Alan

If it's a solid sphere and you turn it into a solid cube, then the mass will stay the same, and because the density is the same, the volume will also be the same.

Volume = (4/3)*pi*8³ cm³

If side of cube is of length L then L³ = (4/3)*pi*8³

The surface area of the cube is 6*L² = 6*(4*pi/3)^2/3*8² cm²

Good explanation Melody.

I sort of cheat and use the quadratic formula first!  If it returns nice integers or small fractions I can see that it probably factorises nicely!

Ok.  It's the largest integer less than or equal to x, whereas I assumed it was the smallest integer greater than or equal to x.  The graph will look pretty much the same though, except it will be shifted along the x-axis by one unit!

And your limit calculations are correct chilledz3non. 

Yes it's correct, but notice that it is inside the square brackets, outside of which is the t⁶ factor that divides it.

Use v² = u² + 2as  where v is final velocity, u is initial velocity, a is acceleration and s  is distance.  Rearrange to get a.

Gravitational force between two objects = G*m*M/r²

where m and M are the masses of the two objects, r is the distance between them and G is the Newtonian constant of gravitation (6.6742*10^-11*m³/(kg*sec²))

7²⁰¹² = 217398482708450874935110043662206633152070679148207679466302388992822041830815475042817406594148784374622623594654845284289563623691212723818946616711961588442962188778536122423284150341243556325959267403868907235837787944455000393668406316769671128099732011124456318716494446064220498382871605913412009208937356064161710801545483726923996809775709573476451646874462989392889218203135338792399598714442526975452537067809289146296462537007600020473507477034486589194992565273829885590041024225276878548725050322051685086598798263571447503689461886995485120079852485102498725659554804323718122761740151912477455444517533168785316073781775704294715589338875123101101058568068798826609217549470348595639804621420407832880960910710402462579551500502284322310426176384235777691722753815775853271354823229100828113125924157381090363229703521184077953482446002673591664855818962061882490758338593801762522271076350724888670572155040635176209439545928084019105453895225614934311127502071502848783424881016786497916463508453282070257116256122133523741546172803049819655504736915908304002079618285791552668635663600502619575634333916381518355007557386465444519950276078945956165526252044379821582354034091266972037860663141302084783045318536393858230270904906275106680669952113926985331363784298218875152802504966592447921950142708495793128405496693742688050515303297142374812851400325183557046658478928806421720464623064523192918568354316499884124574194701381638874010511554654713730849091614054688365740996051993502864442876673182263056352394681392977649351347889154828562384346851218397404555389695960050674430699685622647355614484746465208507133207471146532609349254922387951673099567759784711360613042487201

You should probably think about the limit as x approaches a from above (i.e. the right) and from below (the left).

4^x - 5*2^x + 4 = 0

Replace 2^x by u so the above becomes:

u² - 5u + 4 = 0   because 4^x = (2*2)^x = 2^x*2^x = u²

This factorizes nicely into:

(u - 1)*(u - 4) = 0

so u = 1 and u = 4

so 2^x = 1 and 2^x = 4 which means that the two values for x are x = 0 and x = 2