Similar Posts

Only rich people can become academics, right?

ByKeinAFDWaehlerr

By academics, I mean academics in research. I'm referring to them in particular. The problem is, most of them, except for professors, are only on temporary contracts and very poorly paid, often only part-time. That means they sometimes earn as little as unskilled laborers. They're also on fixed-term contracts, and of course, they have to…

Subscribe
Notify of
1 Answer
Oldest
Newest Most Voted
Inline Feedbacks
View all comments
eterneladam
eterneladam
4 months ago

Is the -0.47 you used correct?

If so, then you don’t need to read any further, because I come up with a different value:

We have

h^2 + (d/2)^2 = L^2

d^2 = a^2 + a^2 = 2a^2, which is used,

h^2 + a^2 / 2 = L^2

h = root( L^2 – a^2 / 2) = 6.67

We differentiate with respect to a:

ie/da = 1 / ( 2 root( L^2 – a^2 / 2) ) * (-a) = -a/(2h) = -2.77

I would have used that instead of -0.47.

Furthermore, V = 1/3 a^2 h

We differentiate again with respect to a (product rule), for the second summand we take dh/da from above:

dV/da = 1/3 ( 2ah – a^3 / (2h) ) = -1101.16

(This seems large to me, but the volume of the original pyramid is around 3000, and that of one where a was shortened by 1 and h was increased by 2.77 is around 4000.)

Choose so that dV = 100 and calculate the new h.

0