All Answers 356004 Answers

Side =x

Length = 17-x

area = side x length

x (17-x) =60

17x-x^2 =60

-x^2+17x-60=0

x^2-17x+60 = 0

(x-12)(x-5)                              x =12     and the side = 17-x = 5     

Pythagorean theorem to find ONE diagonal     12²+ 5² =d²         so d = 13     13 x 13 = 169 in²

Call the number of pages  he has read, R

Call the number of pages he hasn't read, 193 - R

So...we have that

R  =  3 + (1/4)(193 - R)       simplify

R  = 3 + 193/4  -  (1/4)R      add  (1/4)R  to both sides

(5/4)R  =  3 + 193/4          multiply through by  4

5R  =  12  +  193

5R  =  205       divide both sides by  5

R  =  41 = pages he has read

So ....  he hasn't  read  (193 - 41)   =  152  pages

Proof :

(1/4)  of the pages he hasn't read  = 152/4   = 38 pages

And 3 more than this  = 41  = pages he has read .....

zoomer!!!!

Assuming exponetial growth.....the function  is

y  = 800 (1.032)^x

Here's the graph  :  https://www.desmos.com/calculator/w6fslnsljd

The y intercept  = (0, 800)

When  x =  35,  y  ≈  2409

Let N be the number  and we have that

.92 N  =  29             divide both sides by .92

N  =  29 / .92  =   29 / (92/100)   =    29 * 100  /92  =   29 *  25 / 23  =    725  / 23

LOL!!!.......

I felt like , if anyone knew one, YOUR answer would 'learn it to me'    Haha....

You are only HEATING the water...not BOILING the water....

   from your calc it appears as though you are heating the water from 10 to 100 degrees C.  The specific heat of water is 4.186 j/(gm-C)

      (you are using 4180 j/(kg-C)     The specific heat of liquid water is relatively constant below the boiling point. 

At a lower pressure (higher altitude) the water will BOIL at a lower temperature....before YOU GET to 100 C, but the enrgy needed to heat each KG of water from it's liquid starting point for each degree C up to the boiling point is still the same.

I don't see one, EP......

Wel-l-l-l  ,  I guess there WASN'T an easier way !  

The smaller area  is the  difference between the area of a sector  of 1/6 of the circle  less the area of a equilateral triangle with a side of 6.....this is given by

[(1/6) pi * 6^2   -  (1/2)6^2 * √3/2  ]    (1)

So....the   larger area  =

Area  of circle  - (1) 

So

pi*6^2  -   [(1/6) pi * 6^2   -  (1/2)6^2 * √3/2  ]  =

(5/6) pi * 6^2  + 9√3   =

[30pi + 9√3] units^2

Draw a line from the center to each of the endpoints of the chord

   this forms a equilateral triangle     the central angle is 60 degrees   (pi/3 radians)

the area of this sector is   60/360 of the TOTAL area of the circle

    pi r^2  x  60/360   = 6 pi

Now subtract the area of the equilateral triangle to get the area enclosed by the chord

  area of equalateral triangle = r^2 (sqrt3) / 4   = 9 sqrt3

6pi - 9 sqrt3 = area of chord

Total area of cicle - area enclosed by chord = larger area

 36 pi      -    ( 6pi  - 9 sqrt3)

30 pi + 9 sqrt3     units²

^{(there has to be a better way! )}

Nope, still not correct     Ooops....  back to the drawing board......

I get 20....

112     202      314     404   516   606   718   808  

134     224      336     426   538   628

156     246      358     448

178     268

The total number  of subcommittees of three members that can be formed  is  C(13,3)  =  286

The total number of subcommittees  consisting of three Republicans  is  C(5, 3)   = 10

So....the probability  is

10  / 286   =       5  / 143

Let the side of the square  be, S

So

S^2  =  260     take the positive root

S   =  √260

The length of the diagonal   =  √2 * √260   =  √2 *√2* √130  =   2√130  miles

1/45 + 1/105 = 7/315 + 3/315 = 10/315 = 2/63

It will take 63/2 = 31.5 minutes to complete it