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8 sec^2 x + 4 tan^2 x − 12 = 0     →     sec^2x = tan^2x + 1

8 [ tan^2x + 1] + 4tan^2x - 12  = 0

8tan^2x + 8 + 4tan^2x - 12  = 0

12tan^2x - 4   = 0     divide through by 4

3tan^2x - 1  = 0

3tan^2x  =  1  

tan^2x  = 1/3      take the square root of both sides

tanx = ±1 / √3

And on the given interval, this happens at     pi/6 , 5pi/6, 7pi/6, 11pi/6

sin 30 ° + cos 60 ° 

sin 45 °  - cos 30 ° 

It is Paris,France. France is a country. 

https://en.wikipedia.org/wiki/Quadratic_formula

3 / (1/3)  =

(3/1)  / (1/3)      invert the second fraction and multiply

(3/1) * (3/1)   =  9/1   =  9

We are  using the property that  a^m * a^n  = a^ (m + n)   .....so....

10^-2 x 10^-8   =

10^(-2 +  -8)  =

10^(-10)

Here's my take on this one.......

Call the identifiable  boxes

A B C D E F

And I'm assuming that every crate  must contain at least one box.

We could select any 4 of the 6 boxes to put in one crate, then select 1 of the 2 remaining boxes to go into a second crate leaving the last box, by default, for the remaining crate....the number of ways to do this is :

4 1 1       6C4 * 2C1 * 1C1  = 30  ways

Or, we could select any 3 of the 6 boxes to put in one crate, then select 2 of the 3 remaining boxes to go into a second crate leaving the last box, by default, for the remaining crate....the number of ways to do this is :

3 2 1       6C3 * 3C2 *1C1  = 60 ways

Or, we could select any 2 of the 6 boxes to put in one crate, then select 2 of the 4 remaining boxes to go into a second crate leaving the last 2 boxes, by default, for the remaining crate....the number of ways to do this is :

2 2 2       6C2 * 4C2 * 2C2   = 90 ways

So....the total number of ways = 30 + 60 + 90  = 180 ways

I know how 2 subtract , add , multiply and divide fractions 

n(5)=57-43e^[-0.01(5)] =  about 16.10

(-9 1/4, -7 1/2), (-4, 5)

First, let's simplify the fractions by getting one common denominator  = 4

-[9 + 1/4]  = -[ 37/4]

-[7 + 1/2]  = -[ 15/2]  = -[30/4]

 5  = 20/4

-4  = -16/4

So  we would have

( -37/4, -30/4) , ( -16/4, 20/4)

sqrt  [  ( -37/4 -  - 16 /4)^2  + ( -30/4 - 20/4)^2  ]  =

sqrt [ ( -21/4)^2  + (-50/4)^2 ]  =

sqrt [ 441/16 + 2500/16 ] =

sqrt [ 2941/16]       we can split this up as :

sqrt [2941] / sqrt [16]  =

sqrt [2941] / 4  =

about 13.56  units

Ok, so he spent $57 to buy 3 books. Now take the $57 and divide it by 3. You should get $19. You are doing this because you need to find how much he spent to buy those 3 books. By doing so, you now take the $19 and try to find the closest number that gets to $95. Example, $19 multiply by 3, gets you $57. You want to go up a couple of numbers to get the closest number to $95. I hope I explained it well, if not I'm sorry, I'm only 13. (Honors student)

If you did everything right your answer should be 5 books will be his maximum buying range. 19 multiply by 5 gets you 95. 

1/8 pound

sqrt(54)/6  + 2/3   =

[3*sqrt(6)] / 6  + 4/6  =

[ 3*sqrt(6) + 4 ] / 6

Theres a calculator on this site....use it

Why no be smart and use metric system instead of 100 years old technology....

france

Capital "P"

Since BC meets AB at right angles, the slope of BC would be the negative reciprocal of that of AB.

The slope of AB =  [0- -2] / [ -3 - 3] = 2/-6   = -1/3

So...the slope of BC   = 3

We are looking for the measure of an angle - in this case, y -  whose sine = 2/3......so we have

arcsin(2/3)  = y  = about  41.81°

How many ways are there to put 6 boxes in 3 crates if the boxes are distinguishable but the crates are not?

You can think of this as a 3 digit number in base 6.  Each digit represents how many boxes in that crate.

There are

\(6^3=216\) 

combinations, however they aren't all distinguishable.  As there are 3 crates any given distribution of the boxes into crates is indistinguishable within a group of 3! other distributions.  

For example 312 is indistinguishable from

123, 132, 213, 231, 321

So the final number is

\(\dfrac {216}{3!} = \dfrac{216}{6} = 36\)

-10 because -8+-2 is the same as -8-2 which is the same as 0-8-2.

Hope that helps

f(x) = −3 cos(4x + π) + 6

Rewrite as

f(x)  = -3 cos4(x + pi/4) + 6

The amplitude is  l -3 l   = 3

The period - call it, m -  is found by solving this: 

4m = 2pi     divide both sides by 4   m = pi/2

The phase shift is pi/4 units to the left

Here's the graph :  https://www.desmos.com/calculator/1slz9abnpw

Paris is the capital of France.

umm...

Over a period of 120 years Bendigo produced 700 tonnes of gold.  With todat's value at around $1200 per ounce what is the value of Bendigo's gold production?

\(value = 700 ton\times ( 2,204.6lb/ton)\times (16oz/lb) \times (1200dollars/oz)=\$29,629,824,000\)

I guess the trick is to note that tonnes refers to 2000kg not lbs.