The moving sofa problem for eighth grade? Most students have mastered the three-dimensional solution by third grade, and many do it by second grade. Certainly the two-dimensional solution is mastered by second grade.
It’s not a wonder you had a problem determining the limit of character space for a post.
It must be a raging case of untreated CDD. Try not to spread it around the forum.
Perhaps I still do not understand your question properly but it sounds like you have simplified it down to a 2 dimensional problem.
like a rectangular piece of paper beong pushed along the floor.
I think the largest area is just a x b where a and b are the widths of the 2 hallways.
I will think about it more though 😕
To clarify (I thought I only had limited characters for a question or something)
The moving sofa problem requires constructing a shape of greatest possible area, such that it is able to move through a 1 wide hallway that bends at a 90 degree angle. (As you probably already know)
I would like to tackle the simpler problem: Try this problem with the restriction that our shape in question can only be a rectangle. In addition, the widths of both hallways (before, then after the bend) could be any length. For example, the width of the hallway before the turn could be 17, then 0.022 after the right angled turn. Let the widths of said hallways be a and b.
Ive been thinking of the idea that I could first represent the base of the rectangle in terms of slope and length, then find the area of the rectangle, then write a 2 argument function f(s,l) to represent this, then try to take the derivative, then... I'm not even sure if this would work as we would be dealing with 3 dimensional graphs, and as an 8th grader I do not want to go there. Hopefully it does not differ too much from simple 2D calc. Anyways, I am almost certain that this approach is far fetched and may not even work at all. If there a better way to approach this problem?
Ava, Grace, Jayden, and Zoe together stacked a total of 50 brownies on a tray. Ava stacked 0.14 of the brownies, Grace stacked 4 of the 50 brownies, Jayden stacked 24% of the brownies, and Zoe stacked the remaining brownies. Who stacked the most brownies?
There are 50 brownies
Grace has 4
Ava has 0.14*50
Jayden has 24/100*50
zoe has the rest.
you see if you can work it out from here.
express in scientificnotation 7,250,000
you put the point between the first and second digit like this
now that is a a big number so the power will be positive
In intially there is an invisable point at the very end. You had to jump it ove 6 numbers to get it where you want it.
the answer is $$7.25*10^6$$.