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Answer:
length of rectangle = 5
width of rectangle = 5
Area of rectangle = 25
Step-by-step explanation:
Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:
Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.
Recall that the formula for the x of the vertex of a quadratic of the form :
is given by the formula:
which in our case gives:
Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.
The area of the rectangle is therefore the product of these two values: 5 * 5 = 25
Which should coincide with the value we obtain when we replace x by 5 in the area formula:
If the midpoint of segment lm where j(5, -1) and m(0, 6), then the coordinates of end point l is (10,-8)..
Midpoint:
Midpoint of a line segment is the point that is halfway between the endpoints of the line segment.
The formula for the midpoint is,
where,
= coordinates of the midpoint
(x₁, y₁) = coordinates of the first point
(x₂, y₂) = coordinates of the second point
Given,
Midpoint = j = (5,-1)
Second point = m = (0,6)
Now, we have to find the first midpoint l.
Let (x,y) be the coordinates of l.
Then apply the values on the formula,
Then we get,
Compare the values in order to find the coordinates,
=> 5 = (x + 0) / 2
=> 5 x 2 = x + 0
=> 10 = x
Similarly,
=> -1 = (y + 6) / 2
=> -1 x 2 = y + 6
=> -2 = y + 6
=> -2 - 6 = y
=> y = -8
Therefore, the coordinates of l is (10,-8).
To know more about Midpoint here.
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