Answer:



Step-by-step explanation:
Given




Required
The dimension that minimizes the cost
The volume is:

This gives:

Substitute 


Make H the subject


The surface area is:
Area = Area of Bottom + Area of Sides
So, we have:

The cost is:



Substitute:
and 



To minimize the cost, we differentiate

Then set to 0


Rewrite as:

Divide both sides by W

Rewrite as:

Solve for 


Take cube roots

Recall that:







Hence, the dimension that minimizes the cost is:



Answer:
y ≥ 3x -1; x +3y ≤ 6
Step-by-step explanation:
Both lines are solid, so the only viable choices are those with "or equal to" in the comparison operators: the 2nd and 4th choices.
The line with a slope of +3 is shaded <u><em>above</em></u> the line, so that will correspond to the inequality ...
y ≥ 3x -1 . . . . . . . . . . found only in the 4th choice.
Add 121/4 to each side:
x²+11x+121/4 < 121/4-8
x²+11x+121/4 < 89/4
(x+11/2)² < √89/2 ⇒ -√89/2 < x+11/2 < √89/2
-11/2-√89/2 < x < -11/2+√89/2
Answer:
The third option
Step-by-step explanation:
First, write the equation out as 700(0.25)=x and 700-x=y (y being your final answer). 700*0.25 is 175. Now, we subtract 175 from 700. 700-175 is 525. $525 is your final answer, which makes the third option correct. Hope this helps!