spherical cell with a 5 um radius "decides" to double its surface area so that it can increase its rate of nutrient import. A) If the cell were to remain spherical while doubling its surface area, what would be the net percent change in its surface area to volume ratio? (show calculations) B) If the cell were to change its shape to a cylinder with a radius of 5 um after doubling its surface area, what would be the

If the rate of change of the length of the short side of a rectangle is 0.5 br/sec, and the length of the short side is 2 br, what is the rate of change in the area of a rectangle whose long side is four times its short side?

The radius of a balloon is increasing at the rate of 10cm/sec. At what rate is the surface area of the balloon increasing when the radius is 15cm.

An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 3 cm, and the height is 11 cm. Find the rate at which the water level is rising when the water level is 2 cm. cm/sec h b₁ b₂

H.W. 1) Calculate the volume of cylinder has 15 m height and 8 m diameter. 2) If we have other cylinder with the same height but it volume greater than first cylinder by 20%, how long its radius? 3) Write a program to calculate the volumetric and mass flow rate of a liquid flowing in a pipe with a velocity equal to 0.5 m/s. Knowing that the diameter of this pipe is 0.1 m and the density of this liquid is 890 kg/m³ ? 4) For the following distillation column write a code to find the value of stream B and the compositions of stream D? D=80 X% ? S%? T%? Z% ? F=100kg 15% X 25% S 40% T 20% Z B=? 15% X 25% S 40% T 20% Z 9 5) Compute the reaction rate constant for a first-order reaction given by the -E/RT Arrhenius law k = A e at a temperature T = 500 K. Here the activation energy is E=20 kcal/mol and the pre-exponential factor is A=10¹3 s¹. The ideal gas constant is R=1.987 cal/mol K.

find the diameter of the cone with a volume of 489.84 cubic meters

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