A metal cube dissolves in acid such that an edge of the cube decreases by 0.53 mm/min. How fast is the volume of the Cube changing when the edge is 6.3 mm?

The volume of the cube is decreasing at a rate of 63.1071 cubic millimeters per minute.

Step-by-step explanation:

The volume of a cube is given by:

Implicitly differentiate the equation with respect to time t:

The edge of the cube decreases by 0.53 mm/min. Therefore, ds/dt = -0.53.

When the edge is 6.3 mm, s = 6.3.

Substitute and evaluate:

The volume of the cube is decreasing at a rate of 63.1071 cubic millimeters per minute.

answer:

it will cost 480 dollars to refurbish the larger wood floor

step-by-step explanation:

as it's a ratio of 4 that costs 384 dollars, divide the price by the ratio

384 / 4 = 96 dollars

96 dollars per unit of the ratio

now to get the price to refurbish the larger wood floor, times the price by the units

96 * 5 = 480

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)