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volume help. show work

At A water tank is being filled by water being pumped into the tank at a volume given by the formula, P(t) = 60t +1060, where t is in minutes. At the same time the water tank has a leak and the volume of water draining out of the tank is given by the formula L(t) = 3t2, where t is in minutes.
 
 
(a.) The volume, V, of water in the tank at any minute, t, is the difference of the volume of the water being pumped into the tank and the volume of water linking out of the tank. Find the volume function, V(t).
 
(b.) What is the volume of water in the tank after 17 minutes? Show work.
 
(c.) The volume function is a quadratic function and so its graph is a parabola. Does the parabola open up or down? How do your know? _______________________ 
 
(d.) Find the vertex of the volume function P(x). Show work.
 
(e.) State the number of time which yield the maximum volume, and state the maximum volume. The maximum volume is _______________ at ____________ minutes
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1 Answer

At A water tank is being filled by water being pumped into the tank at a volume given by the formula, P(t) = 60t +1060, where t is in minutes. At the same time the water tank has a leak and the volume of water draining out of the tank is given by the formula L(t) = 3t^2, where t is in minutes.


(a.) The volume, V, of water in the tank at any minute, t, is the difference of the volume of the water being pumped into the tank and the volume of water linking out of the tank. Find the volume function, V(t).
 
V(t) = (P–L)(t) = 60t +1060 – 3t^2 = – 3t^2 + 60t +1060

(b.) What is the volume of water in the tank after 17 minutes? Show work.
 
 
17 | –3   60    1060
            –51     153         
       –3     9 | 1213 = V(17)


(c.) The volume function is a quadratic function and so its graph is a parabola. Does the parabola open up or down? How do your know? _______________________
 
Opens down because leading coefficient is negative.

(d.) Find the vertex of the volume function P(x). Show work.
 
h = –b/2a = –60/(2(–3)) = 10
 
k = c - ah^2 = 1060 - -3(10^2) = 1360
 
Vertex = (h,k) = (10,1360)


(e.) State the time which yields the maximum volume, and state the maximum volume. The maximum volume is ___1360______ at ___10_______ minutes