Tetration

V = pi * r²h

pi ≈ 3.14, r is the radius, h is the heigth

"Circumference" is the linear distance around an object such as a circle. Usually, one uses "perimeter" when one discuss polygons and "circumference" when refering to closed curves and circles. 

length of rope: 16 ft

length of one side of the square: x

area of square: A_s(x) = x²

length of the "square piece": 4x

length of "circle piece": 16 - 4x

We know that: C = 2 * pi * r   =>    r = C/(2 * pi)

Area of cicle: Ac = pi * r² = pi * [C/(2 * pi)]² = pi * (C²/4 * pi²)

Ac = C²/4pi = (16 - 4x)²/4pi = 4(4 - x)²/4pi

Ac = (4 - x)²/pi

Ac(x) = (4 - x)²/pi

Pi is always the same number. It is a mathematical constant with the approximate value 3.14. The definition of pi is the ration of a circle's circumference to its diameter. 

s = 45 km    

t = 1 h, 15 min = 1.25 h (since 15 min = .25 h)

 v = s/t = 45 km/1.25 h = 36 km/h

The formula for the area is: A = pi * r²

Where r is the radius, and pi i the mathematical constant ≈ 3.14

And for the circumference: C = 2 * pi * r      =>      r = C/(2 * pi)

We combine the two formulas: A = pi * r² = pi * [ C/(2 * pi) ]² = pi * ( C²/4pi² )

A = C²pi/4pi²

A = C²/4pi

Now you just fill in for C = 45 m and pi ≈ 3.14 

An isosceles triangle where tho of the sides have the length 2x + 3, and the third side has the length 2x ?

The perimeter is 36 cm.

2(2x + 3) + 2x = 36      Solve the paranthesis:

4x + 6 + 2x = 36      Subtract (-) 6 from both sides:

4x + 2x = 30     Add the X'es together

...

...

Can you take over from here?

11/12 + (-23/28) =

11/12 - 23/28

When one subtracts (-) [ or adds (+) ] one fraction from another, one has to make common denominator (bottom).

Remember that the value of a fraction is retained when one multiply (*) or divide (:) the numerator (top) and the denominator (bottom) with the same number.

12 factorized is 2 * 2 * 3

28 factorized is 2 * 2 * 7 

We see that in order to get common denominator (bottom) one has to multiply the "12-fraction" by 7 and the "28-fraction" by 3:

$$\frac{11}{12}-\frac{23}{28}=
\frac{11*7}{12*7}-\frac{23*3}{28*3}=
\frac{77}{84}-\frac{69}{84}=\frac{8}{84}$$

Divide both the numerator and the denominator by 4:

8/84 = 2/21

Yeah, I know :)

Darn, it took me at least 5 min to find out how to solve this... :)