An engineer is using computer-aided design (CAD) software to design a component for a space shuttle. The scale of the drawing is 1 cm : 60 in. The actual length of the component is 12.75 feet. What is the length of the component in the drawing?

Work Shown

1 foot = 12 inches

12.75 ft = 12.75*12 inches = 153 inches

The scale of 1 cm : 60 in allows us to form the proportion below

(1 cm)/(60 in) = (x cm)/(153 in)

1/60 = x/153

1*153 = 60*x cross multiply

153 = 60x

60x = 153

x = 153/60

x = 2.55

The length of the component in the drawing is 2.55 cm

Side note: This is equivalent to 25.5 mm since 1 cm = 10 mm (ie you multiply by 10 to go from cm to mm).

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

41*67/2=1373.5

step-by-step explanation:

i just used a calculator