How could you convince someone that the square root of 50 must be just a tiny bit more than 7?
2 answers:
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The number of solutions possible to a system of equations that include a conic section depends on the type of equations involved
<h3>How to determine the number of solutions?</h3>A system of equation that has a conic section may or may not have solutions.
It would have a solution if the equations intersect, when plotted on a graph and it would not, if otherwise
A conic section can be any of:
- Parabola
- Ellipse
- Hyperbola
- Circle
<u>Example 1: No solution</u>
Consider the following system of equations
- y = x² - 10 --- parabola equation
- (x - 1)² + (y - 2)² = 5 --- circle
The above system of equations has no solution because they do not intersect when plotted on a graph (see graph 1)
<u>Example 2: One solution</u>
Consider the following system of equations
- x = 2 --- linear equation
- y = x² - 10 --- parabola
The above system of equations has one solution because they intersect at one point (see graph 2)
<u>Example 3: One solution</u>
Consider the following system of equations
- y = 2x + 1 --- linear equation
- y = x² - 10 --- circle
The above system of equations has two solutions because they intersect at two points (see graph 3)
The above examples imply that a system of equations that involves conic section can have as many solutions as possible.
The number of solutions depends on the type of equations involved
The attached graphs illustrate how a system of equations can have 0 to 4 solutions
Read more about system of equations at:
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To find the area of a rectangle, we multiply the Base by the Height. In this case the: Base = AB and Height = BC
So to get the area, we multiply AB by BC. (and we know that <em>BC = 5x+5/x+3</em> <em>and BC = [3x+9/2x-4)</em>
So we would do:
x
Note: When multiplying fractions together, we multiply the numerator by the numerator, and the denominator by the denominator.
For example x
=
Answer: x
=
=
[<em>Note: </em><em>we are able to factorise some brackets to make the sum easier. For example we can factor out the 5 in (5x+5) to get: 5(x+1) ]</em>
Now lets simplify by multiplying the 5 and 3 together in the numerator:
=
If you notice, there is a (x+3) in numerator and the denominator. This means that we can cancel out the (x+3), to get the most simplified expression for the area:
=
Final Simplified Answer: which is the last option