Answer:
Height: 3/2 inches
Length: 12 inches
Width: 4 inches
Step-by-step explanation:
Let x is the side length of the square
The height of the box by cutting squares off :x
- The new length of the cardboard = 15 -2x (because we cut from 4 corners)
- The new width of the cardboard = 7 -2x (because we cut from 4 corners)
The new volume of it is:
V = (15 -2x) (7 -2x) x
<=> V =
To maximum volume, we use the first derivative of the volume
<=> 
<=> 
<=> 2x -3 = 0 or 6x -35 = 0
<=> x = 3/2 or x = 35/6
To determine which value of x gives a maximum, we evaluate
= 24x -88
= 24(3/2) -88 = -52
= 24(35/6) -88 = 52
We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.
So the dimensions (in inches) of the box is:
Height: 3/2 inches
Length: 15-2(3/2) = 12 inches
Width: 7 - 2(3/2) = 4 inches
The answer to the question
Answer:
6
Step-by-step explanation:
5+5=10, so 4+6=10
Let, that number = x
It would be: x * 0.65 = 52
x = 52 / 0.65
x = 80
So, that number and your answer is 80
18 is 45% of 40
45%/100 = 0.45
0.45*40=18
Answer:
x = -2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 3x - 1
f(x) = -7
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute: -7 = 3x - 1
- Isolate <em>x</em> term: -6 = 3x
- Isolate <em>x</em>: -2 = x
- Rewrite: x = -2