Find a function y=f(x) that satisfies both conditions: $\frac{d y}{d x}=3 x^{-1}-x^{-2} \quad f(1)=5$

A person standing 1.00 m from a portable speaker hears its sound at an intensity of $7.50 \times 10^{-3} \mathrm{W} / \mathrm{m}^{2}$. Find the corresponding decibel level.

Assume that the random variable Z is described by a standard normal curve $f_{Z}(z)$. For what values of z are the following statements true? (a) $P(Z \leq z)=0.33$ (b) $P(Z \geq z)=0.2236$ (c) $P(-1.00 \leq Z \leq z)=0.5004$ (d) $P(-z<Z<z)=0.80$ (e) $P(z \leq Z \leq 2.03)=0.15$

Find each indefinite integral. Check by differentiating. $\int 8 x d x$

Evaluate the integrals. $\int_{0}^{1} x e^{x^{2}} d x$

Three methods to dispose of nonhazardous waste have been developed-land application, fluidizedbed incineration, and private disposal contract. Use AW analysis and an associated scatter chart of AW versus i values to select the economically best alternative for interest rates between i = 6 % and i = 24% in 3% increments.

$$\begin{array}{lcc} \text{ } & \text{Land} & \text{Incineration} & \text{Contract}\\ \hline \text{First cost, \$} & \text{-150,000} & \text{-900,000} & \text{0}\\ \text{AOC, \$/year} & \text{-95,000} & \text{-60,000} & \text{-140,000}\\ \text{Salvage value, \$} & \text{25,000} & \text{300,000} & \text{0}\\ \text{Life, years} & \text{4} & \text{6} & \text{2}\\ \hline \end{array}$$

For each of the following functions, identify the x-intercepts (roots), y-intercept, horizontal asymptotes, vertical asymptotes, and the function's domain. (State DNE in cases when an intercept or asymptote does not exist.) Use this information to sketch a graph of the function. a. $a(x)=\frac{3}{x-7}$ b. $b(x)=\frac{x}{2 x+6}$ c. $d(x)=\frac{9 x}{3 x+3}$ d. $f(x)=\frac{-x+3}{2 x-1}$ e. $g(x)=\frac{9 x^{2}-144}{x^{2}-1}$ f. $h(x)=\frac{14 x}{3 x-4}$ g. $k(x)=\frac{x-11}{x^{2}-5 x+6}$ h. $P(x)=\frac{x(x+2)}{4 x+1}$ i. $q(x)=\frac{\left(x^{2}+2 x-3\right)}{x^{2}-1}$

Describe the radian measure between 0 and $2 \pi$ of an angle $\theta$ that is in standard position with a terminal side that lies in: Quadrant ll

Evaluate the given expressions. Compare the results to the fifth and sixth rows of Pascal's triangle. a.

$$\left(\begin{array}{l} 5 \\ 0 \end{array}\right)$$

b.

$$\left(\begin{array}{l} 5 \\ 1 \end{array}\right)$$

c.

$$\left(\begin{array}{l} 5 \\ 2 \end{array}\right)$$

d.

$$\left(\begin{array}{l} 5 \\ 3 \end{array}\right)$$

e.

$$\left(\begin{array}{l} 5 \\ 4 \end{array}\right)$$

f.

$$\left(\begin{array}{l} 5 \\ 5 \end{array}\right)$$

Scuba divers search for dive locations with good visibility, which can be affected by the murkiness of the water and the penetration of surface light. The table shows the percent of surface light reaching a diver at different depths as the diver descends. $$ \begin{matrix} \text{Depth (ft)} & \text{Light (\\%)}\\ \text{15} & \text{89.2}\\ \text{30} & \text{79.6}\\ \text{45} & \text{71.0}\\ \text{60} & \text{63.3}\\ \text{75} & \text{56.5}\\ \text{90} & \text{50.4}\\ \text{105} & \text{44.9}\\ \text{120} & \text{40.1}\\ \end{matrix} $$ Use the graph of your regression equation to approximate the percent-of surface light that reaches the driver at a depth of 83 feet.

Graph each function using a graphing calculator, and apply the horizontal line test to determine whether its inverse function exists. Write yes or no. $f(x)=-\frac{3}{x 6}$

A recent study showed that the number of Australian homes with a computer doubles every 8 months. Assuming that the number is increasing continuously, at approximately what monthly rate must the number of Australian computer owners be increasing for this to be true? A. 6.8%. B. 8.66%. C. 12.5%. D. 8.0%. E. 2%

Using techniques from calculus, we can show that $(1+x)^{n}=1+n x+\frac{n(n-1) x^{2}}{2 !}+\frac{n(n-1)(n-2)}{3 !} x^{3}+ \cdots, \text { for }|x|<1.$ This formula can be used to evaluate binomial expressions raised to noninteger exponents. For this exercise, use the first four terms of this infinite series to approximate the given expression. Round to 3 decimal places if necessary. $(1.4)^{3 / 2}$

Sketch each angle. than find its reference angle. $\frac{13 \pi}{6}$