CPhill

Archimedes provided a rather ingenious proof of this by noting that the volume of a hemisphere is equal to the sum of the differences in the cross-sections of a cylinder and an associated cone both having the same radius as the hemisphere, i.e....... pi*r^2h - (1/3)pi*r^2h = (2/3)pi*r^2h. But, the cylinder and the cone also have a height equal to this radius, so we have (2/3)pi*r^2h = (2/3)pi*r^2*r = (2/3)pi*r^3

So....twice this equals the volume of a whole sphere = 4/3pi*r^3

To prove that, in congruent triangles, the bisectors of congruent angles are themselves congruent segments.

Let ABC  and DEF be congruent triangles

And let CC' be the angle bisector of of angle C ....and let FF' be the angle bisector of F

Then, since angle C = angle F, then the bisected angles BCC' and EFF' will also be equal.

And BC = EF.  And angle B = angle E.

Thus, by ASA, triangle BCC' = triangle EFF'.

Thus, the angle bisectors (segments) CC' and FF' are equal

(I think this is something on the order of what you might need...I hope)

Yep....you got it correct.....!!!

–3.5(2 – 3n) – 2.5n      distribute the -3.5 across the terms in parentheses

-7 + 10.5n - 2.5n         combine like terms

-7 + 8n

360 minutes = 6 hrs

So....he must have worked out 1 hour per day since he worked out 6 times and the length of each was the same.

So.....45 minues of each hour was devoted to the bike......then......the other 15 minutes each day must have been devoted to jogging, since there are 60 minutes in an hour.

Thanks for that answer, geno......!!!

(2x^5 + 3x^2)(x^4 - 4x^2 + 3x - 8)

Multiply the terms in the first set of parentheses over the four terms in the second set of parentheses...so we have

(2x^5 + 3x^2)(x^4) =        2x^9                 + 3x^6

(2x^5 + 3x^2)(-4x^2) =                 -8x^7                            -12x^4

(2x^5 + 3x^2)(3x)                                       + 6x^6                         + 9x^3

(2x^5 + 3x^2)(-8)                                                      -16x^5                         -24x^2

Adding down, we have   2x^9  - 8x^7 + 9x^6  -16x^5  -12x^4  + 9x^3 - 24x^2  

(2x^5 + 3x^2)(x^4 - 4x^2 + 3x - 8)

Multiply the terms in the first set of parentheses over the four terms in the second set of parentheses...so we have

(2x^5 + 3x^2)(x^4) =        2x^9                 + 3x^6

(2x^5 + 3x^2)(-4x^2) =                 -8x^7                            -12x^4

(2x^5 + 3x^2)(3x)                                       + 6x^6                         + 9x^3

(2x^5 + 3x^2)(-8)                                                      -16x^5                         -24x^2

Adding down, we have   2x^9  - 8x^7 + 9x^6  -16x^5  -12x^4  + 9x^3 - 24x^2  

a)  We could have any of 10 digits in any of the nine positions......so, the total number of different identifiers  = 10⁹ = one billion

b) I don't understand this one.......could you be a little clearer ???

N = s * t