All Answers 358514 Answers

√2 *√15 = √30

We might also use a trig identity to solve this....note that sin(pi/6)*cosx-cos(pi/6)*sinx= sin(pi/6 -x)......so we have

sin(pi/6 - x) = -1/2

Since the sinθ = -1/2 when θ = 7/6pi, we can solve (pi/6 - x) = 7/6pi, and find that x = -pi. But, -pi is the same coterminal angle as pi. So x = pi is one answer (as Aziz found). As a check, note that sin(pi/6 - pi) = sin (-5/6pi) = -1/2

Also, sinθ = -1/2 when θ = 11/6pi. And in a like manner, we have (pi/6 - x) = 11/6pi, and we find that x = -10/6pi or -5/3pi. But -5/3pi is the same coterminal angle as pi/3... (again, as Aziz found). As a check, note that sin(pi/6 - pi/3)  = -1/2.

Using the identity saves a bit of work....but you also obtain answers that you must "convert" to stay within the specified interval....!!! Your choice....

Thanks, Alan...I was assuming the questioner was asking for ending zeros.......

3/8 is less than 3/4.

To find the answer, find the lowest common denominator.

To find the lowest common denominator, write down the multiples of 8 and 4.

$$8=8,16...

4 = 4, 8...$$ 

So, 8 is your lowest denominator.

Now, change 3/4 into 6/8 by multiplying 3/4 by 2.

Now, you can see that 3/4 is greater than 3/8.

You got your answer.

Sorry!!!!!!!!! I did a mistake. I will fix the mistake right now. Thanks AzizHusain.

I will re edit my post.

Sorry.

DS, remember the order of operations - pemdas --> multiplication before addition

Yeah. I have a ruler.

You can go to this website.

Because Melody didn't tell you the answer, I will tell you it.

First multiply 66 by 3.

$$66*3=198$$

Then, you add 198 by 55.

$$198+55=253$$

So, your answer is 253.

$$Answer=253$$ 

Now, you got your answer.

I am fine.

Yes, I agree with NinjaDevo. The answer is $$a^6$$. 

Steps to solve the problem:

Step 1) Change (a^3)2 into  a^3*2. 

Step 2) Multiply 3 by 2. $$a^3*2=a^6$$.

Step 3) Your answer is $$a^6$$.

Hope it helps!

First, change 3/4 into a decimal.

$$3/4 = 0.75$$ You have to change 3/4 into a decimal so it can be easier to multiply.

Now, multiply 0.75 by 2,728.

$$0.75*2,728=2,046$$ So, 2,046 addresses will be incorrect.

$$10/sin(50 degrees)=13.0540728933224117$$

You can use the calculator too.

(I didn't copy AzizHusain)

10/sin(50 degrees) = 13.0540728933224117.

Thank you! 

9^x = 27^x+1

Rewrite: 3^2x = 3^3(x+1) -->

2x = 3(x+1) -->

2x = 3x + 3 -->

-3 = x --> 

x = -3.

3 players compete result in 1 winner advancing to next round. The other two are eliminated.

27 -> 9 -> 3 -> 1

If we extend this to where the player who came second in each round was awarded double elimination. Then in the first stage we have 9 players going into the loser's bracket.

I have the following arrangement but I am unsure if it is correct.

The top image is dynamic seeding and bottom image is static seeding. The numbers are the seed numbers and the top seed is assumed to win.

3/4 of 2728 = 0.75*2728 = 2,046 --> 2,046 of the addresses on that list will be incorrect.

To find the fraction of how many dimes there are, add up all the coins.

$$4+3+2+2 = 7+4

= 11$$

Now, because you have the total number of coins, count how many dimes there are and then, write the fraction.

Answer: $$3/11$$ 

4 quarters + 3 dimes + 2 nickels + 2 pennies = 11 coins total

We are interested in finding out how much of the collection is dimes only --> 3 dimes / 11 total = 3/11.

Melody, how do I write a graph so I can write it in an answer or a question with @@LaTex?

zegroes, why did you say, "lieing like ds, huh?"

I don't know why you said that.

sin(pi/6)*cosx - cos(pi/6)*sinx = -1/2; interval [0, 2pi]

Using the unit circle, we know that sin(pi/6) = 1/2 & cos(pi/6) = sqrt(3)/2 -->

1/2*cosx - sqrt(3)/2*sinx = -1/2

If x = pi/2 --> 1/2*cos(pi/2) - sqrt(3)/2*sin(pi/2) = 0 - sqrt(3)/2*1 = 0 - sqrt(3)/2 = -sqrt(3)/2

If x = pi/3 --> 1/2*cos(pi/3) - sqrt(3)/2*sin(pi/3) = 1/2*(1/2) - sqrt(3)/2*sqrt(3)/2 = 1/4 - 3/4 = -2/4 = -1/2

If x = pi/4 --> 1/2*cos(pi/4) - sqrt(3)/2*sin(pi/4) = 1/2*(sqrt(2)/2) - sqrt(3)/2*(sqrt(2)/2) = sqrt2/4 - sqrt6/4 = [sqrt(2) - sqrt(6)] / 4 = -0.259

If x = pi --> 1/2*cos(pi) - sqrt(3)/2*sin(pi) = 1/2*(-1) - sqrt(3)/2*0 = -1/2

If x = 2pi --> 1/2*cos(2pi) - sqrt(3)/2*sin(2pi) = 1/2*(1) - sqrt(3)/2*0 = 1/2

Note: We have x = pi/3 & x = pi so far, but we can also consider 2pi/3, 4pi/3, etc.

If x = 2pi/3, we notice that we would get -1/4 - sqrt(3)/2*sqrt(3)/2 = -1/4 - 3/4 = -4/4 = 1

If x = 4pi/3, -1/4 - sqrt(3)/2*-sqrt(3)/2 = -1/4 + 3/4 = 2/4 = 1/2

If x = 5pi/3, 1/4 - sqrt(3)/2*-sqrt(3)/2 = 1/4 + 3/4 = 4/4 = 1.

So, x = pi/3 & x = pi satisfy the equation.

1 inch ≈ 2.5 centimeters.

Radiated energy is proportional to absolute temperature to the fourth power.

$$16^\frac{2}{3} = (2^4)^\frac{2}{3}=2^\frac{8}{3}=(2^6)^\frac{1}{3}\times(2^2)^\frac{1}{3} = 2^2\times(2^2)^\frac{1}{3}=4\times4^\frac{1}{3}$$

or

$${{\mathtt{16}}}^{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)} = {\mathtt{6.349\: \!604\: \!207\: \!872\: \!797\: \!4}}$$