# Recent questions and answers in Math

Centrifugal ultra-fine grinding machine

Centrifugal ultra-fine grinding machine (referred to as ultra-fine grinding) is my company at home and abroad advanced milling equipment developed on the basis of a new generation of ultra-fine milling equipment, has been national patent, can replace Raymond Mill, Fine powder, fineness can be adjusted between 80 mesh and 1500 mesh.
Centrifugal ultrafine mill Scope:
Mainly applicable to barite, calcite, limestone, kaolin, bentonite, marble, gypsum, refractory quartz stone, glass, ceramics and other hardness of not more than 9.3, humidity below 6% of the mineral powder processing, 80 mesh -1500 mesh between the arbitrary adjustment.
Centrifugal ultra-fine milling machine performance characteristics:
1, the noise is small, small vibration, pressure, fine powder, high yield;
2, grinding ring and roller wear evenly, long service life;
3, the equipment can be continuous operation, oiling non-stop, power consumption is small;
4, high efficiency, easy installation and maintenance;
5, the mill without blade feed, low failure rate.

Which city has the median population value?
City Population in Millions Melbourne 3.2 Bangkok 7.2 Nairobi Paris 9.6 São Paulo 17.7 Tokyo 28.0 Seattle 2.1
Suppose Aaron is pumping water into a tank (in the shape of an inverted right circular cone) at a rate of 1600 ft^3/min.
If the altitude is 10 ft and the radius of the base is 5 ft, find the rate at which the radius is changing when the height of the water is 7 ft.
For each positive integer n , defind H(n) as the following. Prove that if n>=2, then H(n) is not an integer

$H(n)=1+ \frac{1}{2}+\frac{1}{3}+ ...+\frac{1}{n}$

Prove the following statement:

$V \subseteq W \Leftrightarrow P(V) \subseteq P(W)$

Where P(X) is the power set of X.

What is c if b and c are constants and

$(x+2)(x+b) = x^2 + cx + 6$

Prove the following using mathematical induction

$\sum_{i=1}^{n}i^3 = (\sum_{i=1}^{n}i)^2$

Find y(1) if

$\frac{dy}{dx} = x y^2 \text { and } y(0) =1.$

Solve equation

$e^x - e^{-x} = e$

The area of an equilateral triangle is increasing at the rate of 5 m^2/hr.

Find the rate at which the height is changing when the area is

$\frac{64}{\sqrt3} m^2$

Suppose that f is a function that has a continuous second derivative and that satisfies

$f(0) = 4, f(1) =3, f'(0) = 5, f'(1) = 7, f''(0) =8 \text{ and } f''(1) = 11.$

Show that

$\int_0^1f(x) f''(x)dx \leq1$

$\int_{0}^{a} \frac{f(x)}{f(x) + f(a-x)} dx = a/2$
$a^3+b^3+c^3 =216$