A rectangular box with a square base is to be constructed from material that costs $9 per ft2 for the bottom, $4 per ft2 for the top, and $3 per ft2 for the sides. Find the box of greatest volume that can be constructed for $193. Round your answer to 2 decimals.

V = 23.85 ft³

Step-by-step explanation:

The dimension of the square base = x ft by x ft

Height of box = y

Volume of the box,

Cost of top = $4 *

Cost of the bottom =  $9 *

Cost of the sides = $3 * 4xy

Total cost = 4x² + 9x² + 12xy

Total cost = 13x² + 12xy

Total cost = $193

193 = 13x² + 12xy

But volume, V = x²y

V =

V = ...................(1)

At maximum value, V' = 0

0 =

x = 2.23

Put the value of x into (1)

V = 23.85 ft³

it costs $20 to interview each person for a survey. find the cost to obtain a +- 3% margin of error.

step-by-step explanation:

copy and paste, put it in google

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.