Tutors Answer Your Questions about Linear Algebra (FREE)
Question 1196500: A trip of 500 kilometres took five and a half hours to complete by car. During the first 30 minutes, travelling was slow because of heavy traffic, but for the rest of the journey, the car's speed was 10km/hr, less than twice the car's speed in heavy traffic. Determine the speed of the car in heavy traffic.
Click here to see answer by ikleyn(52781)   |
Question 1196500: A trip of 500 kilometres took five and a half hours to complete by car. During the first 30 minutes, travelling was slow because of heavy traffic, but for the rest of the journey, the car's speed was 10km/hr, less than twice the car's speed in heavy traffic. Determine the speed of the car in heavy traffic.
Click here to see answer by josgarithmetic(39617) |
Question 1196504: A rectangular storage container with an open top is to have a volume of 10m cubed. The length of the base of the container is twice its width. Assume that the width of the base of the container is x metres and the height is y metres. Assume that material costs $15 per square metre, while material for the side costs $20 per square metre.
Find an equation to express the volume of the container in terms of the variables X, and then write Y in terms of X.
My notes so far...
base width=X
base length=2X
height= 1.33X
I am lost.
If I can figure out the first part, then the following two parts of the question will become easier.
Click here to see answer by MathLover1(20849)  |
Question 1196504: A rectangular storage container with an open top is to have a volume of 10m cubed. The length of the base of the container is twice its width. Assume that the width of the base of the container is x metres and the height is y metres. Assume that material costs $15 per square metre, while material for the side costs $20 per square metre.
Find an equation to express the volume of the container in terms of the variables X, and then write Y in terms of X.
My notes so far...
base width=X
base length=2X
height= 1.33X
I am lost.
If I can figure out the first part, then the following two parts of the question will become easier.
Click here to see answer by math_tutor2020(3817) |
Question 1196630: Writing Algebraic Expressions
Suppose that each semester at a particular community college Angelo has to pay $1312 in tuition and $85 in fees.
If Angelo has x semesters remaining, write an algebraic expression representing the total amount he will need for tuition.
If Angelo has x semesters remaining, write an algebraic expression representing the total amount he will need for the fees.
If Angelo has x semesters remaining, write an algebraic expression representing the total amount of money he will spend for tuition and fees.
Click here to see answer by josgarithmetic(39617) |
Question 1196630: Writing Algebraic Expressions
Suppose that each semester at a particular community college Angelo has to pay $1312 in tuition and $85 in fees.
If Angelo has x semesters remaining, write an algebraic expression representing the total amount he will need for tuition.
If Angelo has x semesters remaining, write an algebraic expression representing the total amount he will need for the fees.
If Angelo has x semesters remaining, write an algebraic expression representing the total amount of money he will spend for tuition and fees.
Click here to see answer by greenestamps(13200)  |
Question 1196771: For two months, Martin used the same snow removal company to help clear his property. The company had a fixed reservation rate per month, plus an hourly rate for the amount of time that is spent clearing snow. Martin received two bills from the snow removal company. The first bill was $130 for 3 hours of snow removal and the second bill was $180 for 5 hours of snow removal. Find the equation of the line that represents the snow removal company’s fixed reservation rate and charge per hour. Round to the nearest cent if necessary.
Click here to see answer by ewatrrr(24785)  |
Question 1196776: For two months, Martin used the same snow removal company to help clear his property. The company had a fixed reservation rate per month, plus an hourly rate for the amount of time that is spent clearing snow. Martin received two bills from the snow removal company. The first bill was $190 for 4 hours of snow removal and the second bill was $250 for 8 hours of snow removal. Find the equation of the line that represents the snow removal company’s fixed reservation rate and charge per hour. Round to the nearest cent if necessary.
Click here to see answer by ikleyn(52781) |
Question 1197126: The sum of the measures of the angles of a triangle sum to 180 degrees. The sum of the measures of the second and third angles is 3 times the measure of the first angle. The third angle is 32.6 more than the second angle. Find the measure of the second angle.
Click here to see answer by josgarithmetic(39617) |
Question 1197126: The sum of the measures of the angles of a triangle sum to 180 degrees. The sum of the measures of the second and third angles is 3 times the measure of the first angle. The third angle is 32.6 more than the second angle. Find the measure of the second angle.
Click here to see answer by Alan3354(69443)  |
Question 1197205: A water balloon is thrown upward from a height of 5 feet with an initial velocity of 35 feet per second.The quadratic equation function h(t)=-16t^2+35t+5 represents the height of the balloon,h,in feet t seconds after it is thrown.
Determine when the balloon is more than 10 feet above the ground.
Please also show me how you got the answer I need both things.
Click here to see answer by math_tutor2020(3817) |
Question 1197275: A water balloon is thrown upward from a height of 5 feet with an initial velocity of 35 feet per second.The quadratic function h(t)=-16t^2+35t+5 represents the height of the balloon,h,in feet t seconds after it is thrown.
Determine when the balloon is less than 20 feet above the ground.
Somebody please help me with this one,I don’t know if it is solved the way I think it is probably not. Please help me I would appreciate it very much
Click here to see answer by ikleyn(52781) |
Question 1197728: A manufacturer can make a profit of $46 on each item if not more than 450 items are produced each week. The profit on each item decreases 4 cents for every item over 450. To maximize profit, how many items should be produced each week?
Click here to see answer by ikleyn(52781) |
Question 1198090: Question 58328: A shoe mfg. makes outdoor and indoor soccer shoes. There is a two- step manufactoring processes for both kinds of shoes. Each pair of outdoor shoes require 2 hours of processing in step one, 1 hour in tep two, and produces a profit of $20 for the company. Indoor shoes require 1 hour of processing step one, 3 hour in step two and produces a profit of $15 for each pair. The company has 40 hours of labor per day avaiable for step one and 60 hours of labor per day available for step two. How many pairs of each type of shoe can be produced per day to maximize profit.
Click here to see answer by ikleyn(52781) |
Question 58328: A shoe mfg. makes outdoor and indoor soccer shoes. There is a two- step manufactoring processes for both kinds of shoes. Each pair of outdoor shoes require 2 hours of processing in step one, 1 hour in tep two, and produces a profit of $20 for the company. Indoor shoes require 1 hour of processing step one, 3 hour in step two and produces a profit of $15 for each pair. The company has 40 hours of labor per day avaiable for step one and 60 hours of labor per day available for step two. How many pairs of each type of shoe can be produced per day to maximize profit.
Click here to see answer by ikleyn(52781) |
Question 1199161: Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $29 monthly fee and charges an additional $0.15 for each minute of calls. The second plan has a $19 monthly fee and charges an additional $0.19 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Click here to see answer by ikleyn(52781) |
Question 1199356: The Lower Colorado River consists of a series of four reservoirs. Mass balances can be written for each reservoir, and the following set of simultaneous linear algebraic equations results:
* I don't know how to type in matrices here without looking messy, please Google search the above statements to obtain the equation :( *
a) Find normalized eigenvectors for Q, you may use MATLAB or any other software to find your answers. [5 marks]
I already calculated the above part, which the eigenvalues are basically just 11.797, 12.252, 12.377 and 13.422, but I couldn't solve the next question:
b) Hence, using your answer in (a), given  ,  (lambda is the eigenvalue), eigenvalue property of  and  , v3 is the eigenvector obtained from the third eigenvalue, 12.377. Calculate matrix K. [1 mark]
It only worth 1 mark, I think there's a faster way to solve it like by using Cayley-Hamilton Theorem, I'm not really sure, please help me
Click here to see answer by MathLover1(20849) |
Question 1200082: Consider the system of equations
2x + 3y = −5
−4x − 6y = 10
(a) Find a single point (x, y) which is a solution to this equation
(b) (Write down the homogeneous system of equations associated with the system above. Then solve the homogeneous system.
(c) Add your answers to the two parts above and plug it in the system to verify that this is the general solution
Click here to see answer by Fombitz(32388)  |
Question 1200371: I. Translate the following verbal phrases into mathematical expressions.
1. Three-fourths of 500
2. The sum of Two numbers less 11
3. 30 percent of selling price
4. Double the quantity of sales less taxes
5. The difference of gross sales and total cost
Click here to see answer by Alan3354(69443) |
Question 1201221: You are given a linear programming problem.
Maximize P = 4x + 4y
subject to 2x + 3y ≤ 12 Resource 1
2x + y ≤ 8 Resource 2
y ≥ 0
x ≥ 0
(a) Use the method of corners to solve the problem.
The maximum is P = __?__ at (x, y) = (__?__)
(b) Suppose P = cx + 4y. Find the range of values that the coefficient c of x can assume without changing the optimal solution.
__?__ ≤ c ≤ __?__
(c) Find the range of values that Resource 1 can assume.
__?__ ≤ (Resource 1) ≤ __?__
(d) Find the shadow price for Resource 1.
__?__
Click here to see answer by ikleyn(52781) |
Question 1201220: You are given a linear programming problem.
Maximize P = 4.5x + 3y
subject to 5x + 3y ≤ 30 Resource 1
2x + 3y ≤ 21 Resource 2
x ≤ 4 Resource 3
y ≥ 0
x ≥ 0
(a) Use the method of corners to solve the problem.
The maximum is P = __?__ at (x, y) = __?__
(b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution.
__?___ ≤ c ≤ __?__
(c) Find the range of values that Resource 1 can assume.
____?____ ≤ (Resource 1) ≤ ____?_____
(d) Find the shadow price for Resource 1.
__?__
Click here to see answer by ikleyn(52781) |
Question 1201218: Hello! I'm not even sure where to start on this.. Any help would be appreciated!!
A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $1.20, and each Type B souvenir will result in a profit of $1.80. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 3 hours available on Machine I and 5 hours available on Machine II.
(a) For a meaningful solution, the time available on Machine II must lie between
_?_ and _?_ min. (Enter your answers from smallest to largest.)
(b) If the time available on Machine II is changed from 300 min to
(300 + k) min, with no change in the maximum capacity for Machine I, then Ace Novelty's profit is maximized by producing __?__ Type A souvenirs and __?__ Type B souvenirs, where
__?__ ≤ k ≤ __?__
.
(c) Find the shadow price for Resource 2 (associated with constraint 2). (Round your answer to the nearest cent.)
$__?__
Click here to see answer by Edwin McCravy(20055)  |
Question 1201941: The length of a rectangular enclosure is twice its width. The perimeter of the enclosure is 180 metres.
Write down two simultaneous equations and Use Cramer’s rule to determine the length and the width of the
enclosure.
Click here to see answer by mananth(16946)  |
Question 1201941: The length of a rectangular enclosure is twice its width. The perimeter of the enclosure is 180 metres.
Write down two simultaneous equations and Use Cramer’s rule to determine the length and the width of the
enclosure.
Click here to see answer by Alan3354(69443) |
Question 1202051: The sum of the measures of the angles of a triangle is 180°. The second angle of a triangle is twice the measure of the first angle. The third angle is 20 more than 5 times the first. What are the measures of the three angles?
Click here to see answer by ikleyn(52781) |
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