Air enclosed in a sphere has density $\rho = 1.4 \mathrm { kg } / \mathrm { m } ^ { 3 }$. What will the density be if the radius of the sphere is halved, compressing the air within?

$\text{\red{Apply Concepts}}$ If every married couple in a country were to decide to have only one child, what would happen to the country’s population growth?

An object is placed to the left of a lens, and a real image is formed to the right of the lens. The image is inverted relative to the object and is one-half the size of the object.

What kind of lens, converging or diverging, is used to produce this image?

A $0.40-\mathrm{kg}$ object is attached to a spring with force constant $160 \mathrm{~N} / \mathrm{m}$ so that the object is allowed to move on a horizontal frictionless surface. The object is released from rest when the spring is compressed $0.15 \mathrm{~m}$. Find (a) the force on the object and

Does the buoyant force on a floating object depend on the weight of the object itself or on the weight of the fluid displaced by the object? Or are these both the same for the special case of floating?

Find the values of the six trigonometric functions of an angle $\theta$ in standard position with point $P(-3,4)$ on the terminal side of the angle.

Use the Limit Comparison Test to determine whether each series converges or diverges. $\sum_{k=1}^{\infty} \frac{k+5}{k^{k+1}}$

ls it possible for an object to have an acceleration when the velocity of the object is constant? When the speed of the object is constant? In each case, give your reasoning.

Perform the indicated addition or subtraction. (-8 + 4i) - (7 - i)

Write the opposite of 22.

Read the definitions below, then write the key term for each one in the column. ____ states that when one object exerts a force·on a second object, the second object exerts a force on the first that is equal in strength and opposite in direction. ____ is the tendency of an object to resist any change in its motion. ____ "The acceleration of an object is in the same direction as the net force on the object, and the acceleration can be calculated from the equation $a=F_{\text {net }} / m$

Someone might claim that air is not matter because you can’t see it. Write a paragraph showing how you would prove to this person that air is matter.

Find and draw an object (or part of an object) that can be modeled by a triangle and an exterior angle. Describe the relationship between the interior angles of the triangle and the exterior angle in terms of the object.

Determine whether the following series converge. Justify your answers. $\sum_{k=3}^{\infty} \frac{(-1)^{k} \ln k}{k^{1 / 3}}$