Homework Answers
A constructible number can be formed by finite number of additions, subtractions, multiplications, divisions, and extraction of square roots of integers. In particular, integers are constructible.
7. If we solve the 2 given equations to find the points of
intersection, we find that the only possibility is for x to be an
integer. Hence 
So, all the coordinates of all the points of intersection of these 2 curves are integers, and therefore constructible numbers.
To show this, we just solve the given system
At any point of intersection, the y coordinates are same. So, we substitute the second expression for y in the first. This will give us a polynomial equation in terms of x alone, which can then solved.
The only value of x satisfying the above is x = 2.
The corresponding value of y is 
The only point of intersection of the given curves is (2, 7).
To conclude, all the coordinates of all the points of intersection of the given curves are constructible.
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6. Consider the system of equations:yy , Consider the system of equations: +1 Are all the coordin...
6. Consider the system of equations:y-y y = 12 + 1 + 1 Are all the coordinates of all the points ...
Abstract algebra
6. Consider the system of equations:y-y y = 12 + 1 + 1 Are all the coordinates of all the points of intersection of these curves constructible numbers? Explain
6. Consider the system of equations:y-y y = 12 + 1 + 1 Are all the coordinates of all the points of intersection of these curves constructible numbers? Explain
(1 point) Consider following the system in two equations and two variables: 2x + y ||...
(1 point) Consider following the system in two equations and two variables: 2x + y || IL X – Select all statements below that use linear algebra vocabulary correctly. A. Solution(s) to the system are points in RP. B. The system is a linear combination. C. The system corresponds to two lines. [2 1 51 D. The system is the same as 11 -1 7] E. The system is two lines. F. The solution to the system is the intersection...
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines....
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the phase plane. Clearly mark the equilibrium points. Also indicate the direction of flow on the nullclines.
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the...
Consider the following system of equations:
Consider the following system of equations:(a) Suppose a = 1. Sketch the nullclines of these equations. (b) Determine what happens if a is increased to large values (a >> 1). How does this influence the number of steady states? (c) Determine what happens when a is decreased (0 < a < 1). How does this influence the number of steady states? (d) Find a condition necessary for the intersection of the nullclines to occur exactly at the minimum of the x-nullcline.
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C"...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
This is all one question. 3. Suppose Romeo and Juliet's love obeys the following differential equations: :/which has...
This is all one question.
3. Suppose Romeo and Juliet's love obeys the following differential equations: :/which has the following eigenvectors: 2 adwth egmao The matrix of this system is with eigenvalue 2, and 1 with eigenvalue-4 We wil use these two eigenvectors to define a new coordinate system, and we will use u and v to represent these coordinates. However, in this problem, we will treat u and v as new variables. Your goal is to rewrite this system...
3. Consider the system of equations: x' = ( 1 3 | -1 6 -2 *...
3. Consider the system of equations: x' = ( 1 3 | -1 6 -2 * (a) [4 pts) Find the general solution. (b) [4 pts) Find the critical points or equilibrium solutions. Plot a few representive trajectories of the system in the phase plane. Indicate the direction of each trajectory using arrows.
Graph the following linear inequalities on the digital graph paper worksheet Problem 10. Show ALL your algebra steps that are required to determine the X and Y intercepts for both equations in the te...
Graph the following linear inequalities on the digital graph paper worksheet Problem 10. Show ALL your algebra steps that are required to determine the X and Y intercepts for both equations in the text box. From the MS Excel ribbon > Insert> Shapes> Lines. Y coefficient 4 Line # X coefficient "RHS" 36 48 0 Use the text box for you answer. Solve algebraically, showing ALL steps, for the solution, or "intersection" of 1. Equation 1 and equation 2. 2....
Graph the following linear inequalities on the digital graph paper worksheet Problem 10. Show ALL your algebra steps that are required to determine the X and Y intercepts for both equations in the te...
Graph the following linear inequalities on the digital graph paper worksheet Problem 10. Show ALL your algebra steps that are required to determine the X and Y intercepts for both equations in the text box. From the MS Excel ribbon > Insert> Shapes> Lines. Y coefficient 4 Line # X coefficient "RHS" 36 48 0 Use the text box for you answer. Solve algebraically, showing ALL steps, for the solution, or "intersection" of 1. Equation 1 and equation 2. 2....
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of diff...
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
Abstract algebra
6. Consider the system of equations:y-y y = 12 + 1 + 1 Are all the coordinates of all the points of intersection of these curves constructible numbers? Explain
6. Consider the system of equations:y-y y = 12 + 1 + 1 Are all the coordinates of all the points of intersection of these curves constructible numbers? Explain
(1 point) Consider following the system in two equations and two variables: 2x + y || IL X – Select all statements below that use linear algebra vocabulary correctly. A. Solution(s) to the system are points in RP. B. The system is a linear combination. C. The system corresponds to two lines. [2 1 51 D. The system is the same as 11 -1 7] E. The system is two lines. F. The solution to the system is the intersection...
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the phase plane. Clearly mark the equilibrium points. Also indicate the direction of flow on the nullclines.
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
This is all one question.
3. Suppose Romeo and Juliet's love obeys the following differential equations: :/which has the following eigenvectors: 2 adwth egmao The matrix of this system is with eigenvalue 2, and 1 with eigenvalue-4 We wil use these two eigenvectors to define a new coordinate system, and we will use u and v to represent these coordinates. However, in this problem, we will treat u and v as new variables. Your goal is to rewrite this system...
3. Consider the system of equations: x' = ( 1 3 | -1 6 -2 * (a) [4 pts) Find the general solution. (b) [4 pts) Find the critical points or equilibrium solutions. Plot a few representive trajectories of the system in the phase plane. Indicate the direction of each trajectory using arrows.
Graph the following linear inequalities on the digital graph paper worksheet Problem 10. Show ALL your algebra steps that are required to determine the X and Y intercepts for both equations in the text box. From the MS Excel ribbon > Insert> Shapes> Lines. Y coefficient 4 Line # X coefficient "RHS" 36 48 0 Use the text box for you answer. Solve algebraically, showing ALL steps, for the solution, or "intersection" of 1. Equation 1 and equation 2. 2....
Graph the following linear inequalities on the digital graph paper worksheet Problem 10. Show ALL your algebra steps that are required to determine the X and Y intercepts for both equations in the text box. From the MS Excel ribbon > Insert> Shapes> Lines. Y coefficient 4 Line # X coefficient "RHS" 36 48 0 Use the text box for you answer. Solve algebraically, showing ALL steps, for the solution, or "intersection" of 1. Equation 1 and equation 2. 2....
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
Problem 6. Consider the system: y. and its corresponding vector field: 1. Sketch a number of different solution curves on the phase plane. 2. Describe the behavior of the solution that satisfies the initial condition (to, o) (0, 2)
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