Answer:
Dimensions are;
2.5 inches height
Base: 10 inches by 10 inches
Max volume; 250 Sq.in
Step-by-step explanation:
Let each side of the square that's cut-off from each corner be represented by x.
This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.
Thus;
Volume of box is:
V = (15 − 2x)(15 − 2x)x
V = (15 − 2x)²x
V = (4x² - 60x + 225)x
V = 4x³ - 60x² + 225x
Let's differentiate with respect to x to get;
dV/dx = 12x² - 120x + 225
Maximum value of x is at dV/dx = 0
12x² - 120x + 225 = 0
Using quadratic formula, we arrive at;
x = 2.5 or 7.5
Now, let's find the second derivative of the volume;
d²V/dx² = 24x - 120
Putting x = 2.5 gives;
d²V/dx² = 24(2.5) - 120
d²V/dx² = -60
Thus, V is maximum at x = 2.5, since d²V/dx² is negative
At x = 7.5;
d²V/dx² = 24(7.5) - 120
d²V/dx² = 60
Thus, V is minimum at x = 7.5, since d²V/dx² is negative
Thus,we will use x = 2.5
Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)
V = 10 × 10 × 2.5
V = 250 Sq.inches
Dimensions are;
(15 − 2x) = 15 - 2(2.5) = 10 inches
(15 − 2x) = 15 - 2(2.5) = 10 inches
x = 2.5 inches
-3=7x -10
-7x=-10+3
-7x=-7
x=1
Answer:
10kg?
Step-by-step explanation:
First, think of your places. You have the ones places, tens places, hundreds places, and so on.
The first number starting from the right is the ones, and as you keep going left, the value of each given digit becomes higher.
Since 5 is in the ones place, its value would be just 5. If it were in the tens place, it would be 50. If it were in the hundreds place, it would be 500, and so on.
Think of it this way;
Ones is just one. If a number is in the 'ones' place, its value would be a single digit. If it were in the tens place, its value would be two digits.
That's how it would be for each place going left.
Every number you move to the left, its value gains a one.
So here's an example:
5555
The value of 5 in the ones place "5555" is simply 5.
In the tens place, you end up adding one zero, so the value of the second five to the left would be, "50"
So with that said, the value of the digit 5 in the number 75 is <em>5.
</em>Haha, hope this cleared up any confusion, and have a <em>wonderful </em>day! :)<em>
</em>
Answer:
B., D., E.
Step-by-step explanation:

This is choice B.
This is choice E.
This is choice D.