(a) use a graphing utility to graph the plane region bounded by the graphs of the equations, and (b) use the integration capabilities of the graphing utility to approximate the volume of the solid generated by revolving the region about the y-axis. y = √1 - x³, y=0, x=0

Find the degree measure of the angle with the given radian measure.

$$- \frac { 3 \pi } { 2 }$$

Find the exact location of all the relative and absolute extrema of each function. $f(x)=x^{4}-4 x^{3}$ with domain $[-1,+\infty)$

Two particles oscillate in simple harmonic motion along a common straight-line segment of length A. Each particle has a period of 1.5 seconds, but they differ in phase by $\pi/6 \text{~rad}$. How far apart are they (in terms of A) 0.50 seconds after the lagging particle leaves one end of the path?

determine the null and alternative hypotheses. According to the CTIA-The Wireless Association, the mean monthly revenue per cell phone was $48.79 in 2014. A researcher suspects the mean monthly revenue per cell phone is different today.

If confined at high temper at ur e, ammonia and oxygen quickly react and com e to equilibrium with their product s, water vapor and nit rogen oxide . Write a balanced chemical equation and an equilibrium express ion for this system.

Make an appropriate u-substitution, and then use the Endpaper Integral Table to evaluate the integral.

$$\int e ^ { - \sqrt { x } } d x$$

Identify the type of conic. Find the center, vertices, and foci of the conic, and sketch its graph.

$$\dfrac{y^2}{16}-\dfrac{x^2}{49}=1$$

The potential energy of a one-degree-of-freedom system is defined by $V=\left(20 x^{3}-10 x^{2}-25 x-10\right) \mathrm{ft} \cdot \mathrm{lb}$, where x is in ft. Determine the equilibrium positions and investigate the stability for each position.

Ms. Hernandez determined that 60% of the students in her classes brought an umbrella to school when the weather forecast predicted rain. If she has a total of 150 students, which statement does not represent Ms. Hernandez's data? (f) On days when rain is forecasted, less than 2/5 of her students bring an umbrella to school. (g) On days when rain is forecasted, 90 of her students bring an umbrella to school. (h) On days when rain is forecasted, more than ½ of her students bring an umbrella to school. (i) On days when rain is forecasted, 60 of her students do not bring an umbrella to school.

Identify the growth and development methods of mosses. Explain why these are advantageous in their environments.

Order the numbers from least to greatest.

$$\sqrt { 220 } , - 10 , \sqrt { 100 } , 11.5$$

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Sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral (a > 0, r > 0).∫_0^8 [x/4 dx]

Without using a calculator, find all the complex roots of each equation.

$$x^4 - 2x³ - x² - 4x - 6 = 0$$