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
Answer:
volume = 73.3ft³
value = $194.4
Step-by-step explanation:
volume of prism = (½bh)l
=(½×4×4)×9.2
=73.6ft³
value of concrete
1ft³ : $4.00
73 .6ft³ : X
X : (73.6ft³ × $4.00) ÷ 1ft³
X : $294.4
X= 9 over 4 is the correct answer
It would be 9/8
Hope this helps!
Answer:
x = 16
Step-by-step explanation:
Supplementary angles = 180
K + L = 180
137 + 3x - 5 = 180
132 + 3x = 180
3x = 180 - 132
3x = 48
x = 48/3
x = 16