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*** edited ***    I forgot July in my calcs

JUly 31st is day 213     so    August 2 nd

   pi (4)^2          -    4 (sqrt2) * (4 sqrt2)   = shaded area             You should be able to get it from here ...     *** edited ***  I left out the '4'

Each side of the rhombus is   148 / 4 = 37

The diagonals of a rhombus intersect at right angles

  the other diagonal could be found via pythag theorem

      28/2 = 14

                               37^2 = 14^2 + x^2

                          x = 34.249             

area = 4  *   1/2 * 14 * 34.249 = 958.97  units²

I believe if you look at the denominator ....and each subsequent denominator term is larger than the last , the series converges

pick a number                       n= 3       denominator = 29.18

   next number in sequence n= 4         denominator = 83.57      SO I think it converges.....I think to value .5

The area of overlap is 76.

Total of   15 books  

  autobio is 2                so   2/15

  fantasy is 3                 so 3/15

2/15  *  3/15 = ___________       You can finish I hope !  

Area of circle  MINUS  area of square    = shaded area

    pi r^2               -        s * s                   = shaded area

    pi (4)^2          -     (sqrt2) * (4 sqrt2)   = shaded area             You should be able to get it from here ......

Oh Thamks o much

ur basically gonna subtract the area of the circle from the area of the square to get the shaded region.
area of circle = pi x 4^2 = 16 pi
area of square = 32 
shaded region = 16 pi - 32 = 18.3 m squared

 

As n increases the value of   60 - 8n   decreases

60 - 8(1) = 52

60 - 8(2) = 44

60 - 8(3) = 36

etc                        

The question is: 

Julie will randomly choose one book. Then she will put it back and randomly choose another

book. What is the probability that she will choose an autobiography and then a fantasy?

What's the question?

a) 10 * 9 * 8= 720

b) 10 * 10 * 10 = 1000

The radius is 2*sqrt(3).

n = 15.

write (a + b)(b – a) as (b + a)(b – a) just to make the difference of squares more visual 

so (b + a)(b – a) = b² – a²      multiply this by –1 and it is [ –1 • (a² – b²) ]   

                                                                   divide the above by (a² – b²)   

the (a² – b²) in the numerator and denominator cancel out, leaving you with  –1  

can you explain why

1. The smallest possible area of triangle OAB is 64.

2. The smallest possible value of f(1) is 86.

YMIR AND BIN  NOT NEXT TO EACH OTHER

y x b x

b x y x

x y x b

x b x y

y x x b

b x x y       six ways       

                   for each of them the other two spots can be filled in two ways with charles and daria   6 x 2 = 12 ways (as ds1119 found)

Great help..thanks a lot!

y = -16t^2 +80t

80 = -16 t^2 + 80t

-16t^2 +80t - 80 = 0       quadratic formula shows t = ~1.4 SECONDS

FIrst one  ....   no values of x have two values of y     YES

Second one  6.6   and 6,8   means the value of x = 6 has two values for y    NO

Third one      7,-4     7, -6                                                                                   NO

Fouth one     -5,1    -5,3       no

x² = 4

     take square root of both sides

x = ± 2

Area of a rectangle =   length x width  = 2 x 1 = 2 units²