I just want to know one divergent formula

In summary, a divergent formula is a mathematical expression that results in values that increase or decrease without bound as the input values approach a certain value or infinity. This is different from a convergent formula, which results in values that approach a specific limit or value. Some examples of divergent formulas include the harmonic series and geometric series. These formulas are important in science as they can help us understand natural phenomena and can be applied in various fields such as finance, physics, and biology.
  • #1
justone
1
0
Hello. I asked my professor and he couldn't figure it out. If train A and B leave the same point at the same time, A traveling 60mph, B traveling 75mph, how long will it take for B to have traveled twice as far as A?
 
Mathematics news on Phys.org
  • #2
justone said:
Hello. I asked my professor and he couldn't figure it out. If train A and B leave the same point at the same time, A traveling 60mph, B traveling 75mph, how long will it take for B to have traveled twice as far as A?

Train B is traveling 5/4 as fast as train A. If they depart at the same time, then train B will always have traveled 5/4 as far as train B...there is no point in time (where $0<t$) for which train B will have traveled twice as far as train A.

I am going to move this thread to our algebra forum, as that is a better fit.
 
  • #3
Recall that $d=st$, where $d$ is distance, $s$ is speed and $t$ is time.

With the speeds of train A and train B denoted as $s_1$ and $s_2$ respectively, we must have

$s_2t=2s_1t\implies s_2=2s_1$, but this is clearly not true.
 

1. What is a divergent formula?

A divergent formula is a mathematical expression that results in values that increase or decrease without bound as the input values approach a certain value or infinity. This means that the output values become increasingly larger or smaller, never reaching a specific limit or value.

2. How is a divergent formula different from a convergent formula?

A convergent formula is a mathematical expression that results in values that approach a specific limit or value as the input values approach a certain value or infinity. This means that the output values become closer and closer to a specific value, never exceeding it. In contrast, a divergent formula does not have a specific limit or value that the output values approach, but rather, they continue to increase or decrease without bound.

3. What are some examples of divergent formulas?

Some examples of divergent formulas include the harmonic series, which is given by the expression 1 + 1/2 + 1/3 + 1/4 + ..., and the geometric series, which is given by the expression 1 + 2 + 4 + 8 + .... Both of these series result in values that increase without bound as more terms are added.

4. Why are divergent formulas important in science?

Divergent formulas are important in science because they can help us understand natural phenomena that do not have a specific limit or value. For example, the concept of infinite growth or decay is often described using divergent formulas. Additionally, divergent formulas can also be used in scientific models to represent complex systems that do not have a specific end point or equilibrium.

5. Are there any real-world applications of divergent formulas?

Yes, there are many real-world applications of divergent formulas. For example, in finance, divergent formulas can be used to model compound interest, which results in values that increase without bound over time. In physics, divergent formulas are used to describe phenomena such as the expansion of the universe and the behavior of black holes. In biology, divergent formulas can be used to model population growth and the spread of diseases.

Similar threads

Replies
4
Views
824
Replies
3
Views
1K
Replies
33
Views
2K
Replies
2
Views
1K
  • General Math
Replies
8
Views
2K
Replies
7
Views
1K
  • General Math
Replies
5
Views
2K
Replies
3
Views
520
Replies
3
Views
950
Replies
26
Views
2K
Back
Top