Answer:
Below in bold.
Step-by-step explanation:
The surface area of the box
= x^2 + 4hx where x = a side of the square base and h is the height.
So x^2 + 4hx = 8
The volume of the box
V = x^2h
From the first equation we solve for h
4hx = 8 - x^2
h = (8 - x^2) / 4x
Now we substitute for h in the formula for the volume:
V = x^2 * (8 - x^2) / 4x
V = 8x^2 - x^4 / 4x
V = 2x - 0.25x^3
Finding the derivative:
V' = 2 - 0.75x^2 = 0 for max/mimn values
x^2 = 2/ 0.75 = 2.667
x = 1.633.
So the length and width of the base is 1.633 m and the height
= ( 8 - 2.667) / (4*1.633)
= 0.816 m
The maximum volume = 0.816 * 2.667 = 2.177 m^2.
The answers are correct to the nearest thousandth.
Answer:
i think it is $106,800.00
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6.5%/100 = 0.065 per year.
Solving our equation:
A = 60000(1 + (0.065 × 12)) = 106800
A = $106,800.00
The total amount accrued, principal plus interest, from simple interest on a principal of $60,000.00 at a rate of 6.5% per year for 12 years is $106,800.00.
9 inches long
9 divided by 10 is .9
multiply it by 10 (to get the length of the purple ribbon) and the answer is 9
answer;
x=0
Step-by-step explanation:
4 + 2 (x + 3x) = 4 - x(2-3) + 2x
let remove d brackets
4 + 2x + 6x = 4 - 2x + 3x + 2x
llet collect like terms
2x + 6x - 3x -2x + 2x = 4-4
5x = 0
x = 0
Answer:
Step-by-step explanation:
So an angle has two parts. Initial side and terminal side.
Inital side like on x axis. and terminal side shows how much it open up. Here the terminal angle terminates in second quadrant so we have the following
- A negative Cosine Value
- A positive Sine value
- A negative Tangent Value.
Now, using Pythagoras identity let solve for cos theta.
Here you on the right track but remeber that son theta=1/3 so sin theta squared would be 1/3 squared so we have
Note since cosine is negative in second quadrant, cos theta is
To find tan theta we do the following
So
Tan is negative in second quadrant