Alan

This can be tackled as follows:

Here's the answer for (a):

I'll leave you to try the same approach for (b).

Here's my solution to 1.

I hope that's right!

a + b + c = 5.     (1)

Divide (1) by b + c:    a/(b+c) + 1 = 5/(b+c).  (2)

Divide (1) by a + c:    b/(a+c) + 1 = 5/(a+c).   (3)

Divide (1) by a + b:    c/(a+b) + 1 = 5/(a+b).   (4)

Add (2), (3) and (4): a/(b+c) + b/(a+c) + c/(a+b) + 3 = 5*6

Hence  a/(b+c) + b/(a+c) + c/(a+b) = 27

Could also simply do the following:

\(\text{If }\lambda=\mu\text{ then }\frac{1}{2}\lambda=1-\mu\text{ becomes }\frac{1}{2}\lambda=1-\lambda\\ \text{ so } \frac{3}{2}\lambda=1\text{ or }\lambda=\frac{2}{3}\)

Deleted. Just noticed my semicircles weren't fully inscribed!!
 

Simply set y = 0 (as the ground is at height 0) and solve the resulting quadratic equation for t.

Use Pythagoras to find the square of the length of the line between the two points as:

(y - 5)² + (-6 - 2)²

Set this equal to 10² and solve for y.

First rewrite the equation by collecting all the terms on one side:

x - 3 + lnx = 0

Can you take it from here?

Decibels use base 10 logarithms, so: