LambLamb

Probably looks like this: \(\frac{\sqrt{23}}{3}\)

Just put 23/9 in fraction form and square root the top and bottom separately.

There are no whole numbers that desribe a ratio that exactly equals sqrt(23/9) since it is an irrational number, so you must use sqrt(23) on top, and of courae sqrt(9) is just 3.

Hope this helps. -LambLamb

Thanks so much, CPhill! I forgot about completing the square. I appreciate your response!

Thank you so much, guest!

Thank you so much, Melody. This answer is perfect. I forgot to mention the altitude remains constant and dx/dt is in fact -600km/h, but you safely assumed those.

Together they work at 2/3 + 1 = 5/3 cars/hour, so they will completley wash 5/3 * 12 hours = 20 cars.

Since Jauncho can wash 2/3 cars per hour, it will take him 20 / (2/3) hours to complete the task.

2/3 cars/hour + 1 car/hour = 5/3 cars per hour

12 hours * 5/3 cars/hour = 20 cars

20 cars * 1 hour/car = 20 hours.

It will take Jauncho 20 hours to complete the task by himself.

*My original post had an error, but this one fixed it*

This original post had an error so I fixed it in a later post.

66% APR is a lot! Are you sure that's what you need to compute?

What you have there is a finite geometric series.

The difference between the infinite sum of this geometric series and each consecutive partial sum has a ratio of 0.5, so you would take the infinite sum and subtract \({\frac{1}{2}}^{10}\).

The infinite sum is equal to exactly 1, and (1/2)^10 is equal to 1/1024, so the answer is

1023/1024.

The infinite sum is calculated by taking an analogous infinite sum (0.5)^0 + (0.5)^1 + (0.5)^2 + (0.5)^3 ... using the formula 1/(1-r) which the ratio is 0.5,  making the sum equal to 1/0.5 = 2, then subtracting the first term (1) because it is not in the original finite geometric series.

Then by looking at partial sums, 0.5, 0.75, 0.875, etc, you can see the ratio between the difference of 1 and each consecutive partial sum is 0.5, so you can conclude 1 - (0.5)^10 will be the right answer.

Certainly not the most mathematically pure approach, but it works.

So it _was_ too easy.

In terms of imaginary and/or complex numbers, 5i means 5 times the square root of negative one.

\(5i = 5\sqrt{-1}\)

Although it could be a variable in physics, especially with certain coordinate systems.

If you could specify the context of " 5i ", we could help you more, but I hope this was helpful!

-LambLamb

Slope is the change in  y  over the change in  x  if that is useful.

You can just use the karat and then type 3

If you wanted to raise 8 to the third power, you would od something like this:

8^3

Hope this was helpful!

Its even worse when that day is your birthday. I haven't been that mad since my last birthday.

64 plus negative 22 = 42

Adding a negative is the same as subtracting.

Hope this was helpful!

Type 2/3 into the calculator (or if you're brave and have pencil and paper, you can long divide)

2/3 = 0.666666...

Hey that's my profile picture!!!

\(\sqrt{10}\) is the number, that when multiplied by itself, results in 10.

It can be negative or positive. In decimal, it is ± 3.1622776601683793 and it's continued fraction expansion is 3;6,6,6,6, ...

I hope this was helpful!

Happy belated birthday Hayley!!

@Hayley1, I addressed it.