Can you solve this problem /sci/. I wasted hours in this shit I couldn't solve it. Am I a brainlet?
Pic related it's exercise 52
>>8477852
What class is this for?
>>8477852
Determine whether a square or a triangle gives more surface area for every foot of fence
Make the less efficient shape tiny and the more efficient shape huge.
>>8477853
Calculus I
>>8477854
I need to have both. The problem states you need 2 pens
>>8477868
Oh I got what you mean but still doesn't work
>>8477852
It's an optimization problem. Try some stuff in that area and if you still can't get it I'll help you, but you need to show some work first.
>>8477852
Start by making a square and a triangle with sides of 14.2857ft in length and go from there
>>8477874
Aka what in saying is find the formula for the areas of a triangle and square, then find their max (where is the graph increasing then decreasing) and you should be able to go from there.
>>8477876
if i can figure out what you're saying without taking calculus, does that mean i'm a genius?
>>8477876
But that's the problem. I can't relate the sides of the triangle with the sides of the square.
Prove first that triangles are just inefficient rectangles by noting that by duplicating a triangle they can be arranged to form a parallelogram. Then show that rectangle is a inefficient square. Lastly note that one square is better than two. The result follows
>>8477874
Here's what I've done so far. Can't relate the area of the triangle with its perimeter.
>>8477852
>an actual problem
KEK, and this is where /sci fails.
this is what the stupid questions general is for anon
>>8477852
All sides the same length with the triangle sharing a side with the square.
>>8477969
Yeah it's the only possible solution imo. But can we assume that based on the exercise?
Area of sqare = x^2
Area of equilateral triangle = sqrt(3)*y^2/2
Circumference of square = 4x
Circumference of triangle = 3y
3y+4x=100
x,y >= 0
maximize f(x,y) = x^2+sqrt(3)*y^2/2
Method, check x=0, y=0 and the line connecting those.
x=0 => f(x,y) = 25^2 = 625
y=0 => f(x,y) =~ 481
del f = (2x, sqrt(3)y/2)
taking the scalar product of this and the normal of the line fields:
4x+3y*sqrt(3)/2 = 0
remember 4x+3y = 100 so we get
(100-3y)+3y*sqrt(3)/2 = 0 =>
y = 100/3(sqrt(3)-1)
Nw just plug it in, see if x is valid (0 to 25) and wheather this is a local max or min and then you are set.
Do you want me to fuck your solution for this puzzle up?
>for one pen, a single entire wall can be one of the walls of the other pen.
Not very got at math, but i suppose the most efficient way to maximize the area is by having the two pens sharing one side. The circumference of the pens are then 4x+2sqt((0,5x^2)+h^2)=100 feet
The area of the pens are x^2+xh/2
you can then subistute h with an epression with x from the circumference exquation. and then find the maximum of the area function with the derivate.
Don't know if this is correct though
>>8477985
>Area of equilateral triangle = sqrt(3)*y^2/2
No, area=height*base/2
y*sqrt(3/4)*y/2=y^2*sqrt(3)/4
>>8477877
How do you not do calculus... I'm from the uk and we just start it at like 16 and i dont get how you can learn maths without it source:from uk and physics undergrad
>>8478002
True, thanks for pointing that out.
>>8478011
OP reporting in. Fuck the area expression is huge as shit specially when derived. Impossible to solve without the calculator. Have I made a stupid mistake? Could someone try to do it?
>>8477852
use degenerate triangle with area zero along one of the square's fences
>>8478272
Bump