Answer:
21
Step-by-step explanation:
Let x represent the side length of the square end, and let d represent the dimension that is the sum of length and girth. Then the volume V is given by
V = x²(d -4x)
Volume will be maximized when the derivative of V is zero.
dV/dx = 0 = -12x² +2dx
0 = -2x(6x -d)
This has solutions
x = 0, x = d/6
a) The largest possible volume is
(d/6)²(d -4d/6) = 2(d/6)³
= 2(108 in/6)³ = 11,664 in³
b) The dimensions of the package with largest volume are
d/6 = 18 inches square by
d -4d/6 = d/3 = 36 inches long
Answer:
The mentioned number in the exercise is:
Step-by-step explanation:
To obtain the mentioned number in the exercise, first you must write the equations you can obtain with it.
If:
- x = hundredths digit
- y = tens digit
- z = ones digit
We can write:
- x = z + 1 (the hundreds digit is one more than the ones digit).
- y = 2x (the tens digit is twice the hundreds digit).
- x + y + z = 11 (the sum of the digits is 11).
Taking into account these data, we can use the third equation and replace it to obtain the number and the value of each digit:
- x + y + z = 11
- (z + 1) + y + z = 11 (remember x = z + 1)
- z + 1 + y + z = 11
- z + z +y + 1 = 11 (we just ordered the equation)
- 2z + y + 1 = 11 (z + z = 2z)
- 2z + y = 11 - 1 (we passed the +1 to the other side of the equality to subtract)
- 2z + y = 10
- 2z + (2x) = 10 (remember y = 2x)
- 2z + 2x = 10
- 2z + 2(z + 1) = 10 (x = z + 1 again)
- 2z + 2z + 2 = 10
- 4z + 2 = 10
- 4z = 10 - 2
- 4z = 8
- z = 8/4
- <u>z = 2</u>
Now, we know z (the ones digit) is 2, we can use the first equation to obtain the value of x:
- x = z + 1
- x = 2 + 1
- <u>x = 3</u>
And we'll use the second equation to obtain the value of y (the tens digit):
- y = 2x
- y = 2(3)
- <u>y = 6</u>
Organizing the digits, we obtain the number:
- Number = xyz
- <u>Number = 362</u>
As you can see, <em><u>the obtained number is 362</u></em>.
To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 1.27 × 100 = 127% (answer)
Answer- (5x-1)(2x+1)
let me know if you need to see work
