Area inside 4 tangents


by jahaddow
Tags: algebraic, area, geometrical, tangent
jahaddow
jahaddow is offline
#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
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#2
Jun5-10, 08:45 PM
HW Helper
P: 6,210
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
jahaddow is offline
#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
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#4
Jun5-10, 09:52 PM
HW Helper
P: 6,210

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
jahaddow is offline
#5
Jun6-10, 12:07 AM
P: 47
So, How do I do that?
rock.freak667
rock.freak667 is offline
#6
Jun6-10, 01:15 AM
HW Helper
P: 6,210
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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