Tuesday

September 2, 2014

September 2, 2014

Posted by **anonymous** on Tuesday, February 26, 2008 at 6:40pm.

- calculus -- PLEASE HELP! -
**Reiny**, Tuesday, February 26, 2008 at 8:08pmThis is a major Calculus question, requiring both integration and differentiation, but it will work out pretty neat.

I am going to the start of the horizontal P(0,h), the right end of the horizontal Q(a,h) and the point where the vertical meets R(a,(a^2)/9)

then PQ + QR = 4

a + (h-(a^2)/9 = 4

h = (a^2 - 9a + 36)/9

The area of the region between the curve y = x^2 /9 and the x-axis from 0 to a is

⌠ x^2 /9 dx from 0 to a, which is (a^3)/27

⌡

So the area of your question would be

A = ah - (a^3)/27

=a(a^2 - 9a + 36)/9 - (a^3)/27

= 1/9(a^3 - 9a^2 + 36a) - (a^3)/27

I then found dA/da and got

1/9(3a^2 - 18a + 36) - (1/9)a^2

setting this equal to zero for a max/min of area I got the nice quadratic

a^2 - 9a - 18 = 0

(a-6)(a-3)=0

so a = 6 or a=3, but the total of the two straight line segments has to be 4, so a=6 is extraneous

then a=3, which makes h=2 and the area=5

**Answer this Question**

**Related Questions**

Calculus Help - Farmer Brown wants to fence in a rectangular plot in a large ...

math - Yolanda is putting up a fence for her dog in the shape of a square. Each ...

college Algebra - A rectangular fence is to be built along a river using the ...

word problem? - A rectangular lot is to be bounded by a fence on three sides adn...

math - Marni wants to fence in a rectangular are of 48 ft squared. she wants to ...

Math - we need to fence off a rectangular section of land in order to make some ...

college algebra word problem - Here's the problem I was asked: You are visiting ...

calculus help - Farmer Brown wants to fence in a rectangular plot in a large ...

Math - Mr. Rogers wants to fence in a rectangular garden next to a straight ...

Calculus 2 - A farmer wishes to build a fence for 6 adjacent rectangular pens. ...