A larger number is five more than twice the smaller number their sum is 80 find the number
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The sum of the interior triangles in a triangle is 180, so if we add all the angle measures together, we should get 180. Therefore, we can make an equation like this,
Simplify this.
Now we can find each angle measure.
So the angle labeled is the largest angle in the triangle.
One way to do it is with calculus. The distance between any point 
on the line to the origin is given by
Now, both
and 
attain their respective extrema at the same critical points, so we can work with the latter and apply the derivative test to that.
Solving for
, you find a critical point of 
.
Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
You have
so indeed, a minimum occurs at.
The minimum distance is then
Now, both
Solving for
Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
You have
so indeed, a minimum occurs at
The minimum distance is then