Brittany and Ashley can paint a room in 7 hours if they work together. If Ashley were to work by himself, it would take him 2 hours longer than it would take Brittany working by himself. How long would it take Brittany to paint the room by himself if Ashley calls in sick? Round to 2 decimal places.

Step-by-step explanation:

Brittany paints the room in x hours, completing 1/x of the room per hour.

Ashley paints the room in x+2 hours, completing 1/(x+2) of the room per hour.

Working together, they complete 1/x + 1/(x+2) = ⅐ of the room per hour.

7(x+2) + 7x = x(x+2)

14x + 15 = x^2 + 2x

x^2 - 12x - 15 = 0

x = [12 ±√(12²+60)]/2= 6±√51

6-√51 is an extraneous solution.

x = 6+√51 ≈ 13.14

Brittany paints the room in 12.14 hours

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

i just took the test, the correct answer is .. 31.5 in.