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liliJ
07.04.2020 •
Mathematics
Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 6cm and a height of 12cm, at the rate of 3 cm3/min. At what rate is the depth of the water changing at the instant when the water in the tank is 9 cm deep? Give an exact answer showing all work and include units in your answer. (10 points)
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Ответ:
Therefore the depth of the water is changing at the instant when the water in the tank is 9 cm deep at rate
/ min.
Step-by-step explanation:
Given that,
Radius of the cone(r)= 6 cm
Height of the cone (h)= 12 cm
The volume of the cone is (V)![=\frac13 \pi r^2 h](/tpl/images/0587/8490/23e2b.png)
Putting![r=\frac h2](/tpl/images/0587/8490/9b962.png)
Differentiating with respect to t
Given that water is drained out of tank at the rate 3
/ min.
It means the rate change of volume is 3
/ min that is ![\frac{dV}{dt}=3 \ cm^3/min](/tpl/images/0587/8490/9292d.png)
Putting the value of
in equation (1)
To find the rate of the depth of water changing at 9 cm depth, we need to put h=9 cm in the above equation.
Therefore the depth of the water is changing at the instant when the water in the tank is 9 cm deep at rate
/ min.
Ответ:
Question:
The options are;
(a) (9 - 2s1, 3 + 3s1, s1)
solution
not a solution
(b) (-4 - 5s1, s1, -(3 + s1)/2)
solution
not a solution
(c) (11 + 10s1, -3 - 2s1, s1)
solution
not a solution
(d) ((6 - 4s1)/3, s1, -(7 - s1)/4)
solution
not a solution
The options that form a solution of the given system are;
(b) and (c)
Step-by-step explanation:
Here we have
3·x₁ + 8·x₂ − 14·x₃ = 9
x₁ + 3·x₂ − 4·x₃ = 1
(a) (9 - 2·s₁, 3 + 3·s₁,s₁)
3·(9 - 2·s₁) + 8·(3 + 3·s₁) − 14·s₁ = 4s₁+51
Not a solution
(b) (-4 - 5s₁, s₁, -(3 + s1)/2)
3·(-4 - 5s₁) + 8·(s₁) − 14·-(3 + s1)/2 = 9
(-4 - 5s₁) + 3·(s₁) − 4·-(3 + s1)/2 = 2
Solution
(c) (11 + 10s₁, -3 - 2s₁, s₁ )
3·(11 + 10s₁) + 8·(-3 - 2s₁) − 14·s₁ = 9
(11 + 10s₁) + 3·(-3 - 2s₁) − 4·s₁ = 2
Solution
(d) ((6 - 4s1)/3, s1, -(7 - s1)/4)
3·(6 - 4s1)/3+ 8·s1− 14·-(7 - s1)/4 = 0.5s₁ +30.5
Not a solution