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I used Desmos online graphing calc to aid me.

I know 2 asymtotes are x=-pi and x=pi

I know that secant isthe inverse of cos. 

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I am much more familiar with the cos function so I will work out what that muct look like.

It must cross the x axis at -pi and pi    That would be half a wavelength.  So the wavelength will be  4pi

It has a maximum at y=8 and a minimum at y=-4

So just by thinking, or sctching what I already know. I can say that (0,8) and (2pi,-4)  will be the max and min.  

     ** Or they could be (0,-4) and (2pi, 8)  but I will wory about that last.

8--4 = 12  the amplitude of the wave is 6,   The average of 8 and -4 is 2   so  y=2 will be the centre line.

So the cos functions is    y=6cos(x/2) + 2               OR      y=-6cos(x/2)+2

The sec function will be    y=6sec(x/2)+2                  or        y=-6sec(x/2)+2

OR

How many faces does the pyramid have?

Hello Guest!

\(The\ pyramid\ has\ \frac{99}{3}=\color{blue}33\ faces. \)

  !

Similar triangles

6 / 10   =   x / 9

x = 9 * 6/10

5 * 6    +     4 * 6      + 3 * 6     +     2 * 1/3 * 3 * 4

It is the area bound by the 2 zeros, which are \(s - 1 = 0 \) and \(s + 8 = 0 \). 

Anything between these ranges work, thus the answer is \(\color{brown}\boxed{-8 \le x \le 1}\)

4/3* pi *5.6^3 = 735.6185806037668392

Coulomb's Law     F= k q1 q2 / d^2         k=Coulomb's constant = 9.0 x 10⁹ N m² /C²

                             q1 =-2 x 10^-5       q2 = 4 x 10^-6   C        d = .004   m           Plug in these numbers to get the force exerted in Newtons

\(y + 1 = 4x - 4\)

\(\color{brown}\boxed{y = 4x - 5}\)

Point-slope equation:  y - y₁  =  m(x - x₁)

m is the slope:  m = 3/2

(x₁, y₁) is the point:  x₁ = 7  and  y₁ = 4

Place the values into the equation and simplify.

"At most one will arrive late" means that either:

1)  all will arrive on time, or

2)  one will be late.

The probability that any one plane arrives on time is 1.00 - 0.22  =  0.78.

1)  all ten arriving on time  =  (0.78)¹⁰

2)  one will be late but nine arrive on time  =  10 x (0.22)¹ x (0.78)⁹

          [the factor of 10 is used because the one that arrives late can be

           the first plane or the second plane or ... the tenth plane; ten ways]

To get the final answer, calculate the two individual probabilities and add them together.

55 = -16t^2 + 32t + 48

-16t^2 + 32t - 7 = 0                    Now use Quadratic Formula to solve for the t's whenthe height = 55 ,  

                                              the smaller t will be on the way UP and the larger will be on the way back down

Only square numbers without any factor pairs (other than 1 and itself) work. These are the numbers: 4, 9, 25, 49, 121, and 169, making for a total of \(\color{brown}\boxed{6}\) factors.

thx smart kangaroo

m + 1/m = 8           find common denominator    .....   multiply first term by   m/m

m * m/m   + 1/m = 8              add numerators

(m^2 +1)/m = 8

The following all have 3 prime factors, not necessarily distinct:

8 , 12 , 18 , 20 , 27 , 28 , 30 , 42 , 44 , 45 , 50 , 52 , 63 , 66 , 68 , 70 , 75 , 76 , 78 , 92 , 98 , 99 , 102 , 105 , 110 , 114 , 116 , 117 , 124 , 125 , 130 , 138 , 147 , 148 , 153 , 154 , 164 , 165 , 170 , 171 , 172 , 174 , 175 , 182 , 186 , 188 , 190 , 195 , >>Total = 48 such numbers.

Well, it would not have been fun if the water came into the house but it didn't.   I was a bit worried though I will certainly admit.

The novelty probably would also have worn off if we were cut off for too long.   

It was a lot less fun for my son, his car filled with water.  Filled might be an exaggeration but all the carpets and seats had to be removed, they were drenched.  If it had comprehensive insurance it would be a write-off but he does not have comprehanceive insurance so we will see.

We had an evacuation order. We didn't have to go but the emergency people were blaring messages over loud speakers and they went to ever house to check people were ok.   If we left we would not have been allowed back in.  At that point we would have had to leave everything, inlcuding our cars.  A lot of people stayed.  It was fun watching the kids play in their canoes and kayaks. People talk to each other more when things like this happen. That is nice.  

I am really sorry to here that. 

I know there have beens some changes to servers or some such thing lately. 

So just try again once in a while and you might get lucky.  What part of the world are you in?  This is relevant if anyone looks at your problem.  (not me, I know nothing about programing)

In the meantime, pick a username and sign your name at the bottom of your posts.

We will get to know you that way :))

You could answer this post and put your name.  That would be good  

Wow!  You have a strange concept of "fun" Melody!!  I don't think I would have found it fun at all.

ok, it is just a weirdly worded question.  :))

Thanks guys,

I was not on the forum yesterday, a very rare occurance for me.

There has been severe flooding down the east coast of Australia, some towns have been totally submerged.

It wasn't bad for me, the water just stopped short of coming in my house but I had a serious waterfront view  lol.

I was cut off and had no electricity for 2 days. 

It was actually quite fun for me.  :))

Here are a couple of photos from my house.

It is good that you had a go guest but  I do not think your method can work.

For instance, the second person may not be different from the first,  

(2 x 10⁸ ) ²   = 4 x 10¹⁶

The calculator at this site will give you the answer.