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Simplify the following:
(12+144+20+3 sqrt(4))/(7)+5×11

sqrt(4) = sqrt(2^2) = 2:
(12+144+20+3×2)/7+5×11

3×2 = 6:
(12+144+20+6)/7+5×11

12+144+20+6 = 182:
182/7+5×11

The gcd of 182 and 7 is 7, so 182/7 = (7×26)/(7×1) = 7/7×26 = 26:
26+5×11

5×11 = 55:
26+55

26+55 = 81:
Answer: |81 THE EQUATION IS TRUE.

You need to know the time taken as speed = distance/time

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6+2/3 → 20/3

number of pieces from 1 rod: n = 3636*3/20 → 545.4

ignore waste: n = 545

number of pieces from 4040 rods = 4040*545

you can crunch the final numbers!

f^-1(a) = (a - 1)/a

f^-1(a)*a*f(a) = (a - 1)/a * a * 1/(1 - a) → -1

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Question 3.

a^2/3 = 9

a = 3sqrt(3)  and  a = -3sqrt(3)

Question 2.

This means. 2(3x + c) + 7 = 3(2x + 7) + c    or    6x + 2c + 7 = 6x + 21 +  c

I'm sure you can find c from this.

Question1.

(1,1) → (6,7) → (2,7) → (2,3) → (7,9) → (3,9) → (3,5) → (3,1) → (8,7) → (4,7) → (4,3) → (9,9) → (5,9) → (1,9) → (1,5) → (1,1)

15 different points.

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Thanks!

From Wikipedia:

"Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles."

I don't think there's a strong reason for expressing the answer this way.  You could have asked the same question if it had been expressed your way!  Sometimes it is easier to do further derivatives if the results are given in one form rather than another, but in this case either form is easy to take further it seems to me.  Certainly, there is no general rule I'm aware of that specifies what form such a derivative should take.

Like so:

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Hi Alan,

Yes I know these are the same, my question was more... would there be a specific reason to give the result as:

ae^-kx(k²x-2k)

Both k²x-2k and kx-2 are suitable for finding the inflection point, so I'm just curious if there is some specific reason to list it that way (typically I just factor everything I can). 

A brute force and ignorance calculation shows you to be correct Chris.

There are 91 numbers in the range that are divisible by both 9 and 11

However, the sum of their digits is 18 for all but one of them (the odd one out is 9999, the digits of which sum to 36).

The digital root of each of the 91 numbers is 9 of course.  (For the digital root you keep summing the digits until you are left with a single digit.)

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6 divided by 3/8 is the same as 6 multiplied by 8/3:   6*8/3 → 2*8 → 16

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These two expressions are the same:

ake^-kx(kx-2)

ae^-kx(k²x-2k)

If you factor a k out of the parentheses in the second expression you get the first expression.

Okay simple mistake (forgot a - sign).

My answer however ended up being.

ake^-kx(kx-2)

And the answer in the book is:

ae^-kx(k²x-2k)

Is it standard practice to keep 'like' terms together to make it simplier to find 3rd derivatives/inflection points? (the original function is actually the first derivative, so here we were finding the 2nd derivative). 

in order to add two fractions they have to be simmilar.  9/1+25/4 are not the same denominator. 9x4=36 1x4=4 therefore

-36/4-25/4=-11/4

Depending on your equation, there are different ways to create a fraction.

The simplest way is just to put a "/" in the typing bar. Above, you will see the fraction appear. 

If you have a complex equation, you should probably use parentheses to make sure the fraction you want is correct. 

You could just plug the equation in the Calculator.

FOR HOW MANY YEARS???!!

(P1V1)/(T1)=(P2V2)/(T2) for T2 Cross multiply

T2 = (P2 T1 V2)/(P1 V1)

19,000 = 9,500.e^(4r) divide both sides by 9,500

2 = e^(4r) take the ln of both sides

0.693147180=4r divide both sides by 4

r=17.33% compounded continuously=18.92% effective annual rate.

Solve:     x² + y²  =  26     and     x + y  =  6

Solve the linear equation for either  x  or  y:     x + y  =  6     --->     y  =  6 - x

Replace this value into the other equation:     x² + y²  =  26

                                                                        x² + (6 - x)²  =  26

Simplify:                                                 x² + 36 - 12x + x²  =  26

                                                                    2x² - 12x + 36  =  26

                                                                    2x² - 12x + 10  =  0

Divide by 2:                                                       x² - 6x + 5  =  0

Factor:                                                            (x - 5)(x - 1)  =  0

Solve:                                                                    x = 5     or     x = 1

Substitute these values into the other equation:

     x = 5     --->     x + y  =  6                                    x = 1     --->     x + y  =  6

                             5 + y  =  6                                                           1 + y  =  6

                                   y  =  1     --->     (5, 1)                                        y  =  5     --->     (1, 5)