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Type: Posts; User: jcaron2

1. ## Question: why f(x+dx)=f(x) + d/dx f(x) dx ?

by jcaron2
1
Views
578

### Any function, no matter how crazy or nonlinear,...

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...
2. ## Question: Help w/proof or equation for daughter's algebra teacher

by jcaron2
3
Views
772

### She could keep it relatively simple and write an...

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 =...
3. ## Question: Hello, can anyone help me with this puzzle?

by jcaron2
3
Views
1,874

### Pready, that doesn't work very well unless you...

Pready, that doesn't work very well unless you swap the numbers around. And since you can't say -99+916-806 without losing the space between "number" and "99", I think the better way is to change...
4. ## Question: Is there a way to harness current from a piezo-electric plate?

by jcaron2
19
Views
12,751

### Unfortunately I don't really know of any good...

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...
5. ## Question: 4x4+4x4+4-4x4=

by jcaron2
3
Views
4,098

### Order of operations says that you do the...

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.
6. ## Question: Is there a way to harness current from a piezo-electric plate?

by jcaron2
19
Views
12,751

### Excellent! I'm glad to hear he got it to work...

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!
7. ## Question: Engineering ask question

by jcaron2
2
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463

### Actually, now that I went through all that,...

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'...
8. ## Question: Engineering ask question

by jcaron2
2
Views
463

### First we need to compute the absolute deflection...

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...
9. ## Question: Heavy water and novelty ice cubes

by jcaron2
1
Views
806

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...
10. ## Question: Problem2.1

by jcaron2
3
Views
618

### It doesn't matter what direction the car goes;...

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
11. ## Question: Geometric Sequences: Finding the sum of an infinite series?

by jcaron2
4
Views
1,102

### Since there are an infinite number of terms with...

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,...
12. ## Question: Geometric Sequences: Finding the sum of an infinite series?

by jcaron2
4
Views
1,102

### I assume you accidentally missed the x^2 term? ...

I assume you accidentally missed the x^2 term?

Is this the question?

1-x+x^2-x^3+...=\sum_{n=0}^\infty (-x)^n = \frac{1}{1+x+x^2}

Mod x? "Mod" to me mean modulo division, which doesn't...
13. ## Question: Geometric Sequences: Finding the initial value?

by jcaron2
1
Views
752

### \sum_{n=0}^\infty ar^n = b Since the series...

\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...
14. ## Question: How to find the distance between two overlapping circles?

by jcaron2
11
Views
5,280

### [Disregard this until you read my EDIT at the...

[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. ...
15. ## Question: How to find the distance between two overlapping circles?

by jcaron2
11
Views
5,280

### \sum_{n=0}^\infty ar^n = b Since the series...

\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...
16. ## Question: How to make curd with in ten minutes?

by jcaron2
1
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821

### I think pretty much any acid will cause the...

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...
17. ## Question: How to find the distance between two overlapping circles?

by jcaron2
11
Views
5,280

### I don't think it's possible to solve this in...

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...
18. ## Question: integrate e^(-(x^2))dx

by jcaron2
1
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1,196

### There's no closed-form solution to the integral,...

There's no closed-form 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...
19. ## Question: Probability - choir members getting same copies back

by jcaron2
6
Views
806

### Brilliant, EB! Thanks for the explanation! ...

Brilliant, EB!

Thanks for the explanation! Unfortunately I can't give you any rep because I need to spread it around first. :)
20. ## Question: Probability brain twister

by jcaron2
9
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1,006

### 33.33% isn't one of the available answers! ...

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

21. ## Question: Probability - choir members getting same copies back

by jcaron2
6
Views
806

### I would be interested. My apologies to the OP...

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...
22. ## Question: Probability - choir members getting same copies back

by jcaron2
6
Views
806

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...
23. ## Question: Nightmare Probability Problem! HELP!

by jcaron2
2
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1,145

### I did a really quick simulation of this "trick"...

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%...
24. ## Question: What state of matter is water vapor?

by jcaron2
7
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24,464

### Because "water" literally refers to the chemical...

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...
25. ## Question: Probability brain twister

by jcaron2
9
Views
1,006

### There is a 0% chance that you'll be correct. ...

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...
26. ## Question: Wave function

by jcaron2
3
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782

### This is the very definition of the inner product...

This is the very definition of the inner product using bra-ket notation. You could change that equals sign into a "is defined as" sign, because this equation is defining the meaning of the left-hand...
27. ## Question: Probability Question

by jcaron2
3
Views
4,478

### Woops, you beat me to it EB! I was reading a...

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...
28. ## Question: Probability Question

by jcaron2
3
Views
4,478

### 95% of the people seeking admission are...

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...
29. ## Question: Is there a way to harness current from a piezo-electric plate?

by jcaron2
19
Views
12,751

### I have a couple of ideas. Just brainstorming...

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...
30. ## Question: 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0 =? My answer is 4, do you agree?

by jcaron2
19
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14,613

### Indeed. Congratulations on reaching the same...

Indeed. Congratulations on reaching the same answer that was explained repeatedly throughout this thread.
31. ## Question: What is the volume of the bubble at the surface of this problem

by jcaron2
1
Views
649

### The ideal gas law says PV=nrT, which can be...

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 left-hand side must...
32. ## Question: Two taps fill a tank in 6 minutes, tap A fills tank in 10 minutes, how long does tap

by jcaron2
2
Views
1,286

### Tap A fills the tank in 10 minutes, so it's flow...

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...
33. ## Question: Suppose a player observes 3 players of roulette. Note: A roulette wheel has 18 red nu

by jcaron2
1
Views
443

### (a) There are 38 possible outcomes of one spin. ...

(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...
34. ## Question: New Light Fixture to existing ceiling box

by jcaron2
12
Views
1,515

### That might be a good sign. When the switch is...

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...
35. ## Question: New Light Fixture to existing ceiling box

by jcaron2
12
Views
1,515

### That's very strange. When you measured them, did...

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...
36. ## Question: Is there one excel formula to round up and down to nearest quarter?

by jcaron2
10
Views
12,707

### If you have the option of typing in the time...

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...
37. ## Question: 1.find the equation of the line tangent to the graph of f(x)=(lnx)^5 at x=4?

by jcaron2
5
Views
2,730

### Well, thanks for switching my reputation back to...

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...
38. ## Question: Trying to put these equal amounts in a 500ml bottle

by jcaron2
2
Views
393

### Leeboy, if you add up all of the volumes of all...

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...
39. ## Question: 1.find the equation of the line tangent to the graph of f(x)=(lnx)^5 at x=4?

by jcaron2
5
Views
2,730

### f(x)=(lnx)^5 at x=4 is (ln4)^5. It can't be...

f(x)=(lnx)^5 at x=4 is (ln4)^5. It can't be simplified more than that.
40. ## Question: A 0.3 kg ball is attached to a string that is 50 cm in length, and completes 2 circle

by jcaron2
2
Views
819

### Sounds like you're missing a diagram. Can you...

Sounds like you're missing a diagram. Can you describe what you mean by the angle theta?
41. ## Question: Finite math help free?

by jcaron2
1
Views
738

### Let a, b, and o be the numbers of apples,...

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
42. ## Question: 1.find the equation of the line tangent to the graph of f(x)=(lnx)^5 at x=4?

by jcaron2
5
Views
2,730

### First you need to compute the derivative to find...

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}
...
43. ## Question: New Light Fixture to existing ceiling box

by jcaron2
12
Views
1,515

### Is there only one set of wires entering the...

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...
44. ## Question: Is there one excel formula to round up and down to nearest quarter?

by jcaron2
10
Views
12,707

### To convert from hours.minutes to decimal hours,...

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)+(A1-ROUNDDOWN(A1,0))*100/60...
45. ## Question: Pie faced teachers

by jcaron2
1
Views
440

### First calculate the probabilities of each coin...

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...
46. ## Question: Father of mathematics

by jcaron2
4
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9,714

### If you believe the biblical story of creation,...

If you believe the biblical story of creation, Adam went forth and multiplied. ;)
47. ## Question: Seafloor depth and sound signal

by jcaron2
1
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4,988

### The short answer is that sound travels at...

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....
48. ## Question: River Velocity Problem

by jcaron2
2
Views
377

### The other way to look at this, by the way, is to...

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...
49. ## Question: River Velocity Problem

by jcaron2
2
Views
377

### This problem doesn't seem to make a lot of sense,...

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....

by jcaron2