Tutors Answer Your Questions about Linear-systems (FREE)
Question 1198049: I am trying to figure this question out, but am having significant problems.
Given the linear system: x+y+z = α
6x-4y+5ßz = 31
5x+2y+2z = 13
Find the values of a and b such that the system:
a) has one single solution, and give the solution values of x,y,z.
b) has infinite solutions, and give the solution values of x,y,z.
c) has no solutions
The α and ß unknowns are really confusing me in this question. I understand the idea behind no solution, infinite solutions and one solution in the augmented matrix, but I can't seem to wrap my head around it when the α and ß are involved
Click here to see answer by math_tutor2020(3817)  |
Question 1198049: I am trying to figure this question out, but am having significant problems.
Given the linear system: x+y+z = α
6x-4y+5ßz = 31
5x+2y+2z = 13
Find the values of a and b such that the system:
a) has one single solution, and give the solution values of x,y,z.
b) has infinite solutions, and give the solution values of x,y,z.
c) has no solutions
The α and ß unknowns are really confusing me in this question. I understand the idea behind no solution, infinite solutions and one solution in the augmented matrix, but I can't seem to wrap my head around it when the α and ß are involved
Click here to see answer by nsisson(1) |
Question 1198073: the monthly cost in dollars of a long-distance phone plan is a linear function of the total calling time in minutes. The monthly cost for 43 minutes is $13.42 and the monthly cost for 91 minutes is $19.66. What is the monthly cost for 55 minutes?
Click here to see answer by ikleyn(52786)  |
Question 1198122: Shana bought sodas and popcorn for the movies .Sodas cost $3 each and popcorn cost $4 per bag . Shana bought 7 things from the concession., all either sodas or bags of popcorn. Shana spent a total of $26 . Write a system of equations involving the number of sodas S ,and the bags of popcorn ,B .Solve the system to see how many of each shana bought
Click here to see answer by josgarithmetic(39617) |
Question 1198712: In 2012, the population of a city was 6.97 million. The exponential growth rate was 3.87% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 10 million?
d) Find the doubling time.
Click here to see answer by Shin123(626)  |
Question 1198777: Two cars start from the same point, at 9:45 am, traveling in opposite directions at 45 and 55 mph,respectively. At what time will they be 550 miles apart?
The correct answer is one of the following. Which one is correct?
A) 3:15 PM
B) 3:30 PM
C) 4:15 PM
D) 4:45 PM
Click here to see answer by Alan3354(69443)  |
Question 1198826: Ticket prices at a theater performance are $2.50 for children and $5.00 for adults. One evening, $6350 is collected from a total of 1900 attending. How many adults and how many children attended?
The correct answer is one of the following. Which one is it?
A) 640 adults, 1260 children
B) 940 adults, 960 children
C) 491 adults, 1409 children
D) 780 adults, 1120 children
Click here to see answer by josgarithmetic(39617) |
Question 1199207: A company manufactures two products, A and B, and each of these products must be processed on two different machines. Product A requires 2 min of work time per unit on machine 1 and 4 min of work time per unit on machine 2. Product B requires 3 min of work time per unit on machine 1 and 1 min of work time per unit on machine 2. Each day 200 min are available on machine 1 and 300 min are available on machine2. To satisfy certain customers, the company must produce at least 8 units per day of product A and at least 10 units per day of product B. If the profit of each unit of product A is Php50 and the profit of each unit of product B is Php60, how many units of each product should be produced daily in order to maximize the company's profits?
Provide the following:
The objective function: blank
The machine 1 constraint: blank
The machine 2 constraint: blank
The production constraints: blank
The implicit constraints: blank
The number of product A and product B to give an optimum profit: blank
The optimum cost:
Click here to see answer by greenestamps(13200)  |
Question 1199207: A company manufactures two products, A and B, and each of these products must be processed on two different machines. Product A requires 2 min of work time per unit on machine 1 and 4 min of work time per unit on machine 2. Product B requires 3 min of work time per unit on machine 1 and 1 min of work time per unit on machine 2. Each day 200 min are available on machine 1 and 300 min are available on machine2. To satisfy certain customers, the company must produce at least 8 units per day of product A and at least 10 units per day of product B. If the profit of each unit of product A is Php50 and the profit of each unit of product B is Php60, how many units of each product should be produced daily in order to maximize the company's profits?
Provide the following:
The objective function: blank
The machine 1 constraint: blank
The machine 2 constraint: blank
The production constraints: blank
The implicit constraints: blank
The number of product A and product B to give an optimum profit: blank
The optimum cost:
Click here to see answer by math_tutor2020(3817) |
Question 1199025: Gardeners on a low carb diet are interested in knowing the carbohydrate content of the vegetables they plant. Together, 1 cup of raw lettuce, 6 raw asparagus spears, and 1 cup of raw tomatoes contain 12 grams of carbohydrates. One cup of raw lettuce and 6 asparagus have one-half of the carbohydrate of 9 cups of raw tomatoes. One cup each of raw tomatoes and raw lettuce has 3 times the carb content of 6 asparagus spears. Find the number of grams in the given portion of size of each vegetable.
Click here to see answer by Shin123(626) |
Question 1199230: Hi! I tried to solve this system by using the graph method but, when I check it with my colleagues, the result is not correct and I do not understand why. The system is: 3x-y=7 , -12x+4y=3. The values that I decided to use for x were: 0,1,2. Thank you in advance for any help you can give me.
Click here to see answer by josgarithmetic(39617) |
Question 1199230: Hi! I tried to solve this system by using the graph method but, when I check it with my colleagues, the result is not correct and I do not understand why. The system is: 3x-y=7 , -12x+4y=3. The values that I decided to use for x were: 0,1,2. Thank you in advance for any help you can give me.
Click here to see answer by ikleyn(52786) |
Question 1199502: A riverboat travelling with the current can go 30 km in 1 hour, on the return trip against the current it took 1.5 hours to travel the 30 km. Which of the following would represent a linear system that could be used to determine the speed of the riverboat and the current where x is the speed of the riverboat and y is the speed of the current?
Click here to see answer by josgarithmetic(39617) |
Question 1199502: A riverboat travelling with the current can go 30 km in 1 hour, on the return trip against the current it took 1.5 hours to travel the 30 km. Which of the following would represent a linear system that could be used to determine the speed of the riverboat and the current where x is the speed of the riverboat and y is the speed of the current?
Click here to see answer by MathTherapy(10552)  |
Question 1200081: 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 josgarithmetic(39617) |
Question 1200579: A hotel has 150 rooms. The charges for a double room and a single room are $270 per night and $150 per night respectively. On a night when the hotel was completely occupied, revenues were $33,300. Which pair of equations can be used to determine the number of double room, d, and the number of single room, s, in the hotel?
Click here to see answer by ikleyn(52786) |
Question 1200628: A factory makes use of two basic machines, A and B, which turn out two different products, yarn and thread. Each unit of yarn requires 1 hour on machine A and 2 hours on machine B, while each unit of thread requires 1 hour on A and 1 hour on B. Machine A runs 8 hours per day, while machine B runs 14 hours per day. How many units each of yarn and thread should the factory make to keep its machines running at capacity?
Click here to see answer by ikleyn(52786) |
Question 1200756: A plane can travel 1,015 miles in 7 hours traveling against the wind. Traveling with the same wind, the plane can travel 820 miles in 4 hours. How fast can the plane travel in still air and how fast is the wind current?
Click here to see answer by ikleyn(52786) |
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