Use the Law of Cosines to solve the triangle. $C=108^{\circ}, \quad a=10, \quad b=7$

Use the RK4 method with $h=0.1$ to obtain a four-decimal approximation to the indicated value. $y^{\prime}=e^{-y}, \quad y(0)=0 ; y(0.5)$

A bar of a steel alloy that exhibits the stress strain behavior is subjected to a tensile load; the specimen is 375 mm (14.8 in.) long and has a square cross section 5.5 mm (0.22 in.) on a side. (a) Compute the magnitude of the load necessary to produce an elongation of 2.25 mm (0.088 in.). (b) What will be the deformation after the load has been released?

You roll a number cube. Tell whether the events are disjoint or overlapping Then find P(A or B). Event A: Roll an odd number. Event B: Roll a 1.

Evaluate or simplify the expression. Tell which properties of exponents you used.

$$(x^2/y^-2)^{-4}$$

The equilibrium constant for the reaction

$$NH 3(g) + HCl(g) ↔NH 4Cl(s)$$

at 340°C is K = 4.0. (a) If the partial pressure of ammonia is Pnh = 0.80 arm and solid ammonium chloride is present, what is the equilibrium partial pressure of hydrogen chloride at 340°C? (b) An excess of solid NH4Cl is added to a container filled with ammon ia at 340°C and a pressure of 1.50 arm. Calculate the pressures of NH3(g) and HCl(g) reached at equilibrium.

Identify the slope and y-intercept of the line with the given equation. Use the slope and y-intercept to graph the equation. 3x + y = -1

Give an example of dependent events.

Sketch the graphs of the quadratic functions, indicating the coordinates of the vertex, the y-intercept, and the x-intercepts (if any). $f(x)=x^{2}+2 x+1$

Evaluate the expression for the given value of x.

$$27 - \sqrt { x }$$

when x = 81

Find each value of $c$ for which the matrix is not invertible.

$$\begin{equation*}\begin{bmatrix}c&&9\\4&&c\end{bmatrix}\end{equation*}$$

Graph each function. State the domain and range.

$$f ( x ) = - \sqrt { 6 x }$$

For a cylindrical metal specimen loaded in tension to fracture, given a set of load and corresponding length data, as well as the predeformation diameter and length, generate a spreadsheet that allows the user to plot (a) engineering stress versus engineering strain, and (b) true stress versus true strain to the point of necking.

Evaluate the following limits.

$$\lim _ { x \rightarrow 0 } \frac { e ^ { x } - x - 1 } { 5 x ^ { 2 } }$$