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.
Answer:
Consider lining up all the blue marbles and placing one red marble in between them. Let that arrangement be fixed. The remaining red marbles will be 5 red marbles. Note that the arrangement will be:
x BR x BR x BR x BR x BR x BR x BR x B x
Note that this is the same even if our arrangement is
x B x RB x RB x RB x RB x RB x RB x RB x
Note that there are 9 spots, denoted by x, where we can put the 5 remaining red marbles. To find the number of ways of putting the remaining 5 red marbles to x, it is similar in finding the number of non-negative solution for the equation
which is given by
= 1287
Hence, there are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.
Answer:
Yes, Holmes is correct.
Step-by-step explanation:
Let's separate each statement of Holmes: (they are all true)
- If Mrs. Smith is lying then Moriarty has not escaped.
- Either Moriarty is dead or he is really Jones.
- If Moriarty is really Jones then he has escaped.
- I am convinced Mrs. Smith is lying.
If we start with the last one, we know that Mrs. Smith is lying. That takes us to the first one, Mrs. Smith IS lying, so Moriarty has not escaped.
If we look the second one, either Moriarty is dead or he is really Jones.
If he is really Jones, that takes us to the third statement that says that Moriarty has escaped. But we know from the first statement that he hasn't escaped, so he can't be Jones.
So, going back to the second statement, Moriarty is dead.
Lets solve the quadratic equation:
<span>7x^2 + 2x = 0
(x)(7x + 2) = 0
therefore, for this equation to hold we need, either one of these conditions:
x = 0
or
7x + 2 = 0
from where:
7x = -2
x = -2/7
then, we have two solutions for the equation as expected being quadratic.</span>