What is the maximum number of regions that can be formed if 6 lines are drawn to cut a circle?
What is the maximum number of regions formed by n lines in a plane?
One line can divide a plane into two regions, two non-parallel lines can divide a plane into 4 regions and three non-parallel lines can divide into 7 regions and so on.
What is the number of maximum regions which can be formed by 5 Straight Lines?
Solution 1 The third line intersects two lines, creating three regions. Similarly, the fourth line intersects three lines and creates four regions, the fifth line intersects four lines and creates five regions, and the sixth line intersects five lines and creates six regions.
What is the maximum number of regions that 8 lines can divide a plane into?
However, the next number that intuition often suggests, i.e., L_3=8 does not hold. Instead, L_3=7. Why so? This is because, if we want to obtain the maximum possible number of regions, we shall not let the new line pass through the intersection of the first two, for then we would get six regions and can do better.
What is the minimum number of regions into which three planes can separate space?
What do you call a line that divides the plane into two regions?
boundary line. A line that divides the coordinate plane into two regions. If points along the boundary line are included in the solution set, then a solid line is used; if points along the boundary line are not included then a dotted line is used.
How many parts do 50 concurrent lines divide the plane?
Is the number of parts into which the lines divide the plane?
Thus, n lines divide the plane into 2n parts.
What is a broken line?
1 : a line composed of a series of dashes often : a guide line painted in dashes on a highway to indicate a stretch on which a driver may lawfully cross the midline of the way (as in passing another vehicle)
What does a broken line mean in math?
broken-line graph is a graph that is used when it is necessary to show change over time. A line is used to join the values, but the line has no defined slope.
What does a broken line graph look like?
A broken line graph is a diagram that has a horizontal axis divided into units of time and a vertical axis that displays the values of the qualitative characteristic studied, and in which the data recorded are represented by points that are then connected to one another by segments to form a broken line that …
Is a broken line a function?
functions, which we might as well call broken-line functions, are typical examples of functions defined on a split, or rather, broken, domain. We show, how ever, that any broken-line graph can also be described by a function on a single, unbroken, domain.
What is broken line graph used for?
Broken line graphs (also called line graphs) are used to show changes in data over time. They display trends (patterns) and help us make predictions.
What is a broken curve?
Broken Back – two curves same direction (avoid) 3. Compound curves: multiple curves connected directly. together (use with caution) go from large radii to smaller. radii and have R(large) < 1.5 R(small)
What is a double broken line graph?
In order to see the relationship between his income and expenses, he will graph them both on the same set of axes, thus resulting in a double broken-line graph.
When should you use a double line graph?
We learned that we can use a double line graph when comparing two sets of data. Also, we learned that a double line graph has a key, two axes, a scale, double lines that can ascend or descend, and a title.
What does a solid line on a graph mean?
Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region. For example, this graph shows the inequality . This can be seen as there is a dashed line at , and the region where the coordinates are less than -1 is shaded.
What symbol is a dotted line?
The inequality symbol will help you to determine the boundary line. If the inequality symbol is greater than or less than, then you will use a dotted boundary line. This means that the solutions are NOT included on the boundary line.
Is a solid line?
If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line. This line divides the xy- plane into two regions: a region that satisfies the inequality, and a region that does not.
What does a solid and dashed line mean?
If both the dashed and solid yellow lines are present, passing is only allowed by one direction of traffic. If the line on your side of the road is solid, you should not pass, even if the other side is dashed. Only the dashed side of the road can pass.
What is solid line?
WHITE LINES painted on the pavement indicate traffic traveling in your direction. Broken White Line: you may change lanes if it is safe to do so. Solid White Line: requires you to stay within the lane and also marks the shoulder of the roadway.
Can a solution be on a dotted line?
If points along the boundary line are included in the solution set, then a solid line is used; if points along the boundary line are not included then a dotted line is used.
What causes a linear equation to have a dotted line?
If the inequality symbol in the statement is either , then the line in the inequality graph will be dotted, not solid, to indicate that the points along the line are not solutions to the inequality.
When two lines are intersecting the system has an infinite number of solutions?
Infinite Solutions If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
Is less than dotted line?
If an inequality is “less than” or “greater than” use a dotted line. If the inequality is “less than or equal to” or “greater than or equal to” use a solid line. If it is “less than” or “less than or equal to” shade downward. Connect the two points together by making a dotted line.
Is less than shade above or below?
Unless you are graphing a vertical line the sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
Is it equal or less?
The less than symbol is <. Two other comparison symbols are ≥ (greater than or equal to) and ≤ (less than or equal to).
Is a dotted graph a function?
For example, the black dots on the graph in the graph below tell us that f(0)=2 f ( 0 ) = 2 and f(6)=1 f ( 6 ) = 1 . If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output.
How many regions can be formed by 4 planes?
Each line plotted on a coordinate graph divides the graph (or plane) into two half‐planes. This line is called the boundary line (or bounding line).
What line that divides the plane into two regions?
How does the number of regions change when another point is added?
We are interested in “differences” in successive R val- ues, so let’s ask what happens to R when we add a new point. How many new regions do we get? Well, each new point necessitates the drawing of a number of new lines, and each of these new lines will create a number of new regions.
Are the point on the line part of the solution set or not?
Answer. Answer: If points along the boundary line are included in the solution set, then a solid line is used; if points along the boundary line are not included then a dotted line is used. divides the plane into two half planes.
How do you determine if a point is in the solution set?
To figure out if an ordered pair is a solution to an equation, you could perform a test. Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.