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Area inside 4 tangents

by jahaddow
Tags: algebraic, area, geometrical, tangent
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jahaddow
#1
Jun5-10, 08:25 PM
P: 47
1. The problem statement, all variables and given/known data
Ok, I have a cubic function, y=(x-6)(x-1)(x-9) or y = x3-16x2+69x-54
I then have four tangents to make a quadrilateral, the tangents are as follows.
y=7.75x+14.75
y=-6.25x+56.25
y=7.75x + -76.231
y=-6.25x + 31.602
I need to find the area inside the tangents, except I have no idea where to start, Thankyou for any help in advance.
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rock.freak667
#2
Jun5-10, 08:45 PM
HW Helper
P: 6,202
Quote Quote by jahaddow View Post
1. The problem statement, all variables and given/known data
Ok, I have a cubic function, y=(x-6)(x-1)(x-9) or y = x3-16x2+69x-54
I then have four tangents to make a quadrilateral, the tangents are as follows.
y=7.75x+14.75
y=-6.25x+56.25
y=7.75x + -76.231
y=-6.25x + 31.602
I need to find the area inside the tangents, except I have no idea where to start, Thankyou for any help in advance.
Start by sketching the lines. What do you notice about these pairs of lines:

y=7.75x+14.75 & y=7.75x + -76.231

y=-6.25x+56.25 & y=-6.25x + 31.602

What sort of quadrilateral figure is formed?
jahaddow
#3
Jun5-10, 09:27 PM
P: 47
A Parallelogram, But I dont see how I can get the area from the equations?

rock.freak667
#4
Jun5-10, 09:52 PM
HW Helper
P: 6,202
Area inside 4 tangents

Quote Quote by jahaddow View Post
A Parallelogram, But I dont see how I can get the area from the equations?
You can find where the lines intersect one another and thus find the coordinates of the corners. You can then find the lengths of the lines. Split the area into two triangles and find the areas.
jahaddow
#5
Jun6-10, 12:07 AM
P: 47
So, How do I do that?
rock.freak667
#6
Jun6-10, 01:15 AM
HW Helper
P: 6,202
Quote Quote by jahaddow View Post
So, How do I do that?
Solve each pair of equations to get the points of intersection. Find the lengths of the lines and then find the area of the shape.

Or you could split the area into two triangles and calculate it.


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