Qualification > Math
Pure math(p3)
astarmathsandphysics:
--- Quote from: ITS MEE... on May 28, 2009, 01:11:15 pm ---can someone solve the last part please
An underground storage tank is being filled with liquid as shown in the diagram. Initially the tank is
empty. At time t hours after filling begins, the volume of liquid is V m3 and the depth of liquid is h m.
It is given that V = 4
3h3.
The liquid is poured in at a rate of 20m3 per hour, but owing to leakage, liquid is lost at a rate
proportional to h2. When h = 1,
dh
dt = 4.95.
(i) Show that h satisfies the differential equation
dh
dt = 5
h2 ? 1
20
. [4]
(ii) Verify that
20h2
100 ?h2 ? ?20 + 2000
(10 ?h)(10 +h). [1]
(iii) Hence solve the differential equation in part (i), obtaining an expression for t in terms of h.
--- End quote ---
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https://studentforums.biz/index.php/topic,740.0.html
ITS MEE...:
thank u
astarmathsandphysics:
--- Quote from: candy on May 28, 2009, 01:02:36 pm ---The polynomial x^4 - 2x^3 - 2x^2 +a is denoted by f(x). It is given that f(x) is divisible by x^2 - 4x +4.
(i) Find the value of a.
(ii) When a has this value, show that f(x) is never negative.
can someone please explain part (ii)
i don't understand the question :(
--- End quote ---
x^2 - 4x +4.=(x-2)^2 so put x=2 and solve f(x)=0 for a
16-16-8+a=a=0 to geta=8 Now do long division by x^2 - 4x +4.to getx^2+2x+2=(x+1)^2+1>0 and since(x-2)^2 is never -ve neither is the product of it and (x+1)^2+1
ITS MEE...:
can u integrate
sin^3xcosx
please :'(
ITS MEE...:
oh i got it no need to solve it but can u integrate this
(1+tanx)^4 sec^2x
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