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If I've understood the question correctly (that's a big if!) then there are results listed below for some small values of x.  I constructed a numerical algorithm to calculate these values.  I haven't been able to think of a generalisation (except when i = 1, in which case y_1av = (x-1)/2).

When I go to the link it says its just a "preview" of the page, and that you can either sign in or buy full access.

I probably won't be able to help you myself, but hopefully this can be corrected so others can help you out. :)

13.6363.....

2.  some things are hard to teach.

This does not seems like a question. 

It will be very useful if you draw your own picture for this.  Start by drawing an arbitrary parallelogram.  the letters ABCD must label the vertices in order either clockwise or counter clockwise.  It does not matter which is which, but this essentially guarantees that A is opposite C and B is opposite D.  Once you have this labeled you'll need segment DB in your picture so that you have angle DBC to label.  Now label the angles you know.  You know angle A=75 and C is opposite A.  In parallelograms opposite angels are congruent so C=75 as well.  Now we know two angles of that triangle because DBC is also in that triangle.  We know triangles Sum to 180 so CDB=180-75-60=45

Angle ADB is alternate interior to DBC they are congruent, therefore ADB=60

and for the equation ??

Yes!that helps lots!i never thought of it that way,thanks for this new easy way ill always remeber it!Its a great help for not losing marks becoz of some silly mistakes!Thanks for it!

Thumbs up with points from me CPhill!Thank you very much!

Yes, it is.

Think of it this way, rosala......"perimeter" is how far you travel if you walk "around" something.......

So the "perimeter" of a rectangle is just the sum of its sides.....namely W + W + L + L = 2W + 2L  = 2(W + L)

Think of "area" as a rug covering something.....in this case, a rectangle!!! And the area is just L X W...........

Does that help???

I would write out the entire decimal approximation but I would be here an infinitely long time so, for today, lets call it 3.14159, that should be enough digits to get you started

OOOHHH!NOOO! 

What a SILLY ,mistake i made!

i thought the perimeter would be lxb instead of 2(l+b)!i thought hard but still the answer in my mind came lxb!Oh no what did i do!why do i always get confused in the perimeter and area of a rectangle! Now i have lost two marks , thats soo sad!is there any way to remember them both corectly CPhill?

Now i'll never make such a mistake!

BTW thank you for the answer!thumbs up from me!

writing sinh inverse (-(48/55)) in logarithim form

$$\\\boxed{\sinh^{-1}{(x)}=\ln{(x+ \sqrt{x^2+1} }) }\\ \\
\sinh^{-1}{( -{48 \over 55} )}
= \ln{ \left(-{48 \over 55}
+\sqrt{ (-{48 \over 55} )^2+1}
\right)} \\\\
=\ln{(0.45454545455)}\\\\
=-0.78845736036$$

Add three to both sides

2sqrt(x+2)=10

Dividee by 2

sqrt(x+2)=5

Square both sides

x+2=25

Subtract 2

x=23

We need to use the cosine inverse to find the angle...

acos(.08696) = 85.011257976987°......Note that the cosine is positive in the 4th quadrant as well, so the angle might also be 360° - 85.011257976987° = 274.988742023013° 

Do an inverse cosine function.

cos x = 0.08696 goes to (acos(0.08696))= x

Plug (acos(0.08696))^-1 into a calculator

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.086\: \!96}}\right)} = {\mathtt{85.011\: \!257\: \!976\: \!987^{\circ}}}$$

x = 85.011 deg.

I suspect that Alan's interpretation might be correct, ND, but I read the problem just as you did. Therefore, I'm giving points to both answers.....it wasn't particularly clear what was meant, IMHO...

First, divide both sides by 9....this gives...

SinA = (.6/9) = (.54)

Using the sine inverse function, we can find A

asin(.54) = 32.683638846258°    But since you specified that this angle lies in the second quadrant, we have 180°-32.683638846258° = 147.316361153742°

I suspect x is meant to be the number of items purchased here. That is:

cost of apples = 3*number of apples + 6 pesos.

cost of oranges = 4*number of oranges - 5 pesos

If that is the case then total cost = 3*12 + 6 + 4*6 - 5 = 61 pesos

405° is 45° beyond 360° and tan(45°) = 1, so tan(405°) = 1.

13pi/3 is pi/3 beyond 4pi (or 2 complete rotations; i.e. 2 rotations of 360°).  pi/3 is the same as 60° and cot(60°) = 1/√3, so cot(13pi/3) = 1/√3  (=√3/3).

Here you have a right-angled triangle with the opposite side = 90ft and the adjacent side = 140ft, so you need to use the inverse tangent function  (as tan(A) = opposite/adjacent)

$${\mathtt{A}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{90}}}{{\mathtt{140}}}}\right)} \Rightarrow {\mathtt{A}} = {\mathtt{32.735\: \!226\: \!272\: \!108^{\circ}}}$$

Angle of elevation ≈ 32.7°

Let the breadth be B. Then, since the length is twice the breadth, call the length 28. And the perimeter of any rectangle is given by P = 2(W + L) where W is the width (breadth) and L is the length. So we have:

108 = 2(B + 2B)     Divide by 2

54 = B + 2B            Simplify on the right

54 = 3B                  Divide by 3

18 = B                    And that's the width (breadth)      And the length is twice that = 2(18) = 36

Check that 36 + 36 + 18 + 18 = 108    .....Yep !!!!