A spherical fish tank of radius 8 meters is being filled with at a constant rate of Rπ meters cube of water per second. At height 3 meters, the rate of change of the height is 1 meter per second. What is the value of R?
Let V be the volume of the three-dimensional structure bounded by the region 0≤z≤1−x^2−y^2. If V=a/bπ, where a and b are positive coprime integers, what is a+b?
Let R be the region bounded by y=−3(x−1)(x−3) and the x-axis. Let S be the solid obtained by rotating R about the y-axis. The volume of S is given by Nπ. What is the value of N?
There are two points P=(a,a^2) and Q=(b,b^2) (a<b) moving along the parabola y=x^2. If the area of the region bounded by y=x^2 and the line segment PQ is always 36, what is the value of lim as a→∞ of PQ/a?
A metal crystallizes in a face-centered lattice. The radius of the atom is 198pm and the density of the element is 6.57g/cm^3. What is the identify of the metal?
Bulb A is 100 mL and contains Helium at 1 atm. Bulb B is 500 mL and contains Argon at 2 atm. The bulbs are connected together by a valve. What is the pressure of gas A after the valves are opened? (assume constant temperature)
What will be the final volume of a 425 mL sample of gas initially at 22 degrees C and 1 atm pressure when the temperature is changed to 30 degrees C and the pressure to 0.471 atm?
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Angle P and Q are a linear pair. Angle Q is 36 degree less than twice of angle P. The measure of angle P is ? degree, and the measure angle Q is ? degree.