Linear Algebra Questions and Answers

Add the polynomials 5x 7x 9x 4x 12x 6x 12x

3 Points DETAILS he terminal point P x y determined by

4 1 point How many um are there in 2 67 x 10 10 ft Type your answer Previous

Product Lemonade Eggs In a city that applies 6 sales tax how much money total will a person pay for eggs A 5 25 B 4 50 C 4 77 D 7 20 Cost per item Subject to sales tax 6 00 Yes 4 50 No

Find the unknown angle measures in the pair of similar triangles The measure of angle B is Simplify your answer Type a whole number A P 380 VY 389 R B

Convert the angle to degrees minutes and seconds form 59 26

A group of retailers will buy 76 televisions from a wholesaler if the price is 350 and 116 if the price is 300 The wholesaler is willing to supply 56 if the price is 280 and 136 if the price is 370 Assuming that the resulting supply demand functions are linear find the equilibrium point for the market q p x

A manufacturer of DVD players has weekly fixed costs of 1 580 and variable costs of 13 50 per unit for one particular model The company sells this model to dealers for 18 50 each a For this model DVD player write the function for weekly total costs C x C x 1 580 13 50x Excellent b Write the function for total revenue R x R x 18 50x Fantastic job c Write the function for profit P x P x 5x1 580 Nice job d Find C 150 C 150 2 775 Interpret C 150 When this many DVD players are produced the cost is 150 This is the cost in dollars of producing 150 DVD players O For every additional DVD player produced the cost increases by this much O For each 1 increase in cost this many more DVD players can be produced That s it Find R 150 R 150 2 775 x Find P 150 P 150 Amazing job Interpret R 150 O This is the revenue in dollars generated from the sale of 150 DVD players When this many DVD players are produced the revenue generated is 150 O For each 1 increase in revenue this many more DVD players can be produced O For every additional DVD player produced the revenue generated increases by this much Interpret P 150 This is the profit in dollars when 150 DVD players are sold and since it is positive it means that the company makes money when 150 DVD players are sold For each additional DVD player sold the profit in dollars increases by this much but since it is positive it means that the company is producing too many DVD players O This is the profit in dollars when 150 DVD players are sold but since it is negative it means that the company loses money when 150 DVD players are sold

6 Jessica s Salary is 3520 monthly Her employer pays 185 towards her RPP each pay period She also receives 155 car allowance each pay period She worked overtime and received 250 She pays 45 union and contributes 135 RPP each pay period Calculate her net taxable income for the month

7 Sarah earns 800 00 in regular wages per weekly pay period She also receives a taxable car allowance of 120 00 per week She worked 4 over time hours this pay period for which she was paid 140 Her employer pays 75 each pay period towards RPP on her behalf She pays 40 00 union dues per week and contributes 20 00 to her company s RPP plan Sarah s federal and provincial claim code is 2 Assume Federal Tax 60 00 and Provincial Tax 70 00 Calculate Sarah s net pay for the week showing the various steps

Two dice are rolled What is the probability P sum is 3 1 4 12 1 2 1 18

Find the exact value of sec tan 7 tan 3 010 Undefined B

ewrite csc cos 5u as csc cos 5u as an algebraic expression in u

A company distributes college logo sweatshirts and sells them for 40 each The total cost function is linear and the total cost for 50 sweatshirts is 3128 whereas the total cost for 260 sweatshirts im 5488 a Write the equation for the revenue function R x R x b Write the equation for the total cost function C x C x c Find the break even quantity XU sweatshirts

The graphs of the demand function and supply function for a certain product are given below Use these graphs to answer the questions P P 600 400 200 200 Demand 400 600 800 a How many units q are demanded when the price p is 50 q b How many units q are supplied when the price p is 50 9 600 400 200 Supply 200 400 c Will there be a market surplus more supplied or shortage more demanded when p 50 surplus 600 800

6 From a 24 inch by 24 inch piece of metal squares are cut out of the four corners so that the sides can then be folded up to make a box Let x represent the length of the sides of the squares in inches that are cut out Express the volume of the box as a function of x Graph the function and from the graph determine the value of x that will yield the maximum volume

curve of radius 950 ft If the vehicle was originally traveling at 45 mi h determine the following Assume that the vehicle traveling at sea level and has a front cross sectional area of 27 ft Also assume the density of air is 0 0766 lb ft3 and the aerodynamic drag coefficient is 0 4 Use the following equation for the rolling resistance R in lb R Crs 2 15C w for which Cr 0 012 Crv rs hp a the additional horsepower on the curve the vehicle must produce to maintain the original speed 102 0 650 x 10 6 sec ft2 u is the vehicle speed in mi h and W is the weight of the vehicle in lb c the total horsepower b the total resistance force in lb on the vehicle as it traverses the horizontal curve 54 22 lb

15 A ladder consists of 31 rungs If the rungs taper uniformly from 18 inches to 28 inches a How much material would be needed for the 20th rung b How much material would be needed for all of these 31 rungs

Find the values of m and b that make f continuous everywhere if x 4 m 20 x x x 4 f x mx b b 3 2 36 When showing your work be sure to include all limit calculations and a sketch of the graph if x 4 1 if x 1

2 22 WP Air contained within a piston cylinder assembly is slowly bom compressed As shown in Fig P2 22 during this process the pressure first varies linearly with volume and then remains constant Deter mine the total work in kJ P kPa 150 100 50 0 0 3 0 015 V m 2 0 055 0 07 129

The first figure takes 5 matchstick squares to build the second takes 13 to build and the third takes 21 to build as car be seen by clicking on the icon below a How many matchstick squares will it take to build the 11th figure b How many matchstick squares will it take to build the nth figure c How many matchsticks will it take to build the nth figure Click the icon to view the matchstick square figures a The 11th figure will take squares to build Simplify your answer

A sign hanging outside Joe s Diner has a mass of 80 kg see the figure If the supporting cable makes an angle of 60 with the wall of the building determine the tension in t cable Use 9 8 m s2 for the acceleration due to gravity 160 30 JOE S DINER

9 3 5 x 106 X 4 110 x 1013 10 6 0300 7 00 x 10

7 27 x 105 14563 9 3211 x 108 7 1112 x 104 777 3256 2 3 x 10

Dotermine whether the given furction is a solition to the given daterentid equation theta e 3 t 5 e 4 t frac d 2 theta d t 2 theta d t 20 31 e 4 t V d 0 dt the two sides of the diflerential equation equvalert on any ertevale of

Solve the system of equations by using graphing 4x 2y 20 x 2y 10 Step 1 We want to solve the following system of equations using graphical methods 4x 2y 20 x 2y 10 To do this graph the lines with equations 4x 2y 20 and x 2y 10 and find the point where their graphs intersect The x intercept of the first equation found by letting y 0 is x y x Submit Skip you cannot come back X The y intercept of the first equation found by letting x 0 is

Using U S Census Bureau projections from 2020 to 2060 the number of U S females under the age of 18 in millions can be modeled by the function N 0 150x 37 4 where x is the number of years after 2020 a Use a graphing calculator to graph this equation for the range x min 0 x max 40 N min 35 N max 45 N N 44 42 40 N 38 36 N 44 42 40 38 36 10 10 20 20 30 30 40 40 44 42 40 38 36 10 20 30 b The point 30 41 9 lies on the graph of this equation Explain its meaning The model projects that the number of U S females under the age of 18 will be 41 9 million in 2030 The model projects that the number of U S females under the age of 18 will be 30 million in 2030 40 44 42 40 38 36 10 20 30

An advertising agency has found that when it promotes a new product in a city of 350 000 people the Fate of of people x who are aware of it and is given by R 31 500 0 09x where x 20 and R 2 0 R 30 000 25 000 20 000 15000 10000 5000 R 60 000 50 000 40000 30000 20000 10000 a Use the intercepts to determine a window and then graph the equation for x 0 R 100000 200000 300000 400000 100000 200000 300000 400000 60 000 50 000 40 000 30 000 20 000 10000 100000 200000 300000 100000 R 30 000 25 000 20 000 15000 10000 5000 b is the rate of change increasing or decreasing Explain why your answer makes sense in the context of the problem The rate of change is decreasing because as the number of people aware of the product increases the rate of change goes down The rate of change is increasing because as the number of people aware of the product increases the rate of change goes down 100000 200000 300000 400000

a x 6 b x 30 c x 5 2x 8 In the diagram three parallel lines cut two transversals Solve for x O a O b OC O d x 1 x 2 d x 12 e x 7 x 4

2 Consider the transformation T of R2 that reflect each point in the plane with respect to the line 1 3 This line goes through the origin and the angle between this line and the horizontal axis is 6 x2 21 a Draw a picture with vectors e e2 T e T e b Write down the standard matrix of T c Compute T x with x

Carl and Ellie split a chocolate bar into 8 pieces of the same size Carl took 7 of the pieces and Ellie took 1 of them they then divided a 2 chocolate bars of the same type into 16 pieces of equal size Then they gave some of them to their sister and then equally split the remaining pieces between the 2 of them After all this Carl s quantity of chocolate ended up being 4 times Ellie s quantity How many pieces of the 2 bar did they each get Write an equation and solve it to answer the question

A student decides to finance a used car over a 5 yr 60 month period After making a down payment of 1000 the remaining cost of the car including tax and Interest is 14 820 The amount owed y A t In is given by A t 14 820 247t where t is the number of months after purchase and 0 st 60 Determine the t intercept and y Intercept and Interpret their meanings in context Amount Owed on Vehicle after Months Amount Owed 15000 12000 9000 6000 3000 10 10 A t 14 820 247t 20 40 Number of Months t

Joe rides his bicycle an average of 15 mph The distance Joe rides d t in mi is given by d t 15t where t is the time in hours that he ric a Evaluate d 3 and interpret the meaning b Determine the distance Joe travels in 35 min Give the exact answer Do not round Parte Part 1 of 2 a d 3 Thus Joe travels mi in hours

a Prove that 22 b Prove that Span 0 0 Span 022 in R Span in R Remember

Convert the numeral to a numeral in the base indicated 9 030 to base 12 OA 5 82612 OB 5 28612 OC 5 02612 OD 5 20612

Find the distance from the point Q to the line l 0 0 0 X Q 0 2 0 l with equation y 222 5

Find the vector form of the equation of the line in R2 that passes through P 3 5 and is parallel to the line with general equation 3x 2y 5 x t

The line passes through the point P 1 1 1 and has direction vector 2 3 1 a Consider the plane P defined by the following equation 2x 3y z 1 Find the normal vector for P n d O 5 1 7 X What is the relationship between d and n Lett be a scalar d n Od tn O neither Determine whether and P are parallel perpendicular or neither parallel O perpendicular Oneither X 5 b Consider the plane P defined by the following equation 5x y 7z 0 Find the normal vector for P 4 X

Find the projection of v onto u 1 5 1 10 1 5 proj v u 2 2 2

Find the angle between u and v 3 4 0 u V

Find u for the given vector 5 U Give a unit vector in the direction of u

Solve for the vector x in terms of the vectors a and b If needed use BOLD vector form on calcPad Vector menu x 4a b 4 x a 2a b X

Perform the indicated calculation 5 2 5 5 in Z

Refer to the vectors below b 3 4 1 c 1 4 1 d 1 1 2 Compute the indicated vector 2b3c d

Find the approximate area of the shaded region below consisting of a right triangle with a circle cut out of it Use 3 14 as an approximation for 90 m 40 m 90 m O 6 844 square meters O 974 square meters O 2 794 square meters O 1 256 square meters

16429 Let there be x y z t 0 00 so that xyzt 1 Show that 4 2 3 4 1 1 x4 3

What is the y coordinate of the point on the line with an x coordinate of 4 Express your answer numerically View Available Hint s Hint 1 How to approach the problem Since the equation is true for all points on the line if you plug in the x coordinate for 2 in the equation then you can solve for y the number that you get will be the y coordinate of that point This procedure is made easier by the fact that the equation is alrea solved for y

Maximum Heart Rate The maximum heart rate is the highest heart rate achieved during maximal exercise In general you get the most benefits and reduce the risks when you exercise within your target heart rate zone Usually this is when your exercise heart rate pulse is about 80 percent of your maximum heart rate The formula M 0 8 220 A gives the recommended maximum heart rate M in beats per minute for a person who is A years of age Determine the age of a person whose target heart rate is 124 beats per minute The recommended maximum heart rate is 124 beats per minute for a person who is years old

A playground is being square with sides 12 yards long he shape of a How much sod grass would need to be bought to cover the playground Amount of sod grass Select an answer Round answers to 2 decimal place as needed b How much fencing would need to be bought to enclose the playground Amount of fencing Select an answer Round answers to 2 decimal place as needed

Israel is planning to build a rectangular raised garden in his back hard He has 18 feet of plastic edging that he wants use to build the perimeter of the garden He knows that the Literal Equation for the perimeter of a rectangle is P 2L 2W where P Perimeter L Length and W Width But he is having trouble figuring out what length and width he should make the garden if he wants to use all of the plastic edging Help Israel find the answer by completing the following steps Israel knows he has 18 feet of plastic edging to use for the Perimeter He rewrites the equation as 2L 2W 18 Step 1 Solve and simplify 18 2L 2W for W Write your answer as an equation Step 2 Use the new equation to complete the following table Length ft 3 4 5 6 Width ft