NEED HELP REAL FAST BROS

I need some explanations for these problems:

1)the difference of a number and its square is 56. find the number.My teacher said it was 5/3. I want to ask how did he got that, please provide an equation.

2) The altitude of a traingle is 2m less than the base. The area of the triangle is 84m^2. FIND the base.

3) Theresa is crocheting an afghan that is already 30in. wide by 40in. long. If she continues to crochet by increasing the width and the length by then same number of inches until the afghan's area is doubled, what will be the new dimensions?

4) The height, h, of a riht circular cylinder of a given volume is inversely proportional to the square of the radius, r. Translate each statement into a formula. Use K as the constant of varation where needed

Please, I really need help and exaplanation along with some equations FAST! Thanks!

Sorry it ain't pretty, I don't have Word.

1) The difference between a number (x) and that number squared (x^2) is 56.

x^2 - x = 56.
x^2 - x - 56 = 0.

Factor; it comes out clean.
(x - 8)(x + 7) = 0.

So, when x is -7, or 8, the above is true. (Don't know why you say 5/3.)

2) Given the area and the height, find the base.

Area = .5 * Base * Height.
This is the formula for the area of triangles

You're given the Area as 84 square meters and the height, or altitude, as Base - 2 meters.
Therefore,
84 = .5 * (B-2) * B
So, solve for B:
168 = B^2 - 2B (or) 0 = B^2 - 2B -168.
Use the quadratic equation or factor to find B as either 14 or 12.

3) Given (30x * 40x = 1,200 square inches), where 30x is the width and 40x is the length, find x, the change, when the area equals 2,400 square inches.
So...
30x * 40x = 2,400.
1,200 * x^2 = 2,400.
x^2 = 2.

x equals the square root of two.
Hence, the new length, 40x, is 40 * sqrt(2) inches.
And the new width, 30x, is 30 * sqrt(2) inches.

4) First, goto Inversely Proportional -- from Wolfram MathWorld for the definition of IP.
Given the Height as inversely proportional to Radius^2,
Height = Konstant/Radius^2
And Volume = Height * Pi * Radius^2
Combine these formulas,

To do this, you are given Height, so substitute it into the volume formula.
Volume = (Konstant/Radius^2) * Pi * Radius^2

Then simplify,
Volume = Konstant * Pi

So....V = K * Pi is your answer, your formula. @MagixAries

NEED HELP REAL FAST BROS

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