x 0 2x 32 where p is the wholesale unit price in dollars and x is the quantity demanded each week measured in units of a thousand Determine the consumers surplus if the market price is set at 8 disc Step 1 We are given that the demand function is given by p 0 01x 0 2x 32 where p is the unit price in dollars and x is the quantity demanded each week Further we are told that the unit market price is set at 8 Therefore p 8 We use this information to find the corresponding demand equation and solve it for x p 0 01x 0 2x 32 8 0 01x 0 2x 32 0 0 01x 0 2x 100 0 100 0 01x 0 2x 0 x 20x 0 x 40 x 40 or x