Decimal Fractional Parts of Segment Dim's on Hypotenuses of Dissimilar Right Triangles

Submitted by BobDH on

DECIMAL FRACTIONS:
The decimal, fractional part of a positive real number is the excess beyond that number's integer part; e.g., for the number 3.75, the numbers to the right of the decimal point make up the decimal, fractional part of the positive real number 3. The decimal fractional part, .75 equals the fraction 3/4.

For sources, see links below;

https://en.wikipedia.org/wiki/Decimal?wprov=sfla1.

A tank is supplied by two pipes A and B and emptied by a third pipe C

Situation
A tank is supplied by two pipes A and B and emptied by a third pipe C. If the tank is initially empty and all pipes are opened, the tank can be filled in 20 hours. If the tank is initially full and A and C are opened, the tank can be emptied in 4 hours. If the tank is initially full and B and C are opened, the tank can be emptied in 2 hours. Pipe A supplies 50 liters per minute more than B.
1.   Find the rate of pipe A in liters per minute.

A.   120 C.   110
B.   130 D.   140

2.   Find the rate of pipe C in liters per minute.

A.   170 C.   150
B.   160 D.   140

3.   Find the capacity of the tank in liters.

A.   12,000 C.   11,500
B.   12,500 D.   13,000

Product of Areas of Three Dissimilar Right Triangles

Submitted by BobDH on

The formula below will find the product P for the areas of 3 right triangles A, B & C, as described in Geometry Post, Three Dissimilar Right Triangles.

P = (ab)^4 / 2c^2

1. Triangle C is a known right triangle, with legs "a" & "b", and hypotenuse "c".

2. a is the short leg and b is the long leg of C

3. Hypotenuse of A = 2(b) of C.

4. Hypotenuse of B = 2(a) of C.

5. Altitudes to hypotenuse in A & B
are identical to that in C.

The Formula for the Curve of a Trumpet Bell

Submitted by Abraxas on

I'm guessing this problem belongs to integral calculus:
I've been tasked with making some anvils, on a metal lathe, for the repair of brass instrument bells. I need to calculate corresponding X-Y values along the curve of that bell.One side only as it's symmetrical. I can certainly take sample measurements at frequent intervals of the bell, but I don't know how to come up with the formula for the curve that will allow me to create a chart of the thousands of points I need to accurately machine it. Any ideas ? Salamat/Thanks.

Perimeter of Right Triangle by Tangents

Submitted by BobDH on

Proposition: The perimeter of a right triangle equals the altitude to the hypotenuse multiplied by the sum of the Tan's of 1/2 the acute∠’s, divided by the product of the Tan's of 1/2 the acute ∠’s

You may say this is a non-problem, and you would be right. Simply add up the lengths of all 3 sides.

However, the proposition seeks to reveal just one of many mysterious and profound ways of mathematics.

EXAMPLE:
To demonstrate, let the 8 15 17 Pythagorean triangle be our selection.