Saturday

August 2, 2014

August 2, 2014

Posted by **Sribava** on Sunday, November 6, 2011 at 3:21pm.

- calculus -
**Steve**, Monday, November 7, 2011 at 5:29amInteresting problem. Check to make sure I get this right.

So, we have a triangle with base k, and vertex where the line through (1,1) and (0,k) intersects y=3x.

The line through (1,1) and (0,k) is

(y-1)/(x-1) = -1/(k-1)

y = (x-1)/(1-k) + 1

So, that line intersects y=3x when

3x = (x-1)/(1-k) + 1

x = k/(3k-2)

y = 3k/(3k-2)

The area a of the triangle is thus

a = 1/2 k * 3k/(3k-2) = 3k^2/(6k-4)

da/dk = (6k(6k-4) - 3k^2 * 6)/(6k-4)^2

= 6k(3k-4)/(6k-4)^2

da/dk = 0 when k=0 or k = 4/3

Thus, the vertex of the triangle is where the line through (1,1) and (4/3,0) intersects y=3x

(y-1)/(x-1) = 1/(-1/3)

y = -3x + 4

That line has slope -3

. . .

-3x + 4 = 3x

6x = 4

x = 2/3

y=2

So, the triangle has base k=4/3, height h=2, area a=4/3

**Related Questions**

Algebra - I'm suppose to write an equation with the following information: Line ...

Geomentry - What is the converse of the theorem statement: If a line parallel to...

algebra - Could you please help me?? point-slope form linear equation y-3 = 3(x+...

math - i have more than one question so if u no any of the answers please tell ...

math - the sum of the lenths of any two sides of a triangle must be greater than...

IRSC - the sum of the lengths of any two sides of a triangle must be greater ...

calculus optimization max min - find the dimensions of the rectangular area of ...

Geometry - m∠1 = 6x and m∠3 = 120. Find the value of x for p to be ...

math - find the missing length in this diagram showing a T-square. (reduce the ...

Geometry - A line parallel to one side of a triangle divides one of the other ...