CPhill

We need to find  "b"

So  we have

200  =  300 (b)^5        divide both sides by 300

2/3   =  b^5        take the 5th root of both sides

b  ≈ .9221

So....the model is

f(t)  =  300(.9221)^t

t²v³/ [ac ]   =

t²v³a^-1c^-1

Here's a "mock"  pic

           C

    10                    20            

A              15                B   

Side  AB  = 15......side  BC  =  20   

If B is bisected....we have this ratio

BC / AB   =  longer segment  DC / shorter segment AD 

20/15   =  DC / AD

4/3  =  DC / AD

Thus.......AC  is split into 7 equal parts...and  DC  is 4 of these....so its length is

(4/7)  * 10   =   40 / 7   units

If he fails because of the practical only...he must have passed the theory part...so....the probability that he failed because of the practical only  is

Pass Theory * Fail Practical =

   0.8              *            0.5     =      0.40

ab^2/  [ x^3y  ]  =

ab²x^-3y^-1

The angle bisector of B  sets up the following ratio :

BC / AB   =  CE / AE

BC / 8  =  4 / 6       multiply both sides by 8

BC  =   8 * 4  / 6     =    32 / 6   =   16 / 3

Good job  !!!!

We have a right triangle......the hypotense is 8  and we are looking for the adjacent side next to the angle

The cosine relates the adjacent and hypotenuse...so we have

cos (10°)  =  adjacent side /  8       multiply both sides by 8

8*cos(10°)  =  adjacent side   ≈  7.9 ft

( x + y)^4

We can use the 4th row of Pascal's Triangle for the coefficients.....the first row is "row 0"

1   4      6      4     1

So  we have

1x^4  +   4x^3y   +  6x^2y^2  + 4xy^3  + 1y^4

Note, Manuel.....the sum of the exponents in each term  = 4  ......

Unfortunately...it's not true that half the radius would mean half the volume

Let's find the original radius

904.32   =  (4/3) pi  * r^3     divide both sides by   (4/3)pi

904.32

______    =  r^3

  (4/3)pi

215.89  =  r^3

Take the cube root  

6   =  r^3

Half of this   =  3

So...the volume of a ball with half of the original radius is

(4/3) pi  (3)^3   = 

36 pi  =  113.09 in^3     ...the answer that is closest is

113.04  in^3

[ The  slight difference may be due to using 3.14 for  pi  ]