CPhill

Here:

https://web2.0calc.com/questions/geometry_74040

A triangle has integer length sides.  If two sides of the triangle are 18 and 44 , and the triangle is obtuse, how many possible lengths are there for the third side?

If obtuse

18^2  + x^2  <  44^2                                           44^2  + 18^2  < x^2

x^2  <  44^2  -18^2                                             2260 < x^2

x^2 < 1612                                                          ceiling sqrt (2260)  <  x  =  48

x < floor  sqrt (1612)  = 40   

So     48  -  40  + 1   =   9  possible integer lengths   

A triangle has integer length sides.  If two sides of the triangle are 18 and 44 , how many possible lengths are there for the third side?

18  + x >  44           18 + 44 > x

 x > 44 - 18               62  > x

x >  26

 So    

26 < x <  62  ......number of possible integer lengths =  61  - 27  + 1   =  35

Test for independence    

P( A and B)  = P(A) * P(B)

1)  P ( winning and playing at home)  =P(winning) * P (playing at home)???

                              .51  =  .85  *  .6   ???

                              .51  =  .51      (independent)

2 )         .6  = .15 * . 4   ???

             .6  =  .06  ???   (No....not independent )

 . 

(921.60) ( 1 +  1.15) (1 + .02)    =   $2021.07

1 and - 2  are roots     and  the point   (0, -2)  is on the graph

So

a ( 0 - 1) (0 + 2)  =   -2

a ( -1) ( 2)  = -2

-2a =  -2

a  = 1

So

The  parabola is

y = a ( x - 1) ( x + 2)

y = a ( x^2 + x - 2)

 y = 1x^2  + 1x  - 2

a +  b +  c  =     1 + 1    - 2     =     0

The greatest angle is opposite the longest side

Using the Law of Cosines   and  doing some rearranging, we have

[ 38^2 - 25^2  - 18^2  ]  /  [ -2 (18)(25)  ] cos   (theta )

arccos ( [ 38^2 - 25^2  - 18^2  ]  /  [ -2 (18)(25)  ] )    = theta ≈  123.4°

We can find the slant height ,s,  as follows

12 =  (1/2) *3 * s

24 = 3 * s

s = 8 cm

And since we have a 30 - 60 -90  right triangle  the  true height  is   (s/2)   =   8 / 2  =  4  cm

So....the volume of the pyramid  =

(base area  * height) / 3  =   (15 cm^2  * 4  cm)  / 3   =   60 / 3  =    20  cm^3

10 km / h  =   10000m/ 60 min  = (500/3) m / min

7 km / h =  7000m  / 60 min   = (350/3)m/ min

  (500 + 350)  / 3 =   850 / 3  =  the number of combined meters  they run every min

And   400  m  =    (  1200 /3   )  meters

So....every minute   they  run    ( 850  / 1200)  = 17/24  of a lap  combined

1 min =  17/24 lap

24/17 min  =  1 lap

So  they  will pass  each other every    24/17  min

So in  60 min  they will pass each other

integer 60 / [ 24 /17]    =  integer  [ 60 * 17 ] /  24   =   42 times

Volume =   ( pi * radius^2  * height)   /  3