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If I read this correctly, the numbers that belong to B are reals and satisfy √ [x^2 ]   =  - x

Note that    √[x^2]  is defined as   l x l

So.......

l x l  = - x        when    x  =   (- infinity, 0 ]

I think this is correct, AT.....

Integers do not have fractional components.

Whole numbers are not fractions.

5/8 = .625    non-repeating decimal = rational number

You can buy any number of packages from one to infinity in + whole numbers.....the domain  [1,+inf)

   b all positive integers

Note that triangle EAC is similar to triangle DBC

Therefore

EA / EC  =   DB / DC       so

80 / 10   = DB / 20

8 / 1  =  DB / 20

8 =  DB /20       multiply both sides by 20

160   =  DB   =   "x"

 (2x+sinx)(3x-cotx)

The derivative is

(derivative of first function ) ( second function ) + ( first function ) ( derivative of second function )  =

(2 + cos x) (3x - cot x)  + (2x + sin x) (3 + csc^2 x)

Thanx, Chris..... here is another method:

Use quadratic formula to find the two roots as  3/4 +- 3.5968i

(3/4+ 3.5968i)^2 = 9/16 +3/2 (3.5968i) - 12.9375

(3/4- 3.5968i)^2  = 9/16 -3/2 (3.5968i)  - 12.9375

Added together   9/8 - 25.875 = - 24.75

Don't know about (a), but here's the rest

(b)  P (x < 4)  =   [ 5 + 10 + 2 + 9 ] / 90  = 26 / 90  =   13 / 45

(c)  P (x = 6)  =   15 / 90   =   1 / 6

(d)  P  ( x ≥ 5 )  = [ 12 + 15 + 3 + 1 ] / 90   =   31 / 90

2x^2 - 3x + 27 = 0          

Let the roots be p and q

The sum of these roots =  3/2

The product of these roots =  27/2

So

p + q   =  3/2       (1)

And

pq =  27/2           

2 pq =  27        (2)

Square both sides of (1)

p^2 + 2pq  + q^2  = 9/4         sub (2) into this

p^2 + (27) + q^2 = 9/4

p^2 + q^2 =      9 / 4 - 27 

p^2 + q^2 =   9/4 - 108 / 4

p^2 + q^2 =  -99 / 4

p^2 + q^2 =  -24.75

Multiply FIRST equation by - 1.5 to get

-6x +1.5y -3z = -10.5      add it to second equation

6x +3y +3z =5

to get

4.5y = -5.5

y = -1.222      (  or  - 11/9)

If a circle has a radius of 1, its curvature is inversely proportional to this = 1

A circle with a curvature of 1/3 of this must have a radius of 3

So....the circumference of this circle  =  2 pi * radius =  2 pi * 3 =  6pi ≈ 18.85 units

Kitchen is 20x15 = 300 sq ft

A.    10% more is   300 x 1.10 = 330 sq ft

B.     Charge for installation will be    ($6   +   .36)300           +   (tile cost * 1.06)  = $ 5600  

   Remember..contractor BUYS 330 sqft but INSTALLS only 300 sq ft

solve for 'tile cost'

                6.36(300) + 1.06 tilecost = 5600

                1908 +1.06 tile cost = 5600

                            1.06 tile cost = 3692

                                    tile cost = 3483.02            for  330 sq ft            

                                 sq ft tile cost =  3483.02/330 = $10.55 sq ft      (again remember 330 sq ft purchased)

Inglés por favor si es posible. Mi español esta oxidado

The function y=-16t^2+8t represents the height y (in feet) of a grasshopper jumping straight up from the ground t seconds after the start of the jump. After how many seconds is the grasshopper 1 foot off the ground?

We need to solve this

-16t^2+ 8t  =  1      subtract 1 from both sides

-16t^2 + 8t - 1  = 0           multiply through by - 1

16t^2 - 8t + 1 =  0           factor

(4t - 1) (4t - 1) = 0

(4t - 1)^2 =  0           take the square root

4t - 1 = 0       add 1 to both sides

4t  = 1           divide both sides by 4

t =  1/4   seconds

The scale factor is given by

 JK  / EF  =  11.2 / 28    =  2 / 5 =  0.4