The volume of a sphere is given by the equation

$$V = \frac { 1 } { 6 \sqrt { \pi } } S ^ { 3 / 2 }$$

, where S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meters. Use 3.14 for

$$\pi$$

.

The mean and standard deviation of the 69 individual average acceleration measurements over the 6-meter distance were 2.962 and .529 meters per second, respectively. a. Find a 95% confidence interval for this population mean. Interpret the interval. b. Suppose you were dissatisfied with the width of this confidence interval and wanted to cut the interval in half by increasing the sample size. How many skaters (total) would have to be included in the study?

The density of an object is the ratio of its mass to its volume. Neptune has a mass of

$$1.02\times 10^{26} kg.$$

The radius of Neptune is

$$2.48\times 10^4 km.$$

What is the density of Neptune in grams per cubic meter? (Hint:

$$V = \frac { 4 } { 3 } \pi r ^ { 3 } )$$

Escribe órdenes directas. Usa la lista de tareas. Lista de tareas parahoy Juan: Analizar el meteorito. Laura: Sustituir el telescopio, Carlos: Ver los resultados del laboratorio. José: Buscar las fotos de la galaxia X. Ana: Meter los datos en la computaciora. Marta: Imprimir las fotos cle la Luna. Laura, avísame __________.

Find the volume of the sphere with the given surface area. Surface area: 16π ft²

A hypothetical metal is known to have an electrical resistivity of $4 \times 10^{-8}(\Omega \cdot \mathrm{m})$. Through a specimen of this metal that is 25 mm thick is passed a current of 30A; when a magnetic field of 0.75 tesla is simultaneously imposed in a direction perpendicular to that of the current, a Hall voltage of $-1.26 \times$ $10^{-7} \mathrm{~V}$ is measured. Compute

(a) the electron mobility for this metal and

(b) the number of free electrons per cubic meter.

The first real length standard, adopted more than 200 years ago, was a platinum bar with two very fine marks separated by what was defined to be exactly one meter. If this standard bar was to be accurate to within $\pm 1.0 \mu \mathrm{m}$, how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion is $9 \times 10^{-6} / \mathrm{C}^{\circ}$.

A 2.0 kg particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by x=3.0 m + (4.0 m/s) t+c t raised to 2 - (2.0 meter/second cube) t raised to 3 with x in meters and t in seconds. The factor c is a constant. At t=3.0 s, the force on the particle has a magnitude of 36N and is in the negative direction of the axis. What is c ?

Jaylen is collecting seashells on a beach at the ocean. He is throwing some of the seashells back into the ocean. He is standing at the origin of a coordinate plane and the shoreline is represented by the graph of the line y = 1.5x + 13. Each unit represents 1 meter. How far does Jaylen need to be able to throw the seashell to throw it into the ocean? Round your answer to the nearest centimeter.

Escribe órdenes directas. Usa la lista de tareas. Lista de tareas parahoy Juan: Analizar el meteorito. Laura: Sustituir el telescopio, Carlos: Ver los resultados del laboratorio. José: Buscar las fotos de la galaxia X. Ana: Meter los datos en la computaciora. Marta: Imprimir las fotos cle la Luna. Marta, enséñame las fotos __________.

Escribe órdenes directas. Usa la lista de tareas. Lista de tareas parahoy Juan: Analizar el meteorito. Laura: Sustituir el telescopio, Carlos: Ver los resultados del laboratorio. José: Buscar las fotos de la galaxia X. Ana: Meter los datos en la computaciora. Marta: Imprimir las fotos cle la Luna. José, llama a Ana __________.

A person moves from the origin along the positive y-axis pulling a weight at the end of a 12-meter rope. Initially, the weight is located at the point (12, 0).

In the indicated exercise, it was shown that the path of the weight is modeled by the rectangular equation

$$y=-12 \ln \frac{12-\sqrt{144-x^2}}{x}-\sqrt{144-x^2}$$

where $0<x \leq 12$. Use a graphing utility to graph the rectangular equation.

A person moves from the origin along the positive y-axis pulling a weight at the end of a 12-meter rope. Initially, the weight is located at the point (12,0).

In the earlier exercise, it was shown that the path of the weight is modeled by the rectangular equation

$$y=-12 \ln \left(\frac{12-\sqrt{144-x^2}}{x}\right)-\sqrt{144-x^2}$$

where $0<x \leq 1$. Use a graphing utility to graph the rectangular equation.

Suppose a person throws a ball upward at a velocity of 16 m/sec from the top of a 20-meter-tall building.

a. Write an equation to describe the height of the ball above the ground after t seconds.

b. How high is the ball after 0.75 second?

c. Use a graph to estimate the ball's maximum height.

d. After 6 seconds, is the ball above or below ground level? Justify your answer.