Alan

Like so:

Yes.

\(U_s=\int_{s_1}^{s_2}(-kx)dx \rightarrow U_s=-\frac{k}{2}(s_2^2-s_1^2)\)

(88 + 94 + 90)*150 + p*250 = 93*(3*150 + 250)

40800 + 250p = 65100

250p = 24300

p = 24300/250

p = 97.2%

perimeter = 2*length + 2*width

so:

40 = 2*18 + 2*width

40 = 36 + 2*width

subtract 36 from both sides

4 = 2*width

Divide both sides by 2

width = 2 (cm)

I also had a problem with uploading images earlier today (and still have!).

The Uploading tab produces a blank page.

The area of this triangle may be found using Heron's formula which says:

\(A=\sqrt{s(s-a)(s-b)(s-c)}\)

where A = area, a, b and c = side lengths, s = semi-perimeter = (a+b+c)/2

You can plug in the numbers.

Let p = number of people and c = number of chairs.

If 3/4 of the chairs are filled then  (1/4)c = 6  so c = 24

 We are told that 2p/3 = 3c/4  so 2p/3 = 3*24/4   or 2p/3 = 18  so p = 3*18/2 or p = 27

There are 27 people in the room.           

Assuming P = (x, 0) and Q = (0, y)

\(x^2+y^2=13^2\)

Differentiate with respect to time

\(2x\frac{dx}{dt}+2y\frac{dy}{dt}=0\)

Substitute 12 for dx/dt and for y and rearrange

\(\frac{dy}{dt}= -12\frac{x}{12}=-x\)

Use the first equation above to replace x

\(\frac{dy}{dt}=-\sqrt{13^2-12^2}=-5\)

So Q moves at 5 m/s down the y-axis.

Possibly.  Certainly it was the only way I could make sense of the question!

The n'th term is given by \(x_n=10x_{n-1}+n\)

See below for some results: