Final answer:
- a. The Java expression "dm = m * (√(1 + v / c) / √(1 - v / c) - 1)" can be written in mathematical notation as: dm = m * (√(1 + v/c) / √(1 - v/c) - 1)
- b. The Java expression "volume = π * r * r * h" can be written in mathematical notation as: volume = π * r² * h
- c. The Java expression "volume = 4 * π * pow(r, 3) / 3" can be written in mathematical notation as: volume = (4/3) * π * r³
- d. The Java expression "z = √(x * x + y * y)" can be written in mathematical notation as: z = √(x² + y²)
Step-by-step explanation:
a. The Java expression 'dm = m * (√(1 + v / c) / √(1 - v / c) - 1)' can be written in mathematical notation as: dm = m * (√(1 + v/c) / √(1 - v/c) - 1). In this expression, dm represents the change in mass, m represents the initial mass of an object, v represents the velocity of the object, and c represents the speed of light.
b. The Java expression 'volume = π * r * r * h' can be written in mathematical notation as: volume = π * r² * h. In this expression, volume represents the volume of a cylinder, r represents the radius of the cylinder, and h represents the height of the cylinder.
c. The Java expression 'volume = 4 * π * pow(r, 3) / 3' can be written in mathematical notation as: volume = (4/3) * π * r³. In this expression, volume represents the volume of a sphere, r represents the radius of the sphere, and π represents the mathematical constant pi.
d. The Java expression 'z = √(x * x + y * y)' can be written in mathematical notation as: z = √(x² + y²). In this expression, z represents the hypotenuse of a right triangle, x represents the length of one side of the triangle, and y represents the length of another side of the triangle.