geno3141

Picture the train's engine just entering the tunnel.

One km later the train's engine will just be leaving the tunnel while the rear of the train is just entering the tunnel.

Then, one km later the rear of the train will be just leaving the tunnel.

So, the train will have to travel two km.

     D  =  R x T     --->     2 km  =  60 km/hr x time     --->    time  =  2 / 60  hr.

Since the axis of symmetry is  x = 5  and the point  (2, -5)  is  3  units to the left of the axis of symmetry,

the reflection of this point will be  3  units to the right of the axis     --->     (8, -5).

The area of a rectangle 1 m by 2 m is  2 square meters.

At $68.00 per square meter, the cost is  $68.00 x 2  =  $136.00.

Since  l(d) = 10 / d²  and  d = 4     --->     l(4)  =  10 / 4²  =  10 / 16  =  5 / 8  =  0.625 lux

It depends upon how you were instructed to round:

  if you were instucted that "5 and more round up", then the answer is  0.63 lux

  if you were instucted that "5 rounds to the even number", then the answer is  0.62 lux.

When multiplying numbers with the same base, add their exponents.

To add  1/3  +  1/9  +  1/27  +  ...

note that it is an infinite geometric sequence whose sum is:  Sum  =  a / (1 - r)

where   a  =  1/3     < the initial term >

and       r  =   1/3    < the common ration >             so:            Sum  =  (1/3) / [ 1 - (1/3) ]

                                                                                                Sum  =  (1/3) / (2/3)

                                                                                                Sum  =  1/2

So:  the product  =  2^1/2  =  sqrt(2)

sqrt(8)  =  sqrt( 4 x 2 )  =  sqrt(4) x sqrt(2)  =  2·sqrt(2)

   18·sqrt(8) - 8·sqrt(2)  =  sqrt(n)

18·2·sqrt(2) - 8·sqrt(2)  =  sqrt(n)

   36·sqrt(2) - 8·sqrt(2)  =  sqrt(n)

                    28·sqrt(2)  =  sqrt(n)             Since  28  =  sqrt( 28 x 28 )  =  sqrt(784)

          sqrt(784)·sqrt(2)  =  sqrt(n)

             sqrt( 784 x 2 )  =  sqrt(n)

                   sqrt(1568)  =  sqrt(n)

If AB is tangent to the semicircle, angle(CBA) = 90^o.

In triangle(ABC), angle(C) = 30^o.

In triangle(ABC):  x + x + y + y + 30 = 180

Since x = 17:  17 + 17 + y + y + 30 = 180

                                   34 + 2y + 30 = 180

                                           2y + 64 = 180

                                                   2y = 116

                                                     y = 58

There are  6 x 6 x 6  =  216  ways for the dice to fall.

The ways to get a sum of 10:

6,3,1     5,4,1     4,5,1     3,6,1     2,6,2     1,6,3

6,2,2     5,3,2     4,4,2     3,5,2     2,5,3     1,5,4

6,1,3     5,2,3     4,3,3     3,4,3     2,4,4     1,4,5

             5,1,4     4,2,4     3,3,4     2,3,5     1,3,6

                          4,1,5     3,2,5     2,2,6

                                       3,1,6

The probability is  27/216

First -- simplify the middle expression:  t - 2 + 7  =  t + 5.

We now have:  t/3 - 5  <  t + 5  <=  - 3t

Divide this into two inequalities:  t/3 - 5  <  t + 5          and          t + 5  <=  -3t

Solve each one independently:    t - 15  <  3t + 15                          4t  <=  -5

                                                        -30  <  2t                                    t  <=  -5/4

                                                         -15  <  t

Combining these answers:       -15  <  t  <=  -5/4