What is the area of this plot in hectares?
2 answers:
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Answer: Second option.
Step-by-step explanation:
The slope of a line can be calculated with this formula:
Then, you need to choose two points of the line shown in the graph and substitute them into the formula for calculate the slope:
Let's pick the points (-4,4) and (4,-2).
Substituting:
Simplifiying, you get that the slope of the line in the graph is:
A) The length of the longer leg is x-1
b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).
c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.
b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).
c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.