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Thanks for your reply! Though, I checked the notation. Maybe it's more clear with superscript: f(x) = sin ² (x)* cos(x) and it's derivative is supposed to be: f'(x) = 2*sin(x) * cos ²(x) -sin ³(x)

It's actually part of a limit where you use the rule of l'Hopital. I don't know if that helps. Any suggestion is welcome!

GuestOct 18, 2013

+259

Your notation is wrong, hence is your confusion, perhaps it should look as (sinx)^2*(cosx):((sinx)^2*(cosx))' = ((sin x)^2)'*cos x + (sin x)^2*(cos x)' = [2sin x cos x] *cos x - (sin x)^2*sin x =2sin x cos ^2 x - (sin x)^3

Really missed something, did that stuff long ago.

scrutinizerOct 18, 2013

+259

To be honest, I trusted an online Russian-English translator that suggested both terms of English analogues of that notion, specifying that the term "symmetric" is applied most commonly to the notion of function and that indeed seemed rather substantiated as it directly corresponds to the graphic interpretation as cosine graph y = cos x is symmetric in respect of 0y axis while the word "even" - as I was able to draw- is used mostly in conjunction with numbers.

"you have ignored the answers when theta = (pi +- pi/6 ) +- 2pi" - this is totally unclear to me and seems quite "overloaded". How did the expression (pi +- pi/6 ) +- 2pi appear? The common formula for the roots of tangential equation is x = arctan y + pi n, where pi is a minimal positive period of tan. Further on, as cosine is symmetric or, if you prefer more, "even" then whether the argument positive or negative, the cosine is always positive. The value of theta was found via transformation to homogeneous via transformation in turn to tangential equation. It had two solutions - positive and negative. sec theta = 1/cos theta. As it follows from above, cos theta is always positive. Hence, the final result in this case is also positive. You preferred to find the roots via sinusoidal equation. So to get cos theta you as I suppose applied the main trigonometric identity, where it's not important if sine is positive or negative. You may assert that the root has two signes, but there's a question: is there indication of what a quadrant of Cartesian coordinate system should be considered? No, and it means both values must be considered and thus I logically came up with denial of myself You were right, but how it happened that I missed that solution? Mine looks formally correct.

scrutinizerOct 18, 2013

GuestOct 18, 2013

sarah mosy:
x^2(x-2)

ok first things first i think it would have been good manners to put a question in there somewhere considering humans and not calculators are answering this

secondly what are you trying to say?
cases: you are saying:

a: (x^2)*(x-2)

or

b: (x)^(2*(x-2))

if you don't see the difference between these look up how parentheses and order of operations works

doing something with both:

a: (x^2)*(x-2) = (x^3)-2(x^2)

b:

-one of the laws of exponents is when take a number with an exponent to another exponent, you multiply the two exponents together
therefore,
(x)^(2*(x-2)) = [ x^2 ]^(x-2) or [x^(x-2)]^2

note that it may be hard for you to "intuitively understand" or "visualize" what it means to take an exponent to a fraction or a variable... just kinda think on it for a bit

look at (x^(x-2)):
--another law of exponents is when you multiply two of the same number/variable with different exponents, you add the exponents.
therefore,
(x^x) * (x^(-2))

so there's the answer to the question you didn't ask

GuestOct 18, 2013

Destinyunique:
:D If there is 45% of gas left in the car and you trying to get to New York.it is a 4 day drive how much gas do you need to get there

hey so you're not giving enough information. I hope that this tutorial will help you understand how i go about doing such a problem and determine what information is needed:

If you have 45% of the gas left that's great, but you need to know the volume of the tank. once you do, volume of the gas you have left can be determined
by finding out "how much" of the total volume of the tank is 45%. here is how you calculate how much gas you have in your car:
- in words: 45% of the total volume of your gas tank is the volume of how much gas you have left
-Call the volume of the gas tank "V." "V" is a "variable." think of it as being whatever number you determined to be the volume of your gas tank

-convert 45% into a decimal. note 45% is the same thing as 45/100 which = 0.45

-The volume of gas you have is V [volume of tank] * [multiplied by] .45 [decimal form of 45%]
-without words: [gas remaining] = V * (0.45)

So that's how much gas you have left. Now, you should be given something like the distance from where you're starting to New York. It sounds like you might be given a time, 2 days or 48 hours, that your journey will take in your question [based on what you asked]. If this is the case, you should also be given an average speed. If you are, the distance is the [average speed] * [amount of time the trip takes] . Make sure your units are correct

You know how much gas you have, and the length of the journey. Now you must know (it should be given in the problem) what is the miles per gallon of your car. That is, how much gas does your car use per mile?

Once you know this, you can calculate the total amount of gas you will need to get to New York. this equation is:
-[length of trip] / [miles per gallon] . as long as your units are correct this should yield the total amount of gas needed for your trip

-The thing is, I don't think that's what your question is asking for (given what you asked). I think it's saying, if you start out with 45% of a gas tank and need to go to New York, how much gas will you need to buy on the way?
-if this is indeed the question you are being asked, then you have to see that although you determined how much gas you would need if you started out with an empty tank, you already have some gas starting out with. So to find out how much gas you need, you must subtract what you started with from the total amount you will need

-it is very useful to know this value when you want to take a trip and you have to pay for gas, because it is expensive and you have to have an estimate of how much it will be so you can know how much it will cost and can decide if you can afford it

I hope you continue learning math in your future it is your friend not your enemy good luck!

GuestOct 18, 2013

4 square root 3 = 6.9 (1dp)
6 square root 6 = 14.7 (1dp)

area of a rectangle = base x height

6.9 x 14.7 = 101.43

GuestOct 18, 2013

im sorry its

3^x-3

my mistake

GuestOct 18, 2013

+118725

I am suspicious that the question was not copied correctly but here is the answer for this question.

3 ^x+ 2 + 9 ^x + 1 = 810

3 ^x+ (3 ²) ^x +3 = 810

3 ^x + (3 ^x ) ²+ 3 = 810

(3 ^x) ² + (3 ^x) -807 = 0

let y=3 ^x

y ² + y -807 = 0

Using the quadratic formuls you end up with

y = [-1 +- sqr(3229)] / 2

y-2 = [-5 +- sqr(3229)] / 2
so
3 ^x - 2 = [-5 +- sqr(3229)] / 2

MelodyOct 18, 2013

+118725

there is no number other than 1 that goes into both 39 and 68
Therefore it is already fully simplified.

MelodyOct 18, 2013

+118725

63/100

MelodyOct 18, 2013

+118725

71-78 = -7 !!

MelodyOct 18, 2013

+118725

50-20=30
30 divided (1/6) = 180 scoops

MelodyOct 18, 2013

+118725

3 candies are 10cents how much is it when you buy 1 and a 1/2 candies.
1 and a half is 3/2 which is easier to write on this computer

one candie costs 10 / 3 cents

so 1 and a half candies cost

(10/3) * (3/2)

5c

Who would buy a half a candie anyway?

MelodyOct 18, 2013

+118725

If you put brackets in like that you will get the wrong answer.
if you enter them both as fractions you will get the correct answer

3 fraction button 1 fraction button 4 - 1 fraction button 1 fraction button 3 =

MelodyOct 18, 2013

+118725

MEGUSTAMILK's answer is good if you just want an estimate.
This is how you simplify
root5 * root60
=root 300 (just as megustamilk said)
Next you have to look for a square number that goes into 300, if there isn't one then you would not be able to simplify any more.
But 100 goes into 300 and it is a square number

root 300 = root(100*3) = root100 * root3 = 10root3

MelodyOct 18, 2013

+118725

Question should read

Question text
Match the description on the left with the salary per pay on the right.
1.Salary: $32,400 How much is this Weekly
2.Salary: $17,400 How much is this Monthly
3.Salary: $21,840 How much is this Biweekly
4.Salary: $24,000 How much is this Biweekly
5.Salary: $28,320 How much is this Semimonthly

These are all 'divide' questions.
Can you do them now Rosey?

MelodyOct 18, 2013

+118725

Hi Rosey,
I think your real problem is with English because these questions are not that hard, especially not the first 2 questions.

1. Louis is currently earning an annual salary of $15,090 at Budget Electronics. He has been offered a job at Delta Tech at an annual salary of $16,660. How much more will Louis earn per week at Delta Tech than Budget Electronics?

Let me give you a less scary looking problem.
Louis earns $15000 every year.
He is offered a new job which will pay $16000
How much more will he get in year if he takes the new job?

I hope that you can see he will get 16000-15000 = $1000 more (it is a subtract problem)
There are 52 weeks in a year. how much extra (more) will he get each week if he gets the extra $1000 in the year?
Well that will be $1000 divided by 52

Your question is similar so i will now let you try it.

2. Sue earns a weekly salary of $350 at Howard's Department Store. Next month she will be promoted from assistant buyer to buyer. In her new position, she will be paid $895 semimonthly. How much more per year with Sue earn?
This time you will need to change each of the amounts into a yearly amount and then you can subtract.

3. Assume your present job pays a monthly gross salary of $1560. You are offered a new position that pays $8.60 per hour with time and a half for all hours over 40 per week. How many hours of overtime per week would you need to work to earn the same amount per week as your present job?
This one is harder
First work out how much will be paid at the second job if just 40 hours every week is worked. $8.60 * 40 * number of weeks in a year
Next work out how much more money needs to be earned. It will be a subtraction
Next work out how much money will be earned for 1 overtime hour at time and a half $8.60 * 1.5 = $12.90
next let x be the number of overtime hours needed.
$12.90 * x = total overtime money needed.
now solve the equation.

I hope this still reads the same when you translate it into spanish.

You said you had a better translator now. What is it? Is it a free one? I use google translator but I know it often does a poor job.

If you still need more help I will keep trying to help you.

MelodyOct 18, 2013

+118725

5(5/8 -7) = 5 * (5/8 -7)
then, do it on your calculator ,

MelodyOct 18, 2013

+259

Considering the body of the task, a linear equation should be composed. In order to do that we have to find the slope coefficient of the line, that is, tangent of the slope angle. Sin angle = 9/10 - 4/10 = 1/2, cos angle = -1/5 - 2/5 = - 3/5, tan angle = -5/6. So f(x) = -(5/6)x

scrutinizerOct 18, 2013

+118725

translation

"I just realized that what I said before was absolutely no sense, and I'm sorry! Hahaha, but yeah, if I have more questions be sure to ask me, it's hard to write in English, but it helps you get into college and stuff (: So thanks again I'll post often! With questions, because I'm to take personal finance and for me is hard."
--------------------------------------------------------

If you are interested in studying overseas (in English) when you finish school you may like to consider Sydney, Australia. My students seemed to be happy there and I thought it was a good learning environment. Of course your English needs to be reasonable first.

Si usted está interesado en estudiar en el extranjero (en Inglés) al terminar la escuela es posible que desee considerar Sydney, Australia. Mis alumnos parecían ser felices allí y me pareció que era un buen ambiente de aprendizaje. Por supuesto, el Inglés tiene que ser razonable primero.

MelodyOct 18, 2013

3x+2x+8=5x+8
5x+8=5x+8
Everything cancels out
0=0

GuestOct 18, 2013

+118725

You are correct to say that the 2 solutions are almost equivalent.

However, when I said that you omited half the answer I was referring to the fact that you found only 7/[2sqrt(3)] and failed to identify -7/[2sqrt(3)] as a solution.

I also think that you misused the word symmetrical, I think you meant that cosine is an even function. Which is certainly true. You have answered correctly for theta = +- (pi/6) +2pi* k (where k is an integer)

but you have ignored the answers when theta = (pi +- pi/6 ) + 2pi* k (where k is an integer)

For example If theta = 5pi/6

7sin ²theta + 3cos ²theta = 4 (first statement true)

sec theta + cos theta = -2/root3 - root3/2 = -7/(2root3)

So I repeat

sec theta+cos theta = +-( 2/root3 + root3/2) = +- [7/(2root3) ]

MelodyOct 18, 2013

+5478

+11

the reciprocal of a number is 1 divided by it
so the reciprocal of 6 would be 1/6

kitty<3Oct 18, 2013

+5478

+11

sry, my bad
*the prime factorization of 98

kitty<3Oct 18, 2013

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