The sides of a small rectangular box are measured to be 1.80±0.01cm, 2.05±0.02cm, and 3.1±0.1 cm long. calculate its volume and uncertainty in cubic centimeters.

The volume of the rectangular box and its uncertainty in cubic centimeters is:

11.44±0.54

Step-by-step explanation:

We know the volume of a rectangular box is the multiplication of the sides:

Now we need to know the uncertainty, the uncertainty of a multiplication is:

(1)

Where:

: Volume uncertainty

: Side 1 uncertainty (0.01cm)

: Side 2 uncertainty (0.02cm)

: Side 3 uncertainty (0.10cm)

: Side 1 (1.80cm)

: Side 2 (2.05cm)

: Side 3 (3.10cm)

Clearing the uncertainty of the volume:

(2)

The volume of the rectangular box and its uncertainty in cubic centimeters is:

11.44±0.54

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.