What is the inverse function of v(x) = 2/3 x - 1/6

Mathematics

1 answer:

vlabodo [156]3 years ago

6 0

I dont know if this is right but I got: (6x+1)/4

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A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op

Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, $\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h$

Volume of cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3$

By differentiating with respect to time t, we get that

$\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}$

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie $\dfrac{dv}{dt}=-4\ in^3$

and h = 2 inches deep.

$-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}$

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

7 0

3 years ago

Find the first 4 terms of the geometric sequence a1=40 and r=0.5

DedPeter [7]

For the answer to the question above,
a1 = 40
a2 = 20 
a3 = 10 
.. 
aN = (1/2^N-1) a1 { in general aN= (r^N-1) A1 

a5 = (1/2^4) 40 = 40/16 = 2.5

So the answer to your question is 2.5
I hope my answer helped you. Feel free to ask more questions. Have a nice day!

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BabaBlast [244]

Answer:

Aight.

Rational, Real, Integer, Negative

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