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1/4 * 8  =   8/4  = 2

You have 6 colours in a row and you want to choose three of them

6C3 = 20

Thanks for responding  Andre. 

So are you saying that at some point in the foreseeable future you will/may be forced to close this site ?

And that this is largely due to 'privacy' law changes supported by very large 'silicon valley' companies designed to squeeze the small site owners out of operation?

It will be a sad day if that happens.  

Hi Elijah,

Sorry that this service uses ad-block detection, but a service like this requires some sort of revenue to pay eg. for the servers and legal fees.

For example Firefox blocks ads if "Enhanced Tracking Protection" is enabled, even if no additional ad blocking extension is installed:

Here is what most users do, they click on "Disagree" in the cookie consent dialog. This choice does not allow the use of cookies for marketing purposes and therefore this website then can't load/show Google ads. Without Google ads of course there is no ad-block detection and you won't get the ad-block message.

Because of all this ad-blocking and privacy related changes (cookie consent dialog..), operating a website based on ads has no future. Since like 4 years every year the ad revenue drops like 50%, now to a point where showing ads almost does no longer make sense. But no problem if all those small websites go out of business as a result of protecting the users privacy, because the multi trillion dollar companies from the silicon valley will love to replace those websites and sure they will love to protect the users privacy..

Hello, I hope this answers your question.

From reading, here are the useful facts to solve this question:

1-A windmill is a device for extracting kinetic energy from the moving air.

2- kinetic energy in the wind is turned into electric energy. Denote kinetic energy: $E_k$ and electrical energy: $E_e$

3-Suppose that when the wind blows at 5.0 m/s the kinetic energy per unit time that blows past a windmill is 0.50 MJ/s

Let the initial speed: $v_{initial}=5.0 m/s$, and given the initial kinetic energy, $E_k=0.50*10^6 J$ 
Hint: (Although the text is talking about power and energy, they are the same here due to "1 second" (Since P=E/t -->P=E if t=1))

By the Kinetic Energy equation:

$E_k=\frac{1}{2}mv^2$, we can find the mass, m of the air. $m=\frac{2E_k}{v^2}=\frac{2*0.50*10^6}{(5.0)^2}=40 000 kg$     (1)

4-Windmills cannot capture all the kinetic energy from the air passing. 

From this, we deduce that windmills are not 100% efficient (Thus, we will use the equation of Efficiency), and the text explained this further:

5-The maximum possible efficiency of a windmill is called the Betz limit. Given, the theoretical Betz limit: 16/27 of the kinetic energy of air passing through it.

Now to the question:
Suppose that the wind speed increases to 10.0 m/s  (Denote, $v_{final}=10.0m/s$)

If the windmill we considered before can operate at 80% of the Betz limit, how many megawatts of power does it produce?

It is crucial to note from this, that it is the same windmill, thus the following is an accurate assumption in solving: mass of air passing through the windmill blades is constant, as found in (1) -->40000kg.

Applying the efficiency equation: $Efficiency=\frac{E_e}{E_k}$

Given, the efficiency is 80% of the betz limit -->$0.80*\frac{16}{27}=0.47407407$ is the efficiency.

$E_k=\frac{1}{2}(40000)(10^2)$ $=2.0*10^6 J$

Thus, $E_e=0.47407407*2.0*10^6=948148.14 J$

Recall, this is the energy per second hence the power.

So the question wans the final answer to be in megawatts:

$948148.14J/s=948148.14W=0.94814814MW$

Which can be approximated to be: $0.95MW$

I am not a statistician but I do not see how this can be answered.

Is there any more information that you have not included?:

$\frac{31}{52}*\frac{4}{51}*\frac{3}{50}=\frac{31}{11050}$

Answer: $2\sqrt6$ and $-2\sqrt6$

Solution:

Multiplying both sides by 3y gives:

$y^2 + 3y = 3y + 24$

Subtracting both sides of the new equation by 3y gives:

$y^2 = 24$

Isolating y gives:

$y = \pm \sqrt24$

The square root of 24 can be simplified into $2\sqrt6$. So y can be $2\sqrt6$ or $-2\sqrt6$.

What about 34?!? 

84 - 14 - 12 - 24 = 34

thanks!

Using CRT + MMI

m = 5 (mod 6)

m = 4 (mod 7)

m = 3 (mod 8)

m = 2 (mod 9)

m = 1 (mod 10)

Product(6, 7, 8, 9)==3,024

m ==2,520k  +  11, where k==0,1,2,3........etc.

m==2,520 is smallest integer that satisfies all 5 congruences. The next number would be: 2,520 x 2 ==5,040.

1 - Since we know the bond's price, its maturity and its par value at maturity, we can easily figure the yield to maturity, at which it was purchased, like this:

2 - [1,000 / 214.55]^(1/20) ==1.08 - 1 x 100 ==8% -bond's yield to maturity

3 - Will use this simple FV formula to find its value 5 years from now: FV ==PV x [1  +  R]^N ==214.55 x 1.08^5 ==214.55 x  1.4693280768 ==Rs 315.24 - bond's value 5 years from now. 

Since it's a zero coupon bond, there's no interest rate. But you can only cash it out after 20 years to make up for that interest. We already know you can only cash that bond out after 20 years. The growth should be linear.

The US Treasury states that:

However, if you hold the bond to its 20-year maturity, your return will jump considerably to a compounded rate of return of roughly 3.5% per year. This is because the U.S. Treasury guarantees that an investment in a Series EE bond will double in value after 20 years.

3.5% per year. We'll assume that you this zero interest bond grows according to the normal interest rate.

Use the equation  A = P(1 + rt), and figure it out. 

Also, since you're using Rupees as your currency, maybe you need to convert to USD or Euros.

In triangle PQR, PQ=13, QR=14, and PR=15. Let M be the midpoint of QR. Find PM.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PM = [sqrt(2 * 13² + 2 * 15² - 14²)] / 2

PM = 12.16552506

X = 0

1+1/x=0

x+1=0

x=-1

1+1/(1+1/x) = 0

1 + 1/x + 1 = 0

2+ 1/x = 0

2x +1 = 0

2x = -1

x = -1/2

0+(-1)+(-1/2)=-3/2

Ah. I constantly forget to pay attention to the details. Thanks for the heads up!

Welcome to web2.0calc. :)

Nice solution, but it says raised to the 8th instead of 2nd. 

To get the constant term, we need 4 "6x" and 4 "1/(3x)". 

Using the binomial theorem, the coefficient is 8C4 = 70.

70 * (6x)^4 * (1/(3x))^4 = 1120

=^._.^=

$\fbox{42}$

Try contacting google/firefox/safari/whatever browser you're using tech support. 

this has never happened before and its still persiting after i turned my ad blocker off

Use Law of Cosines for all three problems and you should get the answer pretty quickly.

$\angle A = \frac{5\pi}{6}$

$\angle D = \frac{\pi}{2}$

$\angle G = \frac{\pi}{4}$

Doesn't seem legit to me. Normally ad blockers use a webscraping script to identify ads whenever you open a page, and it should be done as soon as soon as the page loads. If it still persists, delete this adblocker and get a new one.

Alright, let's break this down by simplifying it.

$(6x+1/3x)^2$

$=(6x+\frac{1}{3x})^2$

Now we can apply the formula

 $(a+b)^2=a^2+2ab+b^2$

or in this case,

$(6x + \frac{1}{3x})^2 = 6x^2+2(6x)\frac{1}{3x}+\frac{1}{3x}^2$

which will become:

6x^2 + 4 + 1/3x², since 2*6x is 12x, and 12x+1/3x is 12x/3x. Divide by 3x and you get the answer, $\fbox{4}$

i cant even enter an equation i get this seconds after opening the site. This forum works though.