Abox is partially filled with sand. the length of the box is 8 mm. the width of the box is 17 mm. if the volume of the sand is decreasing at a rate of 562 cubic mm per minute, what is the rate, in mm per minute, at which the height of the sand is changing when the height of the sand is 2 mm?

- 4.13 mm/min

Explanation:

length of box, l = 8 mm

width of box, w = 17 mm

dV/dt = - 562 cubic mm per minute

let the height is h.

dh /dt = ? when h = 2 mm

The volume of the box is given by

V = l x w x h

Differentiate with respect to h

here, l and w be the constants as the length and width are not changing

dV/dt = l x w x dh/dt

-  562 = 8 x 17 x dh/dt

dh/dt = - 4.13 mm/min

negative sign sows that the height is decreasing.

ammonium chloride & tallow

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day