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for example, if \(3*\sqrt{6}= 3\sqrt{6}\)

this sounds familiar... almost like a plane hiting a building... or was it two... what if the question stated 3 planes intersected 2 rectangular prisms :0 XD

Proof by induction:

n = 1:     256^1 - 1 → 255 → 15*17  hence divisible by 17

n → n+1:    256^(n+1) - 1 - (256^n - 1) → 256^n*(256 - 1) → 256^n*15*17  hence divisible by 17

The length of diagonal EK is sqrt(5^2 + 4^2) ≈ 6.403m

Hence perimeter = 2*(12 + 6.403) → 36.8 m (to the nearest tenth of a metre)

.

width = x

length = 2x

perimeter = 2*(2x+x) → 6x

6x = 42

x = 42/6 → 7 cm

.

Here is another maybe better pic

Which intersection forms a parabola?

1.) A plane intersects only one nappe of a double-napped cone, and the plane is parallel to the generating line of the cone.   Umm  What is the generating line of a cone?  idk  

a generator is a (any) straight line which runs from the apex of the cone to the base 

Yep it must be this one becasue the plane has to inersect with the base of the cone.

This is really confusing though ://

2.) A plane intersects both nappes of a double-napped cone, and the plane does not intersect the vertex.  Nope - not this one! That would be  hyperbola

3.) A plane intersects only one nappe of a double-napped cone, and the plane is not parallel to the generating line of the cone.   This would be an ellipse!

4.) A plane intersects only one nappe of a double-napped cone, and the plane is perpendicular to the axis of the cone.  No that would be the circle

the answer is provided in the site that I have referenced below :)

This is what you must remember.

\(y=a*cos[b(x+c)]+d\\~\\ \text{a is the amplitude}\\ \text{d is the vertical shift}\\ \text{c is the horizontal, or phase, shift}\\ \text{and last but not least, the period is}\frac{2\pi}{b}\\ \text{The angle is in radians}\\ \)

If you remember that then these questions become almost trivia.

Sine functions work the same way.

How do I find the equation of a cosine function with a maximum of 3, a minimum of -3, and a period of 4?

lets see

y=3cos b(x+c)

c can be any constant becasue you have not mentioned phase shift.

where period = 2pi/b

\(\frac{2\pi}{b}=4\\ \frac{\pi}{b}=2\\ b=\frac{\pi}{2}\)

so it is

\(y=3cos[\frac{\pi }{2}(x+c)]\)

check (here is your graph )

By the way, simplifying these expressions has nothing to do with calculus.

Do you mean something different?  Maybe you want them differentiated or integrated?

I think I will let you comment before I play with any more of them.

Hi,

Firstly you cannot get a solution becasue there is no equal sign.

All you can do it try to simplify them :)

I am confused about what the actual questions are.  

I assume there are a number of powers here.

23: sec4 (x) - tan4 (x)

I assume

\(sec^4 (x) - tan^4 (x)\\ \qquad \text{Difference of 2 squares}\\ =(sec^2 (x) + tan^2 (x))(sec^2 (x) - tan^2 (x))\\ \qquad sec^2x=\frac{1}{cos^2x}=\frac{sin^2x+cos^2x}{cos^2} =tan^2x+1 \\ =(1+tan^2(x) + tan^2 (x))(1+tan^2x- tan^2 (x))\\ =1+2tan^2(x) \\ \)

Are you talking about me, Question?

I do not understand what you are asking :/

3825=1750e^.23t

\(3825=1750e^{0.23t}\\ \frac{3825}{1750}=e^{0.23t}\\ 2.187514286\approx e^{0.23t}\\ ln{(2.187514286)}\approx ln{e^{0.23t}}\\ ln{(2.187514286)}\approx 0.23t\\ t \approx \frac{ln(2.187514286)}{0.23}\\ \)

t= ln(2.187514286)/0.23 = 3.4033298694398451

Now you already know CPhil, after a couple of milllion years Red got tired of being red, he wanted a new look so together we died him green!  Green goes better with MY red glasses that Red stole from me too!

I bit of trivia here:

In Australia red headed men are often nicknamed 'bluey'. 

May, you cannot multiply two dollar amounts together. It does not make sense. 

The second graph......the circle's center is (2, - 6)   and the radius   =  2

what is log10

log 10 base 10 is 1 because   \(10^{1}=10\)

 \(log_{10}10=1\)

only negative numbers are less than negative numbers.

Think about a number line.

Hey, MJ.....shouldn't Melody's dinosaur be named, "Green??".......LOL!!!!!

y = a(r)^x      divide both sides by a

(y / a)  =  r^x     take the log of both sides

log ( y / a)  =  log r^x       and by a log property we can write

log ( y / a)  =  x * log r      divide both sides by log r

log ( y / a)  / log r    =   x

And Melody's Is a photo of her pet dinosaur named Red

(not trying to speak for you Melody )

My avatar is "Aflred E Neuman" from "MAD" magazine......his image is readily available online....!!!

It is a letter of the alphabet :)