# Recent questions in Math

stone production in various fields

With the development of economy, the progress of science and technology, endless new things. Innovation of science and technology but also promote the progress of the society and the times. The introduction of new technology and new things, but also for the development of brick crushing machine, in this case, a single stage gold ore crusher manufacturer to keep pace with the times and synchronized with the domestic and foreign advanced technology, the R amp; D investment money and energy, steadfast unremitting research a single-stage single segment hammer type higher quality the crushing machine, has become the latest help motive force to promote the new development of infrastructure construction.

Single stage gold ore crusher manufacturer single-stage gold ore crusher more intelligent automation, has the ability of automatic detection and automatic alarm mechanism, so monotonous maintenance burden of people is greatly reduced; the single stage gold ore crusher manufacturer single-stage single stage gold ore crusher manufacturing processed stone grain shape is a cube, very good meet the infrastructure construction of stone strictly demand; single stage gold ore crusher manufacturer single-stage gold ore crusher is reinforced by the concept of environmental protection, increase the variety of environmental protection equipment, very conducive to environmental protection.

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
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.

Prove the following using mathematical induction

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

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 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.
Solve equation

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

Find y(1) if

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

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

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

Show that for any positive continuous function f on [0, a]

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

Find the value of abc if a+b+c=0 and

$a^3+b^3+c^3 =216$

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