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2.) Find the value of the constant A so that y = Asin3t satisfies the equation d^2y/dt^2 + 2y = 4sin3t 

I assume this is

d²y/dt² + 2y= 4sin3t

If y= Asin3t

dy/dt = 3Acos3t

And  

d²y/dt²  = -9Asin3t

So

d²y/dt² + 2y= 4sin3t

-9Asin3t + 2(Asin3t) = 4sin3t

-7Asin3t = 4sin3t

A = -4/7

I'm going to amend Melody's answer a bit

cos x  = ±1/√2    at   pi/4 ± n (pi/2)

Using the Pythagorean Theorem, we have

AB² + BC² = AC²

5² + 8² = AC²

25 + 64  = AC²

89 = AC²

√89  = AC

C(15,3)  = 455 different committees

So...I assume we have   

780x = y   and

.08(y + x ) = 3,000,000     ????

Divide the second equation on both sides by .08

y + x =  37,500,000     (2)  

And since 780x = y, let's substitute this  into (2)  for y

780x + x = 37,500, 000

781x  = 37,500,000     divide both sides by 781

x = about 48015.3649167733674776

And using (2) to find y, we have

y + 48015.3649167733674776  = 37,500,000

y = about 37,451,984.6350832266325224

Yes it is very important. 

If you understand it there is really nothing to remember but it makes many trig problems much easier.

So put some effort into understanding what it represents.

Here is a clip on it

$${\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{{\mathtt{2}}} = {\mathtt{28.274\: \!333\: \!882\: \!308\: \!139\: \!1}}$$     cm^2

1.) Find all values of x for which the line that is tangent to y = 3x - tanx is parallel to the line y - x = 2

ALWAYS remember that when you differentiate you are finding the gradient to the tangent of a curve

$$\\y=3x-tanx\\
y'=3-sec^2x\\\\
y-x=2\\
y=x+2\\
y'=1\\\\
1=3-sec^2x\\
-2=-sec^2x\\
2=sec^2x\\
\frac{1}{2}=cos^2x\\
cos x = \pm\frac{1}{\sqrt2}\\
x= n\pi\pm \frac{\pi}{4}\qquad n\in Z$$

8^5

The hat or caret   ^   is the symbol for power of

$${{\mathtt{8}}}^{{\mathtt{5}}} = {\mathtt{32\,768}}$$

Where is your working Bertie LOL

Don't worry, I'll take your word for it :)

I didn't know that,  thanks Alan.

Thanks guys,

sometimes it pays to finish a question. 

I suppose it also pays to look at a question sensibly before plowing headlong into the algebra   :)

Thanks Alan,

I like this question :)

Thanks Chris :)

I got it. I think I really have got it. 

I  hope these probability/combination/permutation questions keep coming in, I want more practice .    

Thanks again Bertie :)

life of pi is a movie about a boy who survives a shipwreck ona little boat with a tiger

Math is a wonderful thinggg, math is a really cool thingggg, lets get out your books and do some math... mathh mathhh mathhhh

Usually divide by 2.

Divide 2800 by 12. Then multiply that answer by 2.30. That's the formula. Now do it yourself.

Studies may show its 21 and it may be true but come on we all know when you add 10 and 9'its 19. You learn it in 1st or 2nd grade.

I only play Xbox. I wish I had a good computer to play minecraft pc.

It's my best subject but not very fun but not bad either.

 6÷2 (3)+4

6/6+4

1+4=5

Operate on the () first.