All Answers

+130561

Example:

Twice a number = 2n

So, 5 less than twice would be

2n - 5

CPhillMar 25, 2014

+893

CPhill:
Bertie

Your method of substituting cos(pi/3) for 1/2 and sin (pi/3) for (√3)/2 is quite ingenious!!!!

I like that MUCH BETTER !!!

Sadly, I can't claim to have had any flash of inspiration, the method I used is standard and routine, (with just a tiny realisation).
Post again if you wish/need details.

BertieMar 25, 2014

+2354

pancakes:
what is a algebraic expression

If this is a serious question:

http://home.avvanta.com/~math/def2.cgi?t=expression

reinout-gMar 25, 2014

+2354

yara:
the area that lies either to the left of 1.56 or to the right of 2.30

I think there is a part missing of your question. Is there a drawing, an equation or something like that which gives me some more information?

Look at this number line:

number line.png

The area in your question is indicated as red.

This means it goes from -infinity to 1.56 or from 2.30 to infinity and therefore the answer would be infinite which is probably not what you're looking for.

Reinout

reinout-gMar 25, 2014

+38

What the f**k?

pancakesMar 25, 2014

+2354

Alan:
Here's my offering:

dfdx.PNG

Aah, thank you allan.
Splitting the function into two domains does indeed make sense.

reinout-gMar 25, 2014

+130561

Take a look at this website, Stu. I've found that his explanations are pretty good. He also gives some examples.

http://tutorial.math.lamar.edu/Classes/CalcI/DerivativeIntro.aspx

If you have any specific questions, post them to the forum.

Hope this helps.

CPhillMar 25, 2014

+6252

Quote:
3 to the power of x equals 30. how to solve?

3 ^x=30

take logs of both sides

x log(3) = log(30)

x = log(30)/log(3) = log(3*10)/log(3) = (log(3)+log(10))/log(3) = 1 + 1/log(3)

RomMar 25, 2014

+6252

product rule
chain rule
addition rule
quotient rule

RomMar 25, 2014

+130561

Although I'm not the most "technical" user of the calculator, it will add and subtract fractions (and reduce them to simplest form). It will also convert an "unknown" decimal to a fraction.

Examples

108/357

9/93+8/102

0.1752055660974067

I'm not sure what you might be after, but if you have more specific questions, post them to the forum and we'll see if we can answer them.

CPhillMar 25, 2014

+6252

It does

Just use the / button to enter denominators

2/3 + 5/7=

RomMar 25, 2014

+130561

First, let sin(x) = x

So

3SIN(x)^2-7SIN(x)-3=0

= 3x^2 - 7x - 3 = 0

Solving, we have.....

3x^2 - 7x - 3 = 0

This implies that sin(x) = (7 - √85) / 6 and sin(x) = (7 + √85) / 6

The second answer is impossible, since it implies that sin(x) > 1

Solving for the first, we have

asin(((7-sqrt(85))/6))

Hope this helps

CPhillMar 25, 2014

+33666

Here's my offering:

dfdx.PNG

AlanMar 25, 2014

+1313

The above would include chain rule, product rule, quotient rule and addition rule. I understand one rule, but then again not well. Not a real good idea about the rest, and trying to read it (i will and am) still doesn't really help make it familiar. Thus, some lay man examples and definitions could be just what I need.

StuMar 25, 2014

+2354

This question has been posed in multiple posts due to the many attachements

CodeCogsEqn (8).gif

part 3/3

Reinout

reinout-gMar 25, 2014

+2354

This question has been posed in multiple posts due to the many attachements

CodeCogsEqn (5).gif

CodeCogsEqn (6).gif

CodeCogsEqn (7).gif

part 2/3

reinout-gMar 25, 2014

+118725

Thanks Bertie, that is what I was hoping for.
I knew there would be something like that I just had a mind blank.

MelodyMar 25, 2014

+130561

Bertie

Your method of substituting cos(pi/3) for 1/2 and sin (pi/3) for (√3)/2 is quite ingenious!!!!

I like that MUCH BETTER !!!

CPhillMar 25, 2014

+893

Melody:
sqrt(3)cos(x) - sin(x)= 1

What is the best way to tackle a question like this one? I need a general formula.
Thanks.

(I am reposting because it hasn't been answered yet.)

Here's an alternative approach.

Start by dividing throughout by 2.

(sqrt(3)/2).cosx - (1/2)sinx = 1/2, and then use some well known trig ratios.

sin(pi/3)cosx - cos(pi/3)sinx = 1/2.

Now a trig identity, sin(pi/3 - x) = 1/2,

so pi/3 - x = sin ^-1(1/2) = pi/6 or 5pi/6 (+2k.pi if you wish).

So x = pi/6 or -pi/2 ( + 2k.pi).

BertieMar 25, 2014

+118725

Thank you Stu and Chris. I really appreciate your answers.

MelodyMar 25, 2014

+130561

sqrt(3)cos(x) - sin(x)= 1

Let's see if this works

(add sin(x) to both sides and square both sides)

3(cos(x)^2 = 1 + 2sin(x) +sin(x)^2

(using cos(x)^2 = 1 - sin(x)^2, we have)

3*(1 - sin(x)^2) = 1 + 2sin(x) +sin(x)^2

(Simplify)

4*sin(x)^2 + 2*sin(x) - 2 = 0

(Divide through by 2)

2*sin(x)^2 = sin(x) -1 = 0

(Factor)

(2sin(x) -1) (sin(x) +1 ) = 0

Solving, we get x = (pi/6 + 2*pi*n , 3*pi/2 +2*pi*n)

Another 2nd quad angle, 5*pi/6, solves (2sin(x) -1 = 0), but it doesn't "work in the original problem) (due to "squaring," we get an extraneous solution??)

I think that may be it.....but check my work and method!!

CPhillMar 25, 2014

+1313

I guess just use most of the answer, and-- aplly the rule for minus not devision etc. If that helps.

StuMar 25, 2014

+1313

I knew only that you should make them both the same form. A quick google search of you typed text gave this > http://au.answers.yahoo.com/question/index?qid=20090219015444AA5lj7o

Answer >
Best AnswerVoter's Choice

Walid J answered 5 years ago
OK
sqrt(3)cosx = 1 + sinx

now square both sides u get:

3 cos^2x = sin^2x + 2sinx + 1

but cos^2x = 1 - sin^2x

so 3(1 - sin^2x) = sin^2x + 2sinx + 1

so it becomes:

4sin^2x +2sinx - 2 = 0
div by 2

2sin^2x + sinx - 1 = 0

(2sinx - 1)(sinx + 1) = 0

sinx = 1/2 ---> x = 30 , 150

sinx = -1 ---> x = 3pi/2

Op attributed.

StuMar 25, 2014

#81

+118725

Hi all,
Ok I was wrong. It was another very quiet day.
I even looked up world holidays to see it that was the reason. It was a holiday today in Maryland (US), Azerbaijan, Cyprus, Greece and San Marino.
Dms comes from Greece but I don't know if any other contibutors come from those places so I guess it is just a conincidence.
Anyway we did have a couple of good answers from Alan and Princess Sophie. Thank you.
That is it for this very quiet Monday/Tuesday.
Melody.

MelodyMar 25, 2014

+118725

Princess Sophie E:
roro wrote: cos(a)=-0.4558
find a.

cos(a)=-0.4558
a=cos^-1(-0.4558)
=> a=117.1164195

Hi Sophie,
You have a second quadrant answer here but what about the one in the 3rd quadrant? Cos is negative there too.

I think that the easiest way to handle a question like this is to first solve
Cos ^-1(0.4558) = B ( just had to use some letter so I used B for beta)
then think about which quadrants you need cos is neg in the second and the 3rd quad
then
a = 180 - B (second quad)
or
a = 180 + B (third quad)

MelodyMar 25, 2014

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