That's a very important thing to know.
The equation for the circle, if you put the circle at the origin, is x^2 + y^2 = r^2 which is the radius.
That is exactly the same thing as the pythagorean theorem.
Now when you shift the circle so that it has a new center, you are using the distance formula to describe the radius. Notice the radius in the formula is unchanged no matter where a and b are. Wherever they are the radius will follow. You've just shifted your location. That's all. The distance formula just takes into account where the two points are (x,y) and (a,b) where a,b is the center. I say again, the distance formula really is pythagoras. And the circle is really pythagoras.
It's a special application of the pythagorean theorem. The Greeks, who developed a^2 + b^2 = c^2, knew nothing about a grid. It took almost 2000 years for that to become clear.
The darkened bold part is the answer. It is the connection between the circle and pythagoras. The bridge from one to the other is the distance formula.
Answer:
no solution
Step-by-step explanation:
One then because we are adding
Some periodic motions, also known as armonic motions, with which much of us are familiar with are:
- The motion of the swinger when a kid is balancing forward and backward
- The motion of a pendulum
- The motion of the needles of a watch.
- The motion of a satelite around a planet.
- The spinning of the wheel of a stationary bycicle.
- A rocking chair
All the motions in which the object passes once and other times through the same point are periodic motions.
Both scientists and businesses are interested in tracking periodic motions using equations because they appear in many situations in nature and in daily life. The cycles are examples of periodic motion. By tracking this type of motion you can make models that permit you to explain the phenomena and predict cycles. This is predict facts that repeast with a certain period.