The calculation of the integral will give us the answer.
Amount = Int (2000e^(-0,2t))dt
With t = 0 to t = 10
A = 2000.In(e^(-0,2t))dt
Making U = -0,2t
U = -0,2t
dU/dt = d(-0,2t)/dt
dU/dt = -0,2
dU = -0,2dt
dt = dU/-0,2
_______________
Then,
A = 2000.Int (e^U).dU/-0,2
A = -10.000.Int(e^U)dU
A = -10.000.e^U
A = -10.000.e^(-0,2t) | (0,10)
A = -10.000.(e^(-2)) - [ -10.000.e^(0)]
A = -10.000.e^(-2) + 10.000
A ~ 8,646 Gallons
The Total Volume is V= 8x6x18 = 864 units³ , Or 864 sugar cubes.
If we calculate V₁, the volume (or number of sugar cubes) that DOESN'T touch the sides of the box, then: V-V₁ = will give the volume (or the Cube number) of those who touch the box.
The following is in respect of the cubes that DO NOT touch the box:
The Length = 8, (or 8 cubes), becomes 6 (or 6 cubes), because already
1 is touching at the right and another is touching at the left.
The Width = 6 , (or 6 cubes), becomes 4 (or 4 cubes), because already
1 is touching at the right and another is touching at the left.
Same for the height = 18, it becomes 18-2 = 16, hence volume of the cubes that DON'T touch the box = V₁ = (8-2)(6-2)(18-2) = 384 Sugar cube
Then V-V₁ = 864 - 384 = 480 sugar cubes that TOUCH the box
Answer: h= 8
Step-by-step explanation:
-3h - 6(5h/3 + 7/2) + 9h = -53 Distribute on the left
-3h - 10h - 21 + 9h = -53 combine like terms on the left side
-4h -21 = -53 Now add 21 to both sides
+21 +21
-4h = -32 Divide both sides by -4
h = 8
Word form - six.seven
Expand form - 6 + 0.7