Set up and solve an appropriate system of linear equations to answer the questions. Through any three
Question:
Set up and solve an appropriate system of linear equations to answer the questions.
Through any three noncollinear points there also passes a unique circle. Find the circles (whose general equations are of the form x2 + y2 + ax + by + c = 0) that pass through the sets of points in Exercise 45. (To check the validity of your answer, find the center and radius of each circle and draw a sketch.)
Step by Step Answer:
a We know that the three points 0 1 1 4 and 2 1 must satisfy the equation x 2 y 2 ax by c 0 Plugg...View the full answer
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics questions
-
In Exercises 1-3, set up and solve an appropriate system of linear equations to answer the questions. 1. Grace is three times as old as Hans, but in 5 years she will be twice as old as Hans is then....
-
Solve the system of linear equations algebraically. x1 - x2 + 2x3 + 2x4 + 6x5 3x, - 21, + 4x3 + 4x4 + 12t5 X4 - 3x5 = -3 10 6. 14 X - X3 - 2x, 2x, + 4x, + 5x, + 15x5 2x1 2x, + 4x3 + 4x4 + 13x5 13
-
The augmented matrix of a system of linear equations has been carried to the following by row operations. In each case solve the system. (a) (b) (c) (d) 120 3101-I 001-110 2 000 0013 1-2020 111 0 01...
-
Consider the following red-black tree. We perform the following sequence of insertions on this tree: 26, 37, 41, 23. Draw the tree after each operation of this sequence (Note that the operations are...
-
Consider an industry whose demand fluctuates over time. Suppose that this industry faces high supplier power. Briefly state how this high supplier power will affect the variability of profits over...
-
Citation Builders, Inc., builds office buildings and single-family homes. The office buildings are constructed under contract with reputable buyers. The homes are constructed in developments ranging...
-
Using the PewHealth data, determine which of these factors have the largest impact on the Health Conditions Index: age, recoded education, and recoded income. Create a table that presents...
-
The shares of Volkswagen trade on the Frankfurt stock exchange. A U.S. investor purchased 1,000 shares of Volkswagen at 56.91 each, when the exchange rate was :$ = 0.9790-0.9795. Three months later,...
-
A company's balance sheet shows the account, Notes Payable. This resulted from a loan made by the company's bank. If the end-of-year balance in the notes payable account exceeds the beginning-of-year...
-
Workers come to tool store room to receive special tools (required by them) for accomplishing a particular project assigned to them. The average time between two arrivals is 60 seconds and the...
-
Set up and solve an appropriate system of linear equations to answer the questions. From elementary geometry we know that there is a unique straight line through any two points in a plane. Less well...
-
The process of adding rational functions (ratios of polynomials) by placing them over a common denominator is the analogue of adding rational numbers. The reverse process of taking a rational...
-
Why is capital budgeting such an important process? Why are capital- budgeting errors so costly?
-
Saskatchewan Soy Products (SSP) buys soy beans and processes them into other soy products. Each tonne of soy beans that SSP purchases for $300 can be converted for an additional $200 into 500 lbs of...
-
Pharoah Acres sponsors a defined-benefit pension plan. The corporation's actuary provides the following information about the plan: January 1, 2025 December 31, 2025 Vested benefit obligation $510...
-
Company panther is compelled to pick between two machines An and B. The two machines are planned in an unexpected way, yet have indistinguishable limit and do the very same work. Machine A costs...
-
On April 30, 2023, a company issued $600,000 worth of 5% bonds at par. The term of the bonds is 9 years, with interest payable semi- annually on October 31 and April 30. The year-end of the company...
-
Identify the following; MethodBodyReturn statementReturn typeParameter Look at this example we saw in our Methods lesson: public double findTheArea (double length, double w idth) { double area =...
-
You are an exobiologist, studying the wide range of life in the universe. You are also an avid dancer and have an excellent model of the way species invent dancing. The key variables are: Sound...
-
Which internal control principle is especially diffi cult for small organizations to implement? Why?
-
Let {v1, . . . , vn} be a basis for a vector space V and let c1, . . . , cn be nonzero scalars. Prove that {c1v1, . . . , cnvn} is also a basis for V.
-
Let {v1, . . . , vn}be a basis for a vector space V. Prove that {v1, v1 + v2, v1 + v2 + v3 , . . . , v1 + . . . + vn} is also a basis for V.
-
Let a0, a1, . . . , an be n + 1 distinct real numbers. Define polynomials p0(x), p1 (x), . . . , Pn(x) by These are called the Lagrange polynomials associated with a0, a1, . . . , an [Joseph-Louis...
-
Deacon Company is a merchandising company that is preparing a budget for the three - month period ended June 3 0 th . The following information is available Deacon Company Balance Sheet March 3 1...
-
Mango Company applies overhead based on direct labor costs. For the current year, Mango Company estimated total overhead costs to be $460,000, and direct labor costs to be $230,000. Actual overhead...
-
Which of the following do we expect to be the horizon growth rate for a company (long term growth rate- say 30-50 years)? A) Inflation B) Industry Average C) Zero D) Market Beta
Study smarter with the SolutionInn App