The equation for the reaction of iron and oxygen gas to form rust $\left(\mathrm{Fe}_2 \mathrm{O}_3\right)$ is written as

$$4 \mathrm{Fe}(s)+3 \mathrm{O}_2(g) \longrightarrow 2 \mathrm{Fe}_2 \mathrm{O}_3(s) \quad \Delta H=-1.7 \times 10^3 \mathrm{~kJ}$$

How many grams of rust form when 150 kJ are released?

Simplify the expression. If necessary, think of moves along a number line. 1 + (-1)

The reaction

$$2 \mathrm { Fe } _ { 2 } \mathrm { O } _ { 3 } ( s ) + 3 \mathrm { C } ( s ) \longrightarrow 4 \mathrm { Fe } ( s ) + 3 \mathrm { CO } _ { 2 } ( g )$$

is involved in the smelting of iron. Use

$$\Delta H _ { f }$$

values given in Appendix Table B–14 to calculate the enthalpy change during the production of 1 mol of iron.

Simplify the given expression to one of the three primary trigonometric functions, $\sin x, \cos x$, or $\tan x$.

$$\dfrac{\sec ^2 x \cos x}{\csc x}$$

Do you think one person tan make a difference when it comes to saving earth's resources? Explain.

Humid air at $75 \mathrm{~psia}$ and $500^{\circ} \mathrm{F}$ and a humidity ratio of $0.018 \mathrm{~lbm} \mathrm{H}_{2} \mathrm{O} / \mathrm{lbm}$ dry air is expanded to $15 \mathrm{~psia}$ in an isentropic nozzle. How much of the initial water vapor has been converted to liquid water at the nozzle outlet?

Billions of neutrinos continually pass through each square centimeter of your body each second. Why don’t you notice them?

State the first term of each product. a. $(2 x+1)(3 x+4)$ b. $\left(x^{4}+x^{2}\right)\left(3 x^{8}+x^{11}\right)$ c. $x(x+9)$ d. $\left(x^{2}+9\right)(3 x+4)(2 x+6)$ e. $\left(x^{3}+4\right)\left(x^{2}+6\right)(x+5)$

For the given problem, determine the equations of the polynomials of degree two whose graphs pass through the given points.

$$(-1,-1),(0,1),(1,-3)$$

Determine the value of $y$ when $x=3.$

Evaluate by using the order of operation: $(2^2+8)\div 4-2$

In a right triangle, the measure of one acute angle is twice the sum of the measure of the other acute angle and 30. Find the measure of each acute angle in the right triangle.

How many neutrons are in an atom with each set of atomic numbers and mass numbers?

Turpentine at $77^{\circ} \mathrm{F}$ is flowing from $\mathrm{A}$ to $\mathrm{B}$ in a $3$ -in coated ductile iron pipe. Point $\mathrm{B}$ is $20\ \mathrm{ft}$ higher than point $\mathrm{A}$ and the total length of the pipe is $60\ \mathrm{ft}$. Two $90^{\circ}$ long-radius clbows are installed between $\mathrm{A}$ and $\mathrm{B}$. Determine the volume flow rate of turpentine if the pressure at $\mathrm{A}$ is $120$ psig and the pressure at $B$ is $105$ psig.

For the following exercise,

Simplify the expression.

$$\frac{\tan \left(\frac{1}{2} x\right)+\tan \left(\frac{1}{8} x\right)}{1-\tan \left(\frac{1}{8} x\right) \tan \left(\frac{1}{2} x\right)}$$