The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. if each of the three measurements has an error of at most 1 centimeter, which of the following is the closest maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?
a. 100,000b. 120,000
c. 160,000
d. 200,000
e. 320,000

C. 160,000

Step-by-step explanation:

The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300cm. If each of the three measurements has an error of at most 1 centimeter, it means that the actual measurement would be

(200 - 1) cm by (200 - 1) cm by (300 - 1) cm. It becomes

199cm by 199 cm by 299 cm

Therefore, the computed capacity would be

200 × 200 × 300 = 12000000 cm^3

The actual capacity would be

199 × 199 × 299 = 11840699 cm^3

The difference, in cubic centimeters, between the actual capacity of the box and the capacity computed would be

12000000 - 11840699 = 159301

Approximately 160000 cm^3

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