A rectangular tank with a square base, an open top, and a volume of 19 comma 65219,652 ft cubedft3 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.

34 and 17 feet.

Step-by-step explanation:

We have that the volume is given by:

V = x * x * y = (x ^ 2) * y

The surface area of the tank would be: x ^ 2 + x * y + x * y + x * y + x * y

SA = x ^ 2 + 4 * x * y

we know that the volume is 19652, replacing it would remain:

 19652 = (x ^ 2) * y, we solve for y:

y = 19652 / (x ^ 2)

replacing in SA we are left with:

SA = x ^ 2 + 4 * x * 19652 / (x ^ 2)

SA = x ^ 2 + 70608 / x

we derive and equal 0:

SA´ (x) = 2 * x - 70608 / (x ^ 2) = 0

2 * x = 70608 / (x ^ 2)

x ^ 3 = 39304

x = 34

for and would be:

y = 19652 / (34 ^ 2) = 17

dimensions are 34 and 17 feet.

step-by-step explanation:

ok so im not 100% sure but you would start by adding 5.1t and 1.9t beacuse they have the same variable. that is 7t.   then add -3.6 + 1.2 which is -2.4

so then keep that as -2.4 + 7t. i apologize if this is incorrect. best luck on your test < 3

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: