I tried to make a list and found 27 ways
tell me if I missed any
order is
(3point,2point,1point)
(0,0,15)
(0,1,13)
(0,2,11)
(0,3,9)
(0,4,7)
(0,5,5)
(0,6,3)
(0,7,1)
(1,0,12)
(1,1,10)
(1,2,8)
(1,3,6)
(1,4,4)
(1,5,2)
(1,6,0)
(2,0,9)
(2,1,7)
(2,2,5)
(2,3,3)
(2,4,1)
(3,0,6)
(3,1,4)
(3,2,2)
(3,3,0)
(4,0,3)
(4,1,1)
(5,0,0)
27 is my answer
Very good job! They are all correct and it shows how you got the answer! ^_^ 100%
Answer:
the rate at which the height of the box is decreasing is -0.0593 cm/s
Step-by-step explanation:
Given the data in the question;
Constant Volume of a rectangular box with a square base = 500 cm³
area of the base increases at a rate of 6 cm²/sec
so change in the area of the base with respect to time dA/dt = 6 cm²/sec
each side of the base is 15 cm long
so Area of the base = 15 cm × 15 cm = 225 cm²
the rate at which the height of the box is decreasing = ?
Now,
V = Ah
dv/dt = 0 ⇒ Adh/dt + hdA/DT = 0
⇒ dh/dt = -hdA/dt / A
we substitute
dh/dt = [ -( 500 / 225 ) × 6 ] / 225
dh/dt = [ -(2.22222 × 6) ] / 225
dh/dt = [ -13.3333 ] / 225
dh/dt = -0.0593 cm/s
Therefore, the rate at which the height of the box is decreasing is -0.0593 cm/s
