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Any function, no matter how crazy or nonlinear, looks like a straight line if you zoom in far enough. When you're looking at the value of a function at two points separated by an infinitesimal...

She could keep it relatively simple and write an equation showing that her ability to learn algebra is inversely proportional to the distance she sits from her old partner. For example,
S =...

Pready, that doesn't work very well unless you swap the numbers around. And since you can't say 99+916806 without losing the space between "number" and "99", I think the better way is to change...

Unfortunately I don't really know of any good research papers to point you to. :( The stuff I work on is very specific, so the papers I read wouldn't be very helpful for gaining g a general...

Order of operations says that you do the multiplication before addition/subtraction, so you get the equivalent formula:
16 + 16 + 4  16 = ?
I'm sure you can take it from there.

Excellent! I'm glad to hear he got it to work somewhat. If he just had access to an oscilloscope, he could figure out how to improve it. Still, fourth place is nothing to scoff at. Congratulations!

Actually, now that I went through all that, there's a much, much simpler way. For a circular arc, if you were to draw a line from the center at 16' (point of maximum deflection) to the edge at 0'...

First we need to compute the absolute deflection at the center of the beam.
Let's assume the beam sags in the shape of a circular chord (i.e. an arc). The maximum slope will be at the outer...

Cool idea!
According to the Wikipedia page, heavy water is 11% denser than regular water at 1.11g/mL. Meanwhile, ice at around 20C is around 8% less dense than regular 0C water at about 0.92...

It doesn't matter what direction the car goes; you're only interested in the distance it travels. Hence, you just need to use the simplest of formulas:
distance = rate x time

Since there are an infinite number of terms with ever increasing exponent, the only way the series can possibly converge is for each subsequent term to be smaller than the one before (in other words,...

I assume you accidentally missed the x^2 term?
Is this the question?
1x+x^2x^3+...=\sum_{n=0}^\infty (x)^n = \frac{1}{1+x+x^2}
Mod x? "Mod" to me mean modulo division, which doesn't...

\sum_{n=0}^\infty ar^n = b
Since the series converges, you know that r must lie between 1 and 1 (that's a precondition of convergence for a geometric series).
Given this condition, we know...

[Disregard this until you read my EDIT at the bottom]
You really need to ask this question in a new thread. These forums are made for people to be able to search at a later point in time. ...

\sum_{n=0}^\infty ar^n = b
Since the series converges, you know that r must lie between 1 and 1 (that's a precondition of convergence for a geometric series).
Given this condition, we know...

I think pretty much any acid will cause the formation of calcium caseinate, which precipitates out in the form of curds. This is why, for example, it doesn't work well to simultaneously add milk and...

I don't think it's possible to solve this in closed form. Using calculus (or looking up the formula for area of a circular segment), you find that the area is a transcendental equation in d...

There's no closedform solution to the integral, though it can be written as an asymptotic series:
First, rewrite the integral into a form where you can do integration by parts:
\int...

Brilliant, EB!
Thanks for the explanation! Unfortunately I can't give you any rep because I need to spread it around first. :)

33.33% isn't one of the available answers! Therefore, you can't possibly be correct 33.33% of the time.
The answer is 0%.

I would be interested. My apologies to the OP who probably doesn't care about all the details.
Ironically when I did the simplified calculation and saw the answer, I immediately saw that it was...

EBaines,
I've been thinking about this problem for a few days. It seems pretty straightforward: each person has a probability of 69/70 of getting back a copy other than their original. Hence it...

I did a really quick simulation of this "trick" on a computer, where it's simple to do a large number of runs. After a trial of 1 million runs, the two cards ended up next to each other only 48.7%...

Because "water" literally refers to the chemical H2O. It could refer to water in the solid phase (what we usually call "ice" in regular English), liquid phase (what we usually just refer to as...

There is a 0% chance that you'll be correct.
TimHathaway is correct that there's a 25% chance of picking any one particular answer. However, both A and D say "25%"; therefore, you'll randomly...

This is the very definition of the inner product using braket notation. You could change that equals sign into a "is defined as" sign, because this equation is defining the meaning of the lefthand...

Woops, you beat me to it EB!
I was reading a book last week called "The Drunkard's Walk" by Leonard Mlodinow (about probability and randomness). In the book he recounted a scary incident from the...

95% of the people seeking admission are authorized, but the device outputs a false negative 2 out of 1900 times. Hence the probability that a given person will be authorized and the alarm will be...

I have a couple of ideas. Just brainstorming here. Do you have any idea how much voltage was generated when he banged on the disks? It might be hard to measure with a simple voltmeter because the...

Indeed. Congratulations on reaching the same answer that was explained repeatedly throughout this thread.

The ideal gas law says PV=nrT, which can be rewritten as PV/T = nr. Since the right hand side of that equation is a constant (the number of moles of gas is not changing), the lefthand side must...

Tap A fills the tank in 10 minutes, so it's flow rate is 1/10 tank per minute. Both taps together fill the tank in 6 minutes, so they have a combined flow rate of 1/6 tank per minute.
flow rate A...

(a) There are 38 possible outcomes of one spin. 18 of them are red. Therefore, the probability of getting red on any ONE spin is 18/38 \approx 0.474. If you want to know the probability of...

That might be a good sign. When the switch is off, the red floats (i.e. it's not directly tied to any hot or neutral. Since the impedance is very high, it's not unusual for resistance in the wire...

That's very strange. When you measured them, did you remove them from the switch, or did you measure them as is with the switch in place? If the latter, then both should be hot when the switch is...

If you have the option of typing in the time using a colon (e.g. 2:36, rather than 2.36), as JBeaucaire suggested, that's certainly the best option.
That being said, I don't know why the formula...

Well, thanks for switching my reputation back to "helpful". :)
Since you have the answer to question #2, I edited my original post to answer that one.
Now I'll show you how to evaluate (4(ln...

Leeboy, if you add up all of the volumes of all of the liquid ingredients you listed in the recipe, it works out to 12.5 tablespoons. The remaining dry ingredients work out to an additional 2.5...

f(x)=(lnx)^5 at x=4 is (ln4)^5. It can't be simplified more than that.

Sounds like you're missing a diagram. Can you describe what you mean by the angle theta?

Let a, b, and o be the numbers of apples, bananas, and oranges.
a + b + o = 18
0.85a + 0.20b + 0.76o = 9
b = a + o

First you need to compute the derivative to find the slope at x=5.
f'(x)=\frac{d}{dx}\[(\ln x)^4\] = 4(\ln x)^3\;\cdot\;\frac{d}{dx}(\ln x)=\frac{4(\ln x)^3}{x}
f'(5)=\frac{4(\ln 5)^3}{5}
...

Is there only one set of wires entering the ceiling box? (i.e. only one white wire, one black, and one ground)? The reason I ask is this: If there are two sets of wires in that box, one set may be...

To convert from hours.minutes to decimal hours, you need to take everything after the decimal point and multiply by 100/60. You could do it this way:
=ROUNDDOWN(A1,0)+(A1ROUNDDOWN(A1,0))*100/60...

First calculate the probabilities of each coin flip scenario:
P(student's flips both the same)
P(student's flips not both the same)
P(teacher's flips all three the same)
P(teacher's flips not...

If you believe the biblical story of creation, Adam went forth and multiplied. ;)

The short answer is that sound travels at approximately 1500 m/s in water. Since it has to travel a total of 6000 m to go to the bottom and back up again, it takes a total of about 4 seconds. (i.e....

The other way to look at this, by the way, is to calculate the swimmer's actual speed (relative to the stationary shore), then subtract their given speed relative to the water.
Swimmer covers 80...

This problem doesn't seem to make a lot of sense, since you'd think the swimmer would be swimming perpendicular to the current.
That being said, let's just assume the swimmer is swimming 80 ft....

distance = rate * time
You know the distance, and you know the rate (the speed of light, or around 3x10^8 m/s).
Just plug in the numbers and solve for time. That will give you the answer in...
