3 years ago

What is (X^3 - 4x^2 + 4x - 1) / (x-1)?

Mathematics

1 answer:

professor190 [17]3 years ago

8 0

Answer:

$x^{2} -3x+1$

Step-by-step explanation:

$\frac{x^{3}-4x^{2} +4x-1}{x-1}=\frac{(x-1)(x^{2}-3x+1 )}{x-1}=x^{2}-3x+1$

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A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10

just olya [345]

Answer:

$\frac{dh}{dt}$ ≅ $0.286\frac{ft^{3} }{min}$

Step-by-step explanation:

$V=\frac{\pi }{3}r^{2}h$ ; rate of change $\frac{dV}{dt}=10\frac{ft^{3} }{min}$ , we must find the rate of change of the depth $\frac{dh}{dt} =?;h=8ft$

5h=12r; $V=\frac{\pi }{3}\({\((5h}/12} )} ^{2}h=\frac{\pi }{3}(\frac{25h^{2} }{144})h; V=\frac{25\pi h^{3}}{432}$ ; deriving $\frac{dV}{dt} = \frac{25\pi }{432}(3h^{2})\frac{dh}{dt}$ → $10=\frac{25\pi h^{2}}{144} \frac{dh}{dt}$ → h=8 then $\frac{dh}{dt}=\frac{1440}{25\pi 64}=\frac{9}{10\pi}$ ≅ 0.286 $\frac{ft^{3} }{min}$