All Answers

+118725

+14

Hi all,
I have recovered from my yesterday's collapse. I thank those people who voiced there support (by private message). I really needed to hear it and I am very grateful.
It is thought that the best way to deal with our 'Professional Troll' is to ignore his/her posts. No response = No fun for the troll.
I guess this forum can cope with 1 rude adult without falling in a heap.

Today was a standard busy mid-week day. Fantastic answers were provided by Reinout-g, Alan, Dms, Samgelinas, Ironn, Mathcalc, ChrisP and unknown.
NerdPro also answered a question but it was answer only with no explanation so it was not very helpful. Sorry NerdPro, I am pleased that you answered but you do need to explain the answers that you give.

ChrisP, it is great that you are answering so many questions. We'd really like you to consider joining up. There are a number of benefits and we would love you to join us formally.
Look here to find out what benefits there could be for you.
http://web2.0calc.com/questions/become-a-member-why-would-you-want-to

Alan sent an email to Andre Massow yesterday. Andre responded and said that moderator rights will be a feature in the new forum design. Andre also said that he was hoping to publish a new Beta version upgrade this weekend so that we can all evaluate it. I am not to sure what that means. I guess we will find out.

Oh there was a question today with notation that I haven't seen before. It was in here http://web2.0calc.com/questions/quads It was just m<ABC which meant measurement of angle ABC. I had no idea what the 'm' meant. Chris knew what it meant. Is it normal notation? Could any comments please be posted on the end of the relevant thread. Please don't post here.

That's it for this Wed/Thurs,
Thank you everyone,
Melody.

MelodyMar 13, 2014

hmmmmmmmmm...... lol

GuestMar 13, 2014

+118725

Guest:
30% of the days in November were sunny how many days were sunny

there are 30 days in november

30% of 30 = 0.30 * 30 = 9 days

MelodyMar 13, 2014

+118725

MultiQuestioneer:
Please explain or showcase your work so I could use this page for future reference.
Rhombus:
ABCD is a Rhombus. AB=21, m<ABE=60. Leave answers in simple radical form.

Hi MultiQuestioneer,
Ok so
m<ABE means measurement of <ABE
I have never seen m used like this before - is it normal or usual notation?? Maybe Chris or someone else can answer this question.
I had no idea what 'm' was. I did ask you earlier on but you didn't answer my question.

Looking back
It still doesn't make sense
Find DC= BD= EC= m<BAC=
m<BCE= m<BEC= m<BAD=
How can an angle = a side length?

Anyway ChrisP's answer look really good. It is probably what you wanted. He is obviously a much better forensic mathematician than I am.
Thanks Chris.

MelodyMar 13, 2014

+33666

rqwr:
find the area of regular octagon with a hyportenuse of one of the triangles made out of the vertices for 2 cm

I think this is probably what is required here:

Octagon.PNG

AlanMar 13, 2014

Whoops!!

Disregard my previous answer....I didn't note that the compounding was annually rather than what I gave you which was continuous compounding!!

Well.... no biggie!!

Here's the "formula" we need

I -= A ( 1 + r/n)^(n*t)

Where .I is the interest we wish to earn (I.m assuming that you want to make $24000 to "quadruple" your money), A is what we started with, 8000 (the principal), r is the interest rate expressed as a decimal (.045) , n is the number of compoundings per period (in this case, 1 time per year) and t is, again, the time - what we're trying to find.

So we have

24000 = 8000(1 + .045)^(t) (Note that since n = 1 , we can ignore it.)

Again, divide both sides by 8000 and we get

3 = (1.045)^(t)

Now, take the LOG of both sides

LOG 3 = LOG (1.045) ^(t)

By the property of logs, we can bring the "t" on the right side "out front" and we have

LOG 3 = (t)* LOG(1.045)

Now, divide both sides by LOG (1.045) and we have

LOG(3) / LOG (1.045) = t = about 24.96 years!! (Note that the time isn't much longer than under continuous compounding!!)

Again, if by "quadruple," you mean that you want to EARN $32000, just replace the "24000" in the above equation with "32000,"...... wash, rinse and repeat!!

Sorry for my previous s***w-up. I hope this helps!!

GuestMar 13, 2014

I'm assuming that the only thing throwing you here is the I -2 I. This stands for the "absolute value" of -2 which is just 2. (Really, the distance on the number line that -2 is from 0.....2 units).

The rest should be pretty easy if you're used to adding and subtracting signed numbers.

GuestMar 13, 2014

I'm assuming that, if you want your money to "quadruple," you want to end up with $32000 - 4 times what you started with,. Thus, you want to earn $24,000 of interest PLUS your original $8000.

The "formula" for the interest computation is I = Pe^(rt), where P is the amount we started with ($8000), e is the base of the natural log (i,e., about 2.718), r is the interest rate expressed as a decimal (i.e., .045), and "t" is what we want to find!! (Note that the "rt" is an exponent on e!!)

So, let's get started!!

We have, 24000 = 8000* e^ (.045t)

Divide both sides by 8000 and we get

3 = e ^(.045t)

Now, take the LN (natural log) of both sides. We have

LN 3 = LN e^ (.045t)

Note, that by the property of logs, the right side just becomes .045t. (That's the beauty of using the LN here - it simplifies things!!)

So we have

LN 3 = .045t

Divide both sides by .045 to get "t"

(LN 3) / (.045) = = about 24.41 years!!

Note...if by "quadruple," you meant that you wanted to EARN $32000 in interest, just replace the "24000" in the equation with "32000" and follow the same process. (It should take longer than 24.41 years if you do everything correctly!!)

Hope this answers your question!!

GuestMar 13, 2014

Let me see if I can help you with this one (it's not too difficult!!)

Since it's a rhombus, all sides are equal, so AB = DC = 21

Since m < ABE = 60,, then the m < BDA = 60 also, because BAD is a triangle with two sides equal (BA, DA). And from a theory in geometry, when a triangle has two equal sides, the angles opposite those sides are equal, too. Then, because we have a triangle with two 60 degree angles, the remaining angle (BAD) is 60, too. So, all sides of triangle BAD are equal. Thus, AB = BD = 21. And since AE bisects BD, then DE = (!/2) * 21 = 10.5.

Well, so what?? How does this help us find CE?? Well, the diagonals of a rhombus intersect at right angles, so triangle CED is a right triangle with < CED being the right angle. and CD the hypotenuse. And we know two sides of this triangle (DE = 10.5 and CD =21). And by the Pythagorean theorem, CE = SQRT (21^2 - 10.5^2) = 18.2 (rounded).

To find the m < BAC, note that EA bisects < BAD, and since < BAD was found to be 60, then m < BAC = 30.

To find m < BCE, note that in triangle ABC, sides AB = BC, so the angles opposite those sides are equal, too. Thus, m < BAC = m < BCA = m < BCE = 30.

We've established that the diagonals form right angles, so m < BEC = 90.

I think that's what you wanted to know (hopefully). If you have any questions about this, feel free to post them. I hope my explanations were clear!!

GuestMar 13, 2014

+118725

Mhelody:
given sin A=3/5;sin B=5/13,find sin(A+B)

Hi mhelody, what a familiar name you have there. where ever could I have seen one like that before?

Use the formula

sin(A+B) = sinAcosB + CosAsinB

If A=3/5
Draw a right angled triangle and lable an acute angle as A
label the opp side 3 and the hypotenuse 5. Now what is the other side? from there you will know what CosA is

Draw a differrent right angled triangle for the B triangle to get cosB

that is about it I guess.

MelodyMar 13, 2014

+118725

MultiQuestioneer:
Just all the measurements I wrote down. M is just the thing I use in place of x, I should have specified, sorry.
So again

The < represents angles, if they dont have it I just want the measurement

Still doesn't make sense
Find DC= BD= EC= m<BAC=
m<BCE= m<BEC= m<BAD=

How can an angle = a side length?

MelodyMar 13, 2014

+118725

Guest:
a spinner that has 3 sections of equal area, numbered from 1 to 3, is spun 2 times in succession. which is not part of the sample space?

Was this a part of a multiple choice question?
It doesn't make any sense to me.

MelodyMar 13, 2014

+118725

fumerios:
Modern whales appeared 5-10 million years ago. The vertebrae of a whale discovered by paleontologists contain roughly 0.25% as much carbon-14 as they would have contained when the whale was alive. How long ago did the whale die? Use k = 0.00012.

Umm
Isn't that A=A ₀ * e ^-kt

0.0025=1 * e ^-0.00012t

ln(0.0025)= ln e ^-0.00012t

ln(0.0025)= -0.00012t * ln e

ln(0.0025)= -0.00012t

t = -ln(0.0025) / 0.00012

49,929 years ago ( assuming that the time frame is in years)

I think that's right but I am not positive.

MelodyMar 13, 2014

+118725

dtrain:
.19=(27x^3(x))/(2.5-2x)^2

19(2.5-2x) ² = 27x ⁴ where 2.5-2x not equal to 0 ==.> x not equal to 1.25

19(6.25+4x ²-10x)= 27x ⁴

-27x ⁴+76x ²-190x+118.75=0

140313 complicated roots.JPG

It is interesting that two different calculators have given 2 different answers This one gives 2 answers, web2.0 calc gives only one.
Maybe i will look at another calculator and go for 2 out of 3

140313 Compicated equation2.JPG

There you go, the 2 graphing calculators agree with each other. How about that.

MelodyMar 13, 2014

+118725

dtrain:
.19=(27x^3(x))/(2.5-2x)^2

[input]19=(27x^3(x))/(2.5-2x)^2[/input]

MelodyMar 13, 2014

Just all the measurements I wrote down. M is just the thing I use in place of x, I should have specified, sorry.
So again

The < represents angles, if they dont have it I just want the measurement

GuestMar 13, 2014

+118725

MultiQuestioneer:
Please explain or showcase your work so I could use this page for future reference.
Rhombus:
ABCD is a Rhombus. AB=21, m<ABE=60. Leave answers in simple radical form.

so E is the intersection of the 2 diagonals.

What is m?
and
What is it that you want to find? Is it the area?

MelodyMar 13, 2014

+118725

Erica:
What number is one hundred more then 712

712+100

MelodyMar 13, 2014

+118725

rqwr:
find the area of regular octagon with a hyportenuse of one of the triangles made out of the vertices for 2 cm

what hypotenuse?
I don't understand your question.

MelodyMar 13, 2014

+118725

keim:
A model ship is built to a scale of 1 centimeter:5 meters.The length of the model is 30centimeters.What is the actual length of the ship?

1*30 = 30cm

5*30 = 150m

MelodyMar 13, 2014

+118725

walkera:
:? Glenda swam the 200 yd freestyle in 100 seconds. if she maintains the same rate in the 500 yd freestyle,how long will it take her to finish the race?

100sec/200yds = x sec/500 yards

mult both sides by 500 yards and you get

100sec/200yds * 500yards

The yards cancel out

100/200 * 500secs

1/2*500 sec

250 seconds

MelodyMar 13, 2014

+118725