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translator.......

i mean check in the translator!

oh thank god!

you can replace the "cat" with "your expression" coz i was really scaredddd!

I am not angry Rosala and your cat gave me a hearty laugh 

seems like melody is angry.....

Sorry Melody!

what's the meaning of that question???

i dont know 

1.4373989364401724091

2 decimal places of that: 1.44

I took it to mean the following:

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Here's one way of looking at this:

I wrote that the solutions are real when |k|>=0.357....  I should have written that the solutions are real when |k|<=0.357... of course!

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Thanks Alan,

I do not understand what is being asked (either way) 

Can you write it out properly so that I have some hope of understanding the question please.

I am impressed with your derivation Nauseated.  I am only just starting to be comfortable with such derivatons, but why did you differentiate it in the first place?

I mean, the question is vague but nothing about finding a derivative is mentioned. 

4sin(theta)=3cos(theta)

$$\\4sin(\theta)=3cos(\theta)\\\\
\frac{sin\theta}{cos\theta}=\frac{3}{4}\\\\
tan\theta=0.75\\\\
\theta=atan(0.75)$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.75}}\right)} = {\mathtt{36.869\: \!897\: \!645\: \!844^{\circ}}}$$

Snarky comments: Anyone too dumb to use parenthetical operators in an equation is probably too dumb to understand this. However, there are others who will.

$$\; \text {Assuming}\\
\ tan(x-y) =\dfrac{y} {(1+x^2)}\; \Leftarrow \text {Find implicit derivative}\\
\ sec^2(x - y)(1 - y') = \dfrac{[(1+x^2)y'-2xy]}{(1+x^2)^2}\\
\ y' [\dfrac{ 1 } {(1 + x^2) + sec^2(x - y) ]} = \dfrac{2xy} {(1 + x^2)^2 + sec^2(x - y)}\\\\
\ y'[ 1+ x^2 + (1+x^2)^2 sec^2(x-y) ] = 2xy + (1+x^2)^2 sec^2(x-y)\\\\
\Large y'= \dfrac{2xy + (1+x^2)^2 sec^2(x-y)}{(1 + x^2) [ 1 + (1+x^2)sec^2(x-y)]} \\$$

Here's another.

$$\; \\
\ y^{\;'} =
\dfrac{-x^4\sec^2\left(x-y\right)-2x^2\sec ^2\left(x-y\right)-\sec^2\left(x-y\right)-2xy}{-x^4\sec ^2\left(x-y\right)-2x^2\sec ^2\left(x-y\right)-\sec ^2\left(x-y\right) -1 - x^2}$$

Two derivatives in the fountain which one should it be?

There isn't one.  just add degrees + minutes/60 + seconds/3600

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You can do this on the calculator as follows:

$${sec}{\left({\mathtt{\,-\,}}{\mathtt{45}}{\mathtt{\,-\,}}{\frac{{\mathtt{6}}}{{\mathtt{60}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{6}}}{{\mathtt{3\,600}}}}\right)} = {\mathtt{1.416\: \!729\: \!662\: \!099\: \!720\: \!5}}$$

.

The limit is just cos(2phi/3).

If you meant to put pi instead of phi, then the limit becomes -1/2  (as cos(2pi/3) = -1/2)

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Greetings Your Majesty:

It would seem mine compassion lacketh, but only to those who embrace the darkness of ignorance as a way of life. Such be not mine attitude to those who be just afflicted by the by. For them I be willing to help.

To expend the energy to help those who embraceth the darkness of ignorance as a way of life, may compel a weariness and apathy in well-doing that so dilutes natural compassion that it may become not effective in helping those who truly desire treatment. Compassion, as with all resources, be of limited supply. I must needs to choose to rightly divide it, lest it become useless for all.

There be a man who came to me for treatment of his arm that he injured by the sharp edge of a tree bough. He waited several days before seeking treatment and his arm became purple and black as the infection moved to his blood. I drained his wound and instilled a tincture made from a crystal often found with salt and it be called iodine.

Many times I useth this and it stopeth the infection well more often than not. I wrappeth his wound and speaketh to him that he not tend to it in any manner and return two days hence for another instilment of tincture, and he sayeth yea. But this man straightway taketh the counsel of those who embraceth dark knowledge and foolishness, and he placeth under the bandage the wing of a bat to aid and expedite the healing.

When he returneth two days hence, his arm be largely consumed with the gangrene, and the fevers of h**l taketh hold of his bode with fury. The crystals of iodine tincture haveth little power over this corruption, and in the end, I sendeth him to oblivion with rum and amputate his arm.

They who gave this counsel bear witness to this result every time, yet they continue to embrace it and persuadeth others it be true and good. For them it be a way of life.

I would ask her Majesty if this man would have done well to avoid contact with those who be willfully afflicted with the dark ignorance that be contagious?

While her Majesty would never be persuaded by their dark foolishness, I would ponder the point of having them near, except perhaps as court jesters. Their foolishness will bring weariness and drag down those who would learn from her Majesty’s wisdom and knowledge.

In your Majesty’s service.

Morgan Tud _M^-1

why can no one understand what i mean!

seems like people are getting serious day by day!

nevermind, i mean that i was reading your old wraps then i read this latest one......so....

*Melody i should be honoured by something.......how about points??*

What are you talking about Rosala?

im seriosly saying that i was checking Melodys old wraps and then i read this latest one.,..........

Melody i should be honoured by something.......how about points??

The figure shown is made up of a square & a triangle. Express the area of the figure in terms of Y

The area of a trapezoid is given by the formula

where
b1, b2 are the lengths of each base
h is the altitude (height)

b1 = Y

b2 = Y + 4

h = Y

$$area = \left(\dfrac {Y + Y +4}{2} \right)* Y\\\\\\
=\left( \dfrac {2Y +4}{2} \right) * Y\\\\
=\left( \dfrac {2Y}{2}+ \dfrac {4}{2} \right) * Y\\\\
=\left( Y +2 \right) * Y\\\\$$

@@ End of Day Wrap     Sat 7/2/15 Sydney,    Australia Time   4:45 pm       ♪ ♫  

Hello everyone,

Great answers today from CPhill, Heureka, geno3141, BrittanyJ, Sasini, Demogarcia4, sevenSins and GoldenLeaf.  A big thank you to each of you:)

Interest posts:

i getit......

when u said "at last what"

i thought melodys burning on fire!

but that smile calmed me!!!

Sun 8/2/15