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What are the points of intersection between the line x -y equals 2 and the curve x2 -4y2 equals 5?
Equations: x -y = 2 and x^2 -4y^2 = 5
By combining the equations into a single quadratic equation in terms of y and solving it: y = 1/3 or y = 1
By means of substitution the points of intersection are at: (7/3, 1/3) and (3, 1)
What else can I help you with?
What are the points of intersection of the line y equals -8-3x with the curve y equals -2-4x-x squared?
They work out as: (-3, 1) and (2, -14)
Point at which a curve crosses itself called?
The point at which a curve crosses itself is called a "cusp" or a "self-intersection." In a self-intersection, the curve intersects itself at some point, while a cusp refers to a point where the curve has a sharp point or corner. These points can have important implications in the study of the curve's properties and behavior.
What are the points of intersection of the line of x -2y equals 1 with the curve of 3xy -y squared equals 8 showing work?
If: x-2y = 1 and 3xy-y2 = 8 Then: x =1+2y and so 3(1+2y)y-y2 = 8 => 3y+5y2-8 = 0 Solving the quadratic equation: y = 1 or y = -8/5 Points of intersection by substitution: (3, 1) and (-11/5, -8/5)
Segments below is a secant?
A secant is a line that intersects a curve at two or more points. In the context of a circle, a secant can be defined as a line that crosses the circle, providing two points of intersection. These intersection points help in calculating various properties of the circle, such as angles and lengths, depending on the specific geometric scenario involved.
What is formed where two surfaces intersect?
Where two surfaces intersect, a line or curve is formed, depending on the nature of the surfaces. In three-dimensional geometry, the intersection can be a line if both surfaces are planes, or a curve if one or both surfaces are curved. This intersection represents all the points that are common to both surfaces. The specific characteristics of the intersection depend on the equations defining the surfaces involved.
What are the points of intersection of the line y equals -8-3x with the curve y equals -2-4x-x squared?
They work out as: (-3, 1) and (2, -14)
What are points of intersection of the line 3x -y equals 5 with the curve of 2x squared plus y squared equals 129?
Straight line: 3x-y = 5 Curved parabola: 2x^2 +y^2 = 129 Points of intersection works out as: (52/11, 101/11) and (-2, -11)
Point at which a curve crosses itself called?
The point at which a curve crosses itself is called a "cusp" or a "self-intersection." In a self-intersection, the curve intersects itself at some point, while a cusp refers to a point where the curve has a sharp point or corner. These points can have important implications in the study of the curve's properties and behavior.
What is the area under the normal curve between z equals 0.0 and z equals 2.0?
What is the area under the normal curve between z equals 0.0 and z equals 2.0?
Where are solutions to a system seen on the graph?
The intersection of the individual graphs. In the simplest case, the graph for each equation consists of a line (or some curve); the intersection is the points where the lines or curves meet.
What are the points of intersection of the line of x -2y equals 1 with the curve of 3xy -y squared equals 8 showing work?
If: x-2y = 1 and 3xy-y2 = 8 Then: x =1+2y and so 3(1+2y)y-y2 = 8 => 3y+5y2-8 = 0 Solving the quadratic equation: y = 1 or y = -8/5 Points of intersection by substitution: (3, 1) and (-11/5, -8/5)
What are the points of intersection when the line y equals 10x -12 crosses the curve y equals x squared plus 20x plus 12?
If: y = 10x -12 and y = x^2 +20x +12 Then: x^2 +20x +12 = 10x -12 Transposing terms: x^2 +10x +24 = 0 Factorizing: (x+6)(x+4) = 0 => x = -6 or x = -4 Points of intersection by substitution are at: (-6, -72) and (-4, -52)
What are the points of intersection when the line y equals -8 -3x passes through the curve y equals -2 -4x - x squared?
If: y = -8 -3x and y = -2 -4x -x^2 Then: -8 -3x = -2 -4x - x^2 Transposing terms: x^2 +x -6 = 0 Factorizing: (x-2)(x+3) = 0 => x = 2 or x = -3 Points of intersection by substitution are at: (2, -14) and (-3, 1)
Segments below is a secant?
A secant is a line that intersects a curve at two or more points. In the context of a circle, a secant can be defined as a line that crosses the circle, providing two points of intersection. These intersection points help in calculating various properties of the circle, such as angles and lengths, depending on the specific geometric scenario involved.
What is a straight line connecting two points on a curve?
A straight line connecting two points on a curve is called a chord. It represents the shortest distance between those two points along the curve. In geometric terms, a chord can help illustrate properties of the curve and is often used in calculus to approximate the behavior of the curve between the two points. The slope of the chord can also provide insight into the average rate of change of the curve over that interval.
What is the intersection of the supply curve and the demand curve?
the equilibrium price of a good or service
What is the curve between 2 points in a circle called?
If the curve is part of the circumference of the circle, it is called an arc.
