Answer:
x = 4 and y = - 5
Step-by-step explanation:
note that the product of a complex number and it's conjugate is real
That is
(a + bi)(a - bi) where a, b are real
= a² - abi + abi - b²i²
= a² + b² ← a real number
For (4 + 5i)(x + yi) to be real
we require (x + yi) to be the conjugate of 4 + 5i , that is 4 - 5i
(4 + 5i)(4 - 5i) ⇒ x = 4 and y = - 5
21 cars, 32 motorcycles.create a system of equations using x for cars and y for motorcycles.

multiply the top equation by 2 to prepare for elimination method

subtract terms

divide both sides by negative 2 to solve for x
x =21
plug in x into original equation to solve for y.
21 + y = 53
subtract both sides by 21
y=32
Answer:
The file contains the solution to the question
Answer:
<em>The mass of the steel ball is 4,235.9 gr</em>
Step-by-step explanation:
<u>Density</u>
The density ρ of a substance is a measure of its mass per unit volume:

If the density and the volume are given, the mass can be calculated by solving the above formula for m:

We know the density of pure steel ρ=8.09 gr/cm3 and the diameter of a solid steel ball d=10 cm.
We need to calculate the volume of the sphere:
The volume of a sphere of radius r is given by:

The radius is half the diameter: r= 10/2 = 5 cm. Thus:

Calculating:

The mass is:

m=4,235.9 gr
The mass of the steel ball is 4,235.9 gr