सदस्य: Melody

slothz:
A machine purchased for $400 000 depreciates at a rate of 20% p.a. After how many years
will the machine have a value of $131 072?
Just don't really know the formula for calculating n plz help
Cheers guys

hI,
what nice manners , thank you.

It is almost the same formula as compound interest which is S=P(1+r) ⁿ
Where S is the future value,
p is the present (or initial) value,
r is the interest rate per compounding period
n is the number of compounding periods

The only difference is that if interest is compounding the amount is getting bigger so it is (1+r)
If the item is depreciating the amount is getting smaller so you use (1-r)

A machine purchased for $400 000 depreciates at a rate of 20% p.a. After how many years will the machine have a value of $131 072?
So the formula you need to use is S=P(1 -r) ⁿ
S is the future value = $131 072
P is the initial value = $400 000
r = 0.2
n = unknown

131 072 = 400 000(1-0.2) ⁿ
divide both sides by 400 000
0.32768 = (0.8) ⁿ

Now, whenever the exponent is the unknown, you have to use logs to solve the question
It doesn't matter what base you use, the calculator deals only with 10 and e so you'd best choose one of those.

log 0.32768 = log (0.8) ⁿ

log 0.32768 = n * log 0.8

n = log 0.32768 / log 0.8
and you can finish it.

Here are the log identities, there are a lot that you are expected to remember.
http://en.wikipedia.org/wiki/List_of_logarithmic_identities

Melody3 Feb 2014

+118692

Guest:
4.46 x 10^-6, Move the decimal 6 places to the left.

0.- - - 446
Fill in the spaces with zeros
Answer: 0.000446

Good try but not quite,
there are not enough zeros

4.46 x 10 ^-6

= 0.00000446

The 46 were already after the point.
you had to jump over the first digit '4' and then five zeros until you got were you needed to go. I put the 0 out the front just to make it easier to read.

Would you like to try another one?

how about
8.903 x 10 ⁵

Melody3 Feb 2014

+118692

Guest:
4.46 x 10^-6, Move the decimal 6 places to the left.

0.- - - 446
Fill in the spaces with zeros
Answer: 0.000446

Good try but not quite,
there are not enough zeros

4.46 x 10 ^-6

= 0.00000446

The 46 were already after the point.
you had to jump over the first 4 and then five zeros until you got were you needed to go. I put the 0 out the front just to make it easier to read.

Would you like to try another one?

how about
8.903 x 10 ⁵

Melody3 Feb 2014

+118692

Guest:
(5^2+2x-1)+(-4^2+x+7)

(10+2X-1)+(-8+X+7)

(2X+9)+(X-1)

Answer: 3X+8

Hi Guest, thank you for contributing to this question. It is good when people join in.
most of you answer is correct.
However,
In this question the hat ^ is used to indicate power or exponent. So 5^2 means 5 ² which is 5*5 = 25
Often on the forum you will see a multiply sign written as a * This is so that it won't get confused with a x if the question has algebra in it.

So the question really is and since there is a plus in between the brackets i can just leave it out

= 5^2+2x-1+ -4^2+x+7
= 5*5 + 2x - 1 + -4 ² + x + 7

Now, -4^2 is really tricky. Is it -4*-4 = +16? or is it - 4*4=-16 It is always best to use brackets in a situation like this so that the message is clear.
If you do it on your calculator with no brackets you will get -16 Try it and see.
The reason is that the calculator interprets it like this -4^2 = -4 ²= -1 * 4 ²

To be perfectly honest I am not sure how a person is supposed to interpret this. I will ask the other mathematicians whether they have a definite take on this.

For the moment I will interpret it like (-4) ²= -4*-4 = +16 Because I think that was the intent but this does need to be checked.
so

= 5*5 + 2x - 1 + (-4 ) ² + x + 7

= 25 + 2x -1 + +16 + x +7

= 25 -1 + 16 + 7 + 2x + x

= 25 -1 + 16 + 7 + 2x + x

= 47 + 3x

= 3x + 47 (It is always nice to put the x term before the constant)

Melody3 Feb 2014

+118692

Guest:
SIMPLIFY 9X+3Y

Hi Guest thank you for your contribution to this problem. I am sure that you were not the only one confused by my answer.

Hi guest, if you are asked to factorise 9X+3Y then the answer is indeed 3(3X-Y) So you can think of factorise as meaning 'put brackets in' if you like.

The factors are 3 and 3X-Y because when you multiply them together you get 9X+3Y

HOWEVER

The question says simplify. simplify means take away the brackets, not put them in!

Therefore 9X+3Y is already as SIMPLE as it can be.

Melody3 Feb 2014

+118692

Guest:
SIMPLIFY 9X+3Y

This cannot be simplified,

Melody3 Feb 2014

+118692

Guest:
5. Plot the complex number .-4sqrt(3) -4i

I think that you just plot (-4sqrt(3),-4)

but the x axis is actually the Real axis
and the y axis is the i axis.

Melody3 Feb 2014

+118692

kseniya:
what is the equation of a line that passes through the points (-4,-5) with the slope of -7/2

Hi kseniya,

Use the forumula

y-y ₁=m(x-x ₁)

Can you do it now?
Have a go, if you get in a mess post again but show me what you have tried already.

Melody3 Feb 2014

+118692

latreace:
billy, sam, and cat is having a candy party there are 13 pieces of candy. how many pieces of candy can billy, sam, and cat have?

well billy gets 1 piece
Sam gets 1 piece
and it is Cat's birthday so she gets 11 pieces.

Melody3 Feb 2014

+118692

drewace22:
a minute hand on a clock is 80 cm long. how far does the tip of the minute hand travel in 30 mins?

It will travel half of the circumference.

so that's 1/2 * (2 * pi * r)

What is r? Draw the picture and you will see.

You can finish it.

Melody3 Feb 2014

यूजर का नाम	Melody
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