Answer:
- ength (l) : (10-2*5/3) = 20/3
- width(w): (10 - 2*5/3) = 20/3
- height(h): 5/3
Step-by-step explanation:
Let x is the side of identical squares
By cutting out identical squares from each corner and bending up the resulting flaps, the dimension are:
- length (l) : (10-2x)
- width(w): (10-2x)
- height(h): x
The volume will be:
V = (10-2x) (10-2x) x
<=> V = (10x-2
) (10-2x)
<=> V = 100x -20 - 20 + 4
<=> V = 4 - 40 + 100x
To determine the dimensions of the largest box that can be made, we need to use the derivative and and set it to zero for the maximum volume
dV/dx = 12 -80x + 100
<=> 12 -80x + 100 =0
<=> x = 5 or x= 5/3
You know 'x' cannot be 5 , because if we cut 5 inch squares out of the original square, the length and the width will be 0. So we take x = 5/3
=>
- length (l) : (10-2*5/3) = 20/3
- width(w): (10 - 2*5/3) = 20/3
- height(h): 5/3
2 consecutive odd integers : x and x + 2
x(x + 2) = 27 + 6(x + x + 2)
x^2 + 2x = 27 + 6(2x + 2)
x^2 + 2x = 27 + 12x + 12
x^2 + 2x - 12x - 12 - 27 = 0
x^2 -10x - 39 = 0
(x + 3)(x - 13) = 0
x + 3 = 0
x = -3 (extraneous solution)
x - 13 = 0
x = 13
x + 2 = 15
so ur 2 integers are 13 and 15, with 15 being the largest
Taylor placed 8 photos on the last page of her scrapbook.
(-8)^2
(-8)(-8)
64
Hope this helps!
Answer: 28.26
Step-by-step explanation:
What your looking for is called the annulus (or the difference of two concentric circles). You can find the annulus by subtracting the area of the inner circle from the area of the outer circle. Volume of a circle= πr²
You are given the diameter in these problems, so you need radius.
For the first circle (8 in one) :
8/2=4 r=4
A=3.14(4)²
A=50.24
For the second one (10 in one) :
10/2=5 r=5
A=3.14(5)²
A=78.5
To find the measure of the annulus, you subtract those numbers, getting 28.26
