Alan

Use  ncr(26,4)

This is a repeat of the question at https://web2.0calc.com/questions/algebra-help_38#r1

(Max, you might want to check your answer to part ii).

I think Lag Tho's reasoning is correct, though his explanation might have been a little cumbersome!

1.  I/I₀ = 300, so R = 10log₁₀(300) decibels

2. Rearrange expression for R to get I/I₀ = 10^(R/10)  Substitute R = 120 in this.  Multiply by I₀ if you want the result in watts per meter².

This should help:

floor function:   floor(x) is the greatest integer less than or equal to x.   e.g.  floor(3.4) = 3

ceiling function:  ceil(x)  is the smallest integer greater than or equal to x.  e.g.  ceil(3.4) = 4

Total energy (TE) = Kinetic energy (KE) + Potential energy (PE)

KE = (1/2).m.v², where m is mass and v is velocity

PE = m.g.h, where g is gravitational acceleration and h is height (above pool surface).

Calculate TE at diving platform (you have already calculated the KE there).

Work out the PE at the point 6metres below the platform.

Then, because TE is conserved, you can set (1/2)mv² + PE_{at6metresbelowplatform}= TE, where v is now the velocity at 6m below the platform. This v is the only unknown, so you can rearrange the equation to find it.

Incidentally, you should really give your results with units: Joules for energy, metres/sec for velocity.

Yes. 225 is the correct result.

If you mean  \(\sum_{n=1}^{15}(2n-1)\) then the following should help:

Can you take it from here?

I think you meant to put (2+p)i + (5+q)j   (you have q in both terms!).

Anyway, here is a solution

"What are the first 10 digits after the decimal point (technically the hexadecimal point...) when the fraction 1/7 is written in base 16?"

\(x = \frac{1}{7}\\x_d=0.\overline{142857}\\x_h=0.\overline{249}\)

I'll leave you to work out the other 7 digits!!