Hello from MrBillDoesMath!
Answer:
Diameter = 2r = 2 (sqrt(24/Pi))
Circumference = 4 sqrt(6Pi)
Discussion:
Given:
Area of circle = Pi r^2
24 = Pi r^2 => (as Pi r^2 is the formula for area of a circle)
24/Pi = r^2 => ( now take the square root of both sides)
r= sqrt(24/Pi)
Diameter = 2r = 2 (sqrt(24/Pi))
Circumference = 2 PI r = 2Pi (sqrt(24/Pi))
= 2Pi (sqrt(24)/sqrt(Pi) )
= 2Pi (2sqrt(6)/sqrt(Pi) )
= 4 (pi/ sqrt(Pi) ) sqrt(6)
= 4 sqrt(Pi) sqrt(6)
= 4 sqrt(6Pi)
Thank you,
MrB
The product of something means multiplying the terms together.
(2x+3) (4x^2-5x+6)
Secondly you need to distribute the terms to each other (Think of problems like FOIL)
2x * 4x^2 + 2x(-5x) + 2x * 6 + 3 * 4x^2 + 3(-5x) + 3 * 6
Then you must take into account that some of the numbers are negative. (minus-plus rules!)
2x * 4x^2 - 2x * 5x + 2x * 6 + 3 * 4x^2 - 3 * 5x + 3 * 6
Now is the tricky part of simplifying everything.
2x * 4x^2 = 8x^3
2x * 5x = 10x^2
2x * 6 = 12x
3 * 4x^2 = 12x^2
3 * 5x = 15x
3 * 6 = 18
8x^3 - 10x^2 + 12x + 12x^2 - 15x + 18
Then you group like terms.
8x^3 - 10x^2 + 12x^2 - 3x + 18
8x^2 + 2x^2 - 3x + 18
The trickiest part of this is distributing all of the terms within the parentheses, once you've done that, it's smooth sailing!
Any number that you can completely write down on paper using digits ... and a fraction bar or decimal point if necessary ... is a rational number. If you add it to 0.5, then the sum is another rational number.
