Use Stokes’ Theorem to evaluate

$$\mathbf{F}(x,y,z)=(x+y^2-2)\mathbf{i}+2xy\mathbf{j}+(x^2+yz^2)\mathbf{k};$$

S is the part of the paraboloid z = 4 - x squared - y squared above the xy-plane with an outward normal

Draw structures for the following: (a) 2,4-Dinitrophenol (b) m-Ethylphenol

Bird Migration Power P is the rate at which energy E is consumed per unit time. Ornithologists have found that the power consumed by a certain pigeon flying at velocity $v \mathrm{~m} / \mathrm{s}$ is described well by the function $P(v)=17 v^{-1}+10^{-3} v^3 \mathrm{~J} / \mathrm{s}$. Assume that the pigeon can store $5 \times 10^4 \mathrm{~J}$ of usable energy as body fat. (a) Find the velocity $v_{\text {pmin }}$ that minimizes power consumption.

At what value of x does the quadratic function $f(x)=a x^{2}+b x+c, a \neq 0,$ have a stationary point? Under what conditions is the stationary point a local maximum or a local minimum?

Approximately how many oxygen molecules arrive each second at the mitochondrion of an active person with a mass of $84 \mathrm{~kg}$ ? The following data are available: Oxygen consumption is about $40 . \mathrm{mL}$ of $\mathrm{O}_2$ per minute per kilogram of body weight, measured at $T=300 .\ \mathrm{K}$ and $P=1.00 \mathrm{~atm}$. In an adult there are about $1.6 \times 10^{10}$ cells per kg body mass. Each cell contains about 800 . mitochondria.

The wattage of an appliance indicates the average power consumption in watts $(W)$, where $1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}$. What is the difference in the number of $\mathrm{kJ}$ of energy consumed per month between a refrigeration unit that consumes $625 \mathrm{~W}$ and one that consumes $855 \mathrm{~W}$ ? If electricity costs $\$ 0.15$ per $\mathrm{kWh}$, what is the monthly cost difference to operate the two refrigerators? (Assume $30.0$ days in one month and $24.0$ hours per day.)

Infection that weakens the heart muscle is called _______.

A sample of 250 observations is selected from a normal population for which the population standard deviation is known to be 25. The sample mean is 20. a. Determine the standard error of the mean. b. Explain why we can use formula to determine the 95 percent confidence interval. c. Determine the 95 percent confidence interval for the population mean

Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply.) -4

What is the product of two squared and two to the sixth power? express using exponents.

How is economic growth measured? Why is economic growth important? Why could the difference between a $2.5$ percent and a $3$ percent annual growth rate be of great significance over several decades?

Write the rational number as a decimal. Then tell whether the decimal is a terminating or a repeating decimal.

$$\frac{4}{12}=$$

Identify and describe two muscle tissues.

Find the molar solubility of SrCO3 (Ksp = 5.4 $\times$ 10 - 10) in pure water