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∫(1/x) dx =  ln x  + C

Note that if we differentiate ln u + C, we have  .......(1/u)du....and if we substitute x for u, we have (1/x)(1) = 1/x....which is the fuction in the original integrand.... !!!!

Try looking here.

1 and 30

2 and 15

3 and 10

5 and 6

I was puzzled at first, but then realised the clue was in the title!

Thanks, Alan....I couldn't make heads or tails of that one......!!!!

I think this might be asking for the value of the 14th term of the expansion (p + q)¹⁷, where p = 0.15 and q = 0.85.

$${\left({\frac{{\mathtt{17}}{!}}{{\mathtt{3}}{!}{\mathtt{\,\times\,}}({\mathtt{17}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{0.15}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{0.85}}}^{\left({\mathtt{17}}{\mathtt{\,-\,}}{\mathtt{3}}\right)} = {\mathtt{0.235\: \!856\: \!391\: \!573\: \!379\: \!6}}$$

Thanks Alan,  I knew this existed but I have never used it.  :)

Geno's answer appears to be good but I think you left some info out of your question.  :)

There is a function called the Gamma function, defined as follows:

                                             $$\Gamma (t)=\int_{0}^{\infty}x^{t-1}e^{-x}dx$$

When t is a positive integer this is equal to (n - 1)! but the Gamma function is defined for all values of t, so it is sometimes thought of as the extended factorial function.  

So 5.6! would be calculated from Γ(6.6) (≈ 344.702...)   (5! = 120,  6! = 720)

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You are not the first surgeon to k**l a patient. Remember they get to bury their mistakes;  mathematicians get to erace theirs. This is the lament: remembering to use a pencel and not a pen.

Yea - I don't have a machete 

My tools are much more refined   LOL

Your "machete" is sharp enough, Melody.......mine needs to go back for a little more honing.......

My "machete" made a hash of that one !!!!

Me or Chris?

Assuming we're taking the % increase on the birth weight, we have

(New - Old) / Old =

(4.7 - 3.2)/ 3.2 = 1.5 / 3.2 = about 46.9%

You are a surgeon with numbers; just sharpen your machete :)

You can't take away my points to you.  It is not polite to throw a gift in the bin!

Nope....I'm "zapping" myself for that stupid error......I should have checked my work more closely !!!!

Assuming that "s" represents the number of tires and c represents the number of cars, we have.....

120 = (1/100)c      multiply both sides by 100

12000 = c

This doesn't make much sense to me......but I can only work with what I'm given !!!

It wasn't much of an error Chris, you didn't need to take your points away! I'll give them back to you.   :)

96-{10+4[-3+8-(11-15) (10-6)]}  .....  whew!!!!   Let's simplify this

Working inside the parentheses, we have

96-{10 + 4[-3 + 8- (-4) (4)]}      next, work within the brackets......  remember to carry out multiplication before addition or subtraction !!!

96-{10 + 4[-3 + 8 + 16]}        add/subtract within the brackets

96-{10 + 4[21]}                     now, work within the braces

96-{10 + 84}

96 - {94}  =

2

Mmmmmm...all that work for just 2  !!!!!!

$$\frac{d}{dx}sec^2x\\\\
=\frac{d}{dx}(cosx)^{-2}\\\\
=-2(cosx)^{-3}(-sinx)\\\\
=-2(cosx)^{-3}(-sinx)\\\\
=2(cosx)^{-3}(sinx)\\\\
=\frac{2sinx}{(cosx)^{3}}\\\\
or\\\\
=2tanx\;sec^2x$$

 or

$$\\2tanx(tan^2x+1)\\\\
or\\\\
2tan^3x+2tanx$$

I got a different answer from Chris - I haven't checked it

I assume, by "length," you mean "arc length"...if so, we need to find the radius , first.......

So we have

s = rΘ   where s is the arc length and Θ is in radians........so converting 43° to radians, we have about .75 rads.

So, the radius is given by

r = (7 cm)/.75 = 9.33cm

And the area is given by:

A = (1/2)r²Θ    where  Θ is in radians..........so we have

A = (1/2)(9.33cm)²(.75) =  about 3.5cm²

To right there mate!

d/dx(secx)² = (using the chain rule)

2(secx)(tanx)²

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Edit..........

Whoops...... I made a slight error......

The derivative of the sec x = sec xtanx...so the final result should be, as Melody said,

2(secx)(secxtanx) = 2tanx(secx)^2

Thanks, Melody, for catching my error !!!!!!