15 POINTS,ANSWER QUICKLY Think about all of the ways in which a line and a parabola can intersect. Select all of the number of w
ays in which a line and a parabola can intersect.
2 answers:
<u>Answer:</u>
3 ways
<u>Explanation:</u>
We know that a parabola has a second degree equation), while a line has a first degree equation.
To get the points of intersection, we will need to solve both simultaneously.
Solving them, we can reach a maximum of two solutions, however, other scenarios are also possible.
<u>Possible scenarios:</u>
1- no intersection occurs as shown in the first attachment
2- one intersection occurs as shown in the second attachment
3- two intersections occur as shown in the third attachment
Based on the above, there are three ways where the line and parabola can intersect
Hope this helps :)
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The question is incomplete. Here is the complete question.
Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
Answer: L = 1; W = 9/4; A = 2.25;
Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:
A = x.y
A = x(-)
A = -
To maximize, we have to differentiate the equation:
=
(-
)
= -3x + 3
The critical point is:
= 0
-3x + 3 = 0
x = 1
Substituing:
y = -x + 3
y = -.1 + 3
y = 9/4
So, the measurements are x = L = 1 and y = W = 9/4
The maximum area is:
A = 1 . 9/4
A = 9/4
A = 2.25
