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$${\mathtt{9}}{\mathtt{\,\times\,}}{\mathtt{24}} = {\mathtt{216}}$$ hours

18=b-7b

18=b(1-7)

b=18/-6

b=-3

Assuming we're dealing only with integers, the first perfect cube after 100 is 125 = 5^3

The last perfect cube before 900 is 9^3 = 729

So, that's 5 perfect cube integers between 100 and 900.

is it acually possible to derive e? isnt it just a number? 

can you explain the number e in words? like pi would be describe as the perimeter of a circkle if the diameter is 1 but what would you say about e?

c has the greatest rate of change, which can be determined by the slope in y=mx+b

a. slope=2  y=2x-2

b. slope=4/3 y=(4/3)x+1

c. slope=2.5

-9 x [25+ (-23)]

-9(2) = -18

43=3d-2

45=3d

15=d

x+1=69

subtract 1 from both sides

x=69-1

x=68

3y=6x-1

divide both sides by 3.

y=2x-(1/3)

Slope is the number in the position of "m", in linear equation y=mx+b

Slope= 2

$${\mathtt{45\,845\,215\,681}}{\mathtt{\,-\,}}{\mathtt{548\,458\,145\,565}} = -{\mathtt{502\,612\,929\,884}}$$

Nevermind, I know how to do this question. Thanks and sorry for wasting the space.

Well i got the first bit all right.

But the algebra bit i got 2 wrong.

But atleast i learnt something.

Also, Melody i will start a new post the second i got a new question.  

her interest rate is over 9000 

Wow never knew it could be solved so easily when you just find the equal opposite of it and/or making sure it adds up to 180.

Thanks CPhill & Melody.

I will try this and hopefully get most of it right.

The circumferebce is the technical name for the perimeter of a circle, the distance of the outside edge of a circle. It can be found using the equation;

2*Pi*r=C      (2 * Pi * Radius= Circumference)

Radius= Diameter/2

I looked for a way to get the sin and cos terms the "same" in some sense, and I could see that if we had integer multiples of some common angle we could expand the result to get both in terms of the one angle.  

There might well be a more straightforward way of doing the integral!

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Thanks, Alan.....

Here's a picture of the vectors for the cross-product:

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Melody has given the dot product - a scalar - of these two vectors...

However....if the cross-product was wanted, we have

(-1,-1,3) x (-1,0,2) = (u1, u2, u3) x (v1, v2, v3)  = (s1, s2, s3)

s1 = [-1*2] - [3*0] = -2 - 0  = -2

s2 = [3*-1] - [-1*2]  =  -3 - (-2)  = -3 + 2 = -1

s3 = [-1*0] - [-1* -1 ] = 0 - 1  = -1

The cross-product produces a vector in three-space that is perpendicular to the given vectors, namely..... (-2, -1, -1)

Nice "double-substitution,"  Alan.

P.S -  How did it occur to you to let cos(x/3)  = cos(2Θ)   and sin(x/ 2) = sin(3Θ)  ???

19.  Use the fact that the stored energy is (1/2)*Q²/C  where capacitance  C = εA/d

 and ε is permittivity, A is area and d is distance between plates.

You can work out Q from the fact that you are given the number of Coulombs per unit area (specified in terms of microCoulombs per unit area)) and you know the radius of a plate so you can find its area. 

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See graph:

a ≈ ±38.816

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Thanks Alan. :)

Thanks....Nauseated.....I'll have to plow through that....

Now......

What if N distinguishable b***s were rolled along all the possible "right and up" paths of a 6 x 6 grid  ???

.....eh, never mind....

 We'll let some other SOB figure that one out......

For the first integral:

This should be carefully checked as I tend to be a little cavalier with constants sometimes!

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