Katherine wants to construct a small box with a volume of 20 cubic inches with the following specifications. the length of a box is five more than its width. its depth is one less than its width. what are the dimensions of the box in simplest radical form and rounded to the nearest hundredth? only and algebraic solution will receive full credit.

Width =√5,length =√5+5 ,Depth =√5-1.

Step-by-step explanation:

volume of box = l.w.h ,where l is length ,w is width and h is the depth  of the box.

It is given  l= w+5

                h= w-1.

Substituting l and h values we have

V= (w+5).w.(w-1)

Or 20 = w(w+5)(w-1) [ volume is 20 cubic in)

or,

Taking common factor of both pairs we have:

 or w+4=0

w=±√5 or w=-w

Length can not be negative so

w=√5

l=w+5=√5+5

h=w-1=√5-1

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°