Answer:
x = 10 - 10sqrt(3)/3
Approximately 4.2265 cm
Volume = 1539.6 cm³
Step-by-step explanation:
Let the height be x
V = (20 - 2x)(40 - 2x)x
V = (800 - 80x - 40x + 4x²)x
V = 4x³ - 120x² + 800x
dV/dx= 12x² - 240x + 800 = 0
3x² - 60x + 200 = 0
x = [60 +/- sqrt(60² - 4(3)(200))]/6
x = [30 +/- 10sqrt(3)]/3
x = 10 +/- 10sqrt(3)/3
Approximately,
15.7735 and 4.2265
d²V/dx² = 24x - 240
For max, d²V/dx² < 0
So, x = 4.2265
V = (20 - 2x)(40 - 2x)x
Plug in x = 10 - 10sqrt(3)/3
V = 1539.600718
Answer:
6 gallons
Step-by-step explanation:
25÷200= 0.125
0.125×48= 6
The area of the shaded region is the square subtract the circle. The radius of the circle is the diameter/2
Area of circle= pi x radius x radius
=3.14 x 5 x 5 = 78.5
Area of the square = side x side
= 10 x 10 = 100
Area of shaded 100 - 78.5 = 21.5
And don’t forget the unit of measurement (meters)
this is the answer I came up with hopes this helps
Expand brackets:
2*53= 106
2*34= 68
(106+68)-43
174-43= 131