Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 40 to 56

  5/7

Step-by-step explanation:

A common factor of 8 can be canceled from numerator and denominator.

  40/56 = (5·8)/(7·8) = (5/7)·(8/8) = (5/7)·1 = 5/7

Since you know your multiplication tables, you know that 40 and 56 are both multiples of 8.

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If you don't know your multiplication tables, you can find the greatest common divisor (GCD) of the two numbers and divide each by that. The GCD can be found using Euclid's algorithm. For that, you divide the larger by the smaller and use the remainder as the new smaller number. The original smaller number is now the larger number. For these numbers, that looks like ...

  56 ÷ 40 = 1 r 16

  40 ÷ 16 = 2 r 8

  16 ÷ 8 = 2 r 0 . . . . . the zero remainder signals that the divisor (8) is the GCD

Now, your fraction is ...

  (40/8) / (56/8) = 5/7

nope

step-by-step explanation:

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