Some people think of functions as “mathematical machines.” Imagine you have a machine that changes a number according to a specific rule, such as “multiply by 3 and add 2” or “divide by 5, add 25, and multiply by −1.” If you put a number into the machine, a new number will pop out the other end, having been changed according to the rule. The number that goes in is called the input, and the number that is produced is called the output.
You can also call the machine “f” for function. If you put x into the box, f(x),comes out. Mathematically speaking, x is the input, or the “independent variable,” and f(x) is the output, or the “dependent variable,” since it depends on the value of x.
f(x)= 4x + 1 is written in function notation and is read “f of x equals 4x plus 1.” It represents the following situation: A function named f acts upon an input, x, and produces f(x) which is equal to 4x + 1. This is the same as the equation as y = 4x + 1.
Function notation gives you more flexibility because you don’t have to use y for every equation. Instead, you could use f(x) or g(x) or c(x). This can be a helpful way to distinguish equations of functions when you are dealing with more than one at a time.
You could write the formula for perimeter, P = 4s, as the function p(x) = 4x, and the formula for area, A = x2, as a(x) = x2. This would make it easy to graph both functions on the same graph without confusion about the variables.
All you need to do is plug -5 into the second equation and you see it is near (-5, -8). When plugged into the top, you get (-5, -27/4) which comes out to ABOUT -6.75 for the Y value. The closest is actually a tie. The first option is .8 from the first and .45 from the second leading in a total distance of 1.25. The second, which is the fellow answer, is 1.2 from the first and .05 from the second, leading to 1.25 away.
The third, which is next closest is 1.8 from the first and .55 from the second leading to a distance of over 2 from the optimal, so only the first two are answers.
I need to know the dimensions to solve. Ex: "Line AC is 2.5 centimeters"
My bad - should've asked that under "Ask For Details."
Sorry :(
Answer:
A = 12√3
Step-by-step explanation:
first find the limits by finding the zeros
0 = 9 − 3x²
3x² = 9
x² = 3
x = ±![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
![A = \int\limits^a_b ({9 - 3x^2\\}) - 0\, dx](https://tex.z-dn.net/?f=A%20%3D%20%5Cint%5Climits%5Ea_b%20%28%7B9%20-%203x%5E2%5C%5C%7D%29%20-%200%5C%2C%20dx)
where b =
and a = ![\sqrt{3\\}](https://tex.z-dn.net/?f=%5Csqrt%7B3%5C%5C%7D)
A = 9x - x³ ![\left \{ {{\sqrt{3} } \atop {-\sqrt{3} }} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B%5Csqrt%7B3%7D%20%7D%20%5Catop%20%7B-%5Csqrt%7B3%7D%20%7D%7D%20%5Cright.)
![A = 9\sqrt{3} - \sqrt{3} ^3 - (9(-\sqrt{3)} - (-\sqrt{3} )^3)](https://tex.z-dn.net/?f=A%20%3D%209%5Csqrt%7B3%7D%20-%20%5Csqrt%7B3%7D%20%5E3%20-%20%289%28-%5Csqrt%7B3%29%7D%20-%20%28-%5Csqrt%7B3%7D%20%29%5E3%29)
![A = 9\sqrt{3} -3\sqrt{3} +9\sqrt{3} - 3\sqrt{3}](https://tex.z-dn.net/?f=A%20%3D%209%5Csqrt%7B3%7D%20-3%5Csqrt%7B3%7D%20%2B9%5Csqrt%7B3%7D%20-%203%5Csqrt%7B3%7D)
![A = 12\sqrt{3}](https://tex.z-dn.net/?f=A%20%3D%2012%5Csqrt%7B3%7D)