<em>The function uses W as the variable but the options show only x's as the variable, so I'm asumming W in the answer</em>
Answer:
0 < W < 50
Correct option: A
Step-by-step explanation:
<u>Domain of functions</u>
Some functions have restricted values of the independent variable x. It can be due to mathematical restrictions, like dividing by 0 or taking the square root of a negative number, of it can be due to practical conditions of the situation being modeled.
In this case, the area of a rectangle is given by the quadratic function.
![A=50W - W^2](https://tex.z-dn.net/?f=A%3D50W%20-%20W%5E2)
Since the area of a rectangle cannot be negative (and should be positive, though it could be zero), the practical domain of A is determined when
![50W - W^2\geq 0](https://tex.z-dn.net/?f=50W%20-%20W%5E2%5Cgeq%200)
Taking common factor W
![W(50 - W)\geq 0](https://tex.z-dn.net/?f=W%2850%20-%20W%29%5Cgeq%200)
Since W must be positive W>0
![50 - W\geq 0](https://tex.z-dn.net/?f=50%20-%20W%5Cgeq%200)
Or equivalently
![50 \geq W](https://tex.z-dn.net/?f=50%20%5Cgeq%20W)
![W \leq 50](https://tex.z-dn.net/?f=W%20%5Cleq%2050)
The total interval is
![0 < W](https://tex.z-dn.net/?f=0%20%3C%20W%3C50)
Correct option: A
Please note: The real restriction should be
![0 < W\leq 50](https://tex.z-dn.net/?f=0%20%3C%20W%5Cleq%2050)
if we allowed the area to be positive, but I'm providing the most possible correct available option
Answer:
1 / (3 - √x³)
Step-by-step explanation:
∛x = x^1/3
^1/3 means the exponent is 1/3
then the derivative is:
d/dx ∛x = d/dx x~1/3 = 1/3*x~(1/3 - 1) = 1/3 x~-2/3 = 1/3 * (1/√x³)
= 1 / (3*√x³)
Hope it helps.
For the first one its a slope of -2/3
The second one is 4/5
and the third one is -1/7
Find out what 1 Foot per centimeter is (1.5 centimeters per foot)
Multiply 13 by 1.5 to find one side and 24 by 1.5 to find the other side