Arectangular tank with a square base, an open top, and a volume of 864 ft cubed is to be constructed of sheet steel. find the dimensions of the tank that has the minimum surface area. let s be the length of one of the sides of the square base and let a be the surface area of the tank. write the objective function.

Tank dimensions:

s = 12 ft

h = 6 ft

Step-by-step explanation:

s = lenght side of the square base

A the total area of of the tank  ( this area is the area of the base plus  the lateral area (4) times

h  = the height of the tank

V  = 864 ft³             V  =  s² * h    ⇒   h = V/s²  ⇒ h = 864/ s²

Then we have :

A (total) =  Base area + 4 * lateral area

Area of the base is  s²

Lateral area is  s * h  but we have 4 wall  so lateral area = 4*s*h

Then Objective function is :

A(s) = s² + 4*s * V/s²           ⇒    A(s) = s²  + 4*864/s     ⇒   A(s) = s²  + 3456/s

Taken derivative of the objective function:

A´(s) = 2s - 3456/ s²

Solving for s

2s - 3456/s²  = 0     ⇒  2*s³  - 3456 = 0   ⇒  s³  = 3456/2  ⇒ s³ =  1728

s = ∛1728      ⇒   s =  12 ft

So h = V/s²       ⇒  h = 864 / 144       ⇒  h = 6 ft

the correct answer is 5 6 and 7

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .