Math Is Fun Forum

slasherex

Member

Registered: 2009-10-25

Posts: 3

Need help plz Ap/Gp

2.
The number of revolutions of
an electric motor observed at one minute intervals is as
follows:

1st min  2nd min  3rd min   4th min

1500      1200         960         768

i)
How many revolutions woul
d be made during the 5th minute?
ii)
How many revolutions woul
d be made during the 10th minute?
iii)
**After what interval would the number
of revolutions be less than 100rpm?
iv)
What total number of revolutions made after the 16th
minute?
v)
**How long would it take for the total num
ber of revolutions to exceed 7400? 
vi)
How many revolutions would the motor
take to come to stand still?

**  -Requires the use of logarithms

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help plz Ap/Gp

Hi slasherex;

Looks like you need to fit an equation to the data. What kind of fit do you require? Because that is going to affect the answer.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Need help plz Ap/Gp

This is a geometric progression, where each step is the previous one multiplied by 0.8.
The nth term of the sequence is given by 1875 * 0.8^n.

That lets you answer i) and ii), and also iii) if you use logarithms.

To answer the last three, you need to come up with an expression for the sum of the first n terms.
Since you've been asked the question, I'm guessing you've been told how to do this.

Once you have that, iv) is answerable straight away, you can do v) if you use logarithms, and you answer vi) by setting n as some very high number (because after a very long time, the wheel will have stopped turning).

---

Why did the vector cross the road?
It wanted to be normal.

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Need help plz Ap/Gp

Judging by the thread title I think the number of revolutions per minute is a geometric progression, starting at 1500 and decreasing by 20% each minute.

i)
How many revolutions would be made during the 5th minute?

Multiply the number of revolutions in the 4th minute by 0.8 for your answer.

ii)
How many revolutions would be made during the 10th minute?

You can brute force this question, but the easier way is to come up with a function to determine the number of revolutions for the x-th minute.  f(1) = 1500, f(2) = 1500 * 0.8, f(3) = 1500 * 0.8 * 0.8, etc.

iii)
**After what interval would the number of revolutions be less than 100rpm?

Use the function you determined in part ii and solve for f(x) < 100.

iv)
What total number of revolutions made after the 16th minute?

Again, find a function s(x) to calculate this value for the x-th minute.

v)
**How long would it take for the total number of revolutions to exceed 7400?

Use the function from part iv to solve for s(x) > 7400.

vi)
How many revolutions would the motor take to come to stand still?

Use the function from part ii to solve for f(x) <= 0.

---

Wrap it in bacon

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help plz Ap/Gp

HI;

The problem is somewhat ill posed.This is the reason I answered the question with another question in post #2.

http://mathforum.org/library/drmath/view/56860.html

It is not reasonable to assume that is the law that generates those 4 points. There are an infinite number of equations that go through those 4 points. Each one is just as good. Also extrapolation past known data points is not recommended.

Question: what is the next term in this sequence 1,2,4,8,16 ... everyone says 32 but it is no more correct than 77... (called the Rat sequence).

(because after a very long time, the wheel will have stopped turning).

I agree, but the formula 1875 * (.8) ^n never stops. Never touches the x axis. This could only be the formula for some frictionless motor operating in a perfect vacuum. This is not stated in the problem.

Last edited by bobbym (2009-10-30 06:18:51)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Sarah12

Guest

Re: Need help plz Ap/Gp

looks,like Geometry But Im not Sure.Sorry I cant Help i got to learn basic Math first,Before i do That.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Need help plz Ap/Gp

Yes, there are technically an infinite amount of continuations to that sequence, but since the topic title says it's either an arithmetic or geometric progression, I think it's safe to assume that we're using the intended one.

And you're right, the wheel will technically never stop turning, but it will nonetheless make a finite number of spins, and so vi) is still answerable.

---

Why did the vector cross the road?
It wanted to be normal.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Need help plz Ap/Gp

Hi mathsyperson;

Agreed, I missed the title. The use of Ap / Gp as opposed to AP / GP caused me to miss that condition ( gotten used to seeing them capitalized, don't know why). Anyway, your idea is the intended one.

Last edited by bobbym (2009-10-30 06:58:44)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.