Alan

From the second of these we have x = 2y - 15  (by adding 2y to both sides).

Replace x in the first equation by 2y - 15

3y -4(2y - 15) = 40

3y - 8y +60 = 40

-5y + 60 = 40

Add 5y to both sides

60 = 40 + 5y

Subtract 40 from both sides

20 = 5y

Divide both sides by 5

y = 4

Using the fact that x = 2y - 15 we have 

x = 2*4 - 15

x = -7

The decrease in the visitor numbers on Monday = 845 - 169 =  676

This as a fraction of the number on Sunday is 676/845

To find this as a percentage just multiply by 100, so the percentage decrease is 100*676/845 = 80%

If the angle is A then its supplement is 180° - A.

180 - A = 8A

Add A to both sides

180 = 9A

Divide both sides by 9

A = 20°

If this means find the coordinates of the midpoint of A and B then you just average the two x-coordinates and average the two y-coordinates.

((8-12)/2, (20+4)/2)  =  (-2, 12)

These are just two ways of saying that y = -x.  That's all!

If d is the distance of the boat from the lighthouse then

tan(13.4°) = 239/d  or  d = 239/tan(13.4°) so the boat is d - 655 ft from the shallow reef:

$${\frac{{\mathtt{239}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{13.4}}^\circ\right)}}}{\mathtt{\,-\,}}{\mathtt{655}} = {\mathtt{348.216\: \!993\: \!063\: \!345\: \!862\: \!1}}$$

The boat is approximately 348 ft from the reef.

There is nothing to solve, but we can simplify it:

$$(\frac{81x^{-4}}{16y^4})^{-\frac{3}{4}}\\\\
(\frac{81}{16x^4y^4})^{-\frac{3}{4}}\\\\
(\frac{81^{\frac{1}{4}}}{16^{\frac{1}{4}}x^{4\frac{1}{4}}y^{4\frac{1}{4}}})^{-3}\\\\
(\frac{3}{2xy})^{-3}\\\\
\frac{2^3x^3y^3}{3^3}\\\\
\frac{8x^3y^3}{27}$$

Maclaurin series of f(x) says:

f(x) = f(0) + f`(0)x + f``(0)x²/2! + f```(0)x³/3! + ...

If

f(x) = (1 + x)^1/2 then  f(0) = 1

f`(x) = (1/2)(1+x)<sup>-1/2</sup> and f`(0) = 1/2

f``(x) = -(1/4)(1+x)<sup>-3/2</sup> and f``(0) = -1/4

... etc.

So f(x) = 1 + x/2 - x²/8 + ...

To first order this is f(x) ≈ 1 + x/2

"The way I have drawn my v-t graph from the origin to  point P  is concave up.

If this is correct shouldn't the acceleration (between the origin and P) always be positive and decreasing. "

Yes, you're right, it should.

log x^a = a*log x  so if a =1/5 then just multiply your number by 1/5.  In other words, just divide your number by 5.

 I'm sure you can do the division yourself.