Are our concepts limited in principle by our everyday experiences or is this only our conceptual starting point? How is this question related to a resolution of the wave-particle duality?

Examine $f(w, z)=w^{3}+z^{3}-3 w z+5$ for relative extrema.

Express the quantity as a single logarithm. $\ln (a+b)+\ln (a-b)-2 \ln c$

What were Keynes's three conjectures about the consumption function?

What does the Squeeze Theorem say?

Explain how implicit differentiation works.

Find the absolute extrema of the given function on the given interval. $f(x)=\frac{1}{3} x^{3}+\frac{1}{2} x^{2}-2 x+1,[-1,0]$

For what values of does the function $y=e^{r x}$ satisfy the equation $y^{\prime \prime}+6 y^{\prime}+8 y=0 ?$

Two barrels filled with sand are similar in shape. The smaller barrel has a height of 4 feet and a volume of 4.5 cubic feet. The larger barrel has a height of 6 feet. What is the weight of the sand in the larger barrel? Round your answer to the nearest tenth. (One cubic foot of sand weighs about 110 pounds.)

Create the following arguments: Two invalid arguments, having the same form, about fast food.

The Cooper Cooler is a novel cooling device that rotates a cylindrical beverage can within a chilled environment in order to cool down the beverage. The correlation for convective heat transfer associated with the liquid film on the inside surfaces of a rotating can is given by (Anantheswaran and Rao, 1985)

$$\mathrm{Nu}=2.9 \mathrm{Re}^{0.436} \mathrm{Pr}^{0.287} \quad \text { with } \quad \mathrm{Re}=\frac{D_{\mathrm{r}}^{2} N \rho}{\mu}$$

where N is the rotation rate (rev/sec) and $D_{r}$ is the diameter of the rotating wheel. In the present process, the chilling chamber is kept constant at $0^{\circ} \mathrm{C}$. The convective heat-transfer coefficient on the outside surface of the can is estimated at $1000 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K},$ and the heat-transfer resistance through the metal can is considered negligible. If the can is 6 cm in diameter, 10 cm long, and $D_{\mathrm{r}} / 2$ is 12 cm, how long will it take to cool the contents of the can down to a refreshing $4^{\circ} \mathrm{C}$ if the beverage can is initially at $20^{\circ} \mathrm{C}$ and the wheel is rotated at 0.5 rev/s? It is assumed that the themophysical properties of water apply for the beverage.

Simplify each of the following, if possible. -(-6 + x)

Change the quality but not the quantity of the following categorical propositions: Some news media are not disseminators of accurate information.

An engineered tissue system consists of a flat plate of cell mass immobilized on a scaffold measuring 5 cm in length, and is 0.5 cm thick. The bottom face of the scaffold is exposed to water and organic nutrients. The top face is exposed to flowing $\mathrm{O}_{2}$ gas to provide $\mathrm{O}_{2}$ for aerobic respiration. At present the specific oxygen consumption of the tissue mass is 0.5 mmol $\mathrm{O}_{2} / \mathrm{cm}^{3}$ cells-hr, and from respiration energetics, the energy released by respiration is $468 \mathrm{J} / \mathrm{mmol} \ \mathrm{O}_{2}$ consumed. We are interested in using the flowing $\mathrm{O}_{2}$ gas at 1 atm to control the temperature at the surface of the tissue scaffold. The properties of $\mathrm{O}_{2}$ gas at 300 K are $\rho=1.3 \mathrm{kg} / \mathrm{m}^{3}, C_{\mathrm{P}}=920 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$, $\mu=2.06 \times 10^{-5} \mathrm{kg} / \mathrm{m}$ sec, and $k=0.027 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$. We are interested in determining the $\mathrm{O}_{2}$ flow rate necessary to keep the surface temperature within $10^{\circ} \mathrm{C}$ of the flowing gas temperature (i.e.. surface temperature below 310 K or $37^{\circ} \mathrm{C}$). a. What is the Prandtl number (Pr) for the flowing fluid? b. Based on the process energy balance and heat transfer, what is the required heat-transfer coefficient, h? c. What is the Nusselt number, Nu?