Answer:
(a) 4.98x10⁻⁵
(b) 7.89x10⁻⁶
(c) 1.89x10⁻⁴
(d) 0.5
(e) 2.9x10⁻²
Step-by-step explanation:
The probability (P) to find the particle is given by:
(1)
The solution of the intregral of equation (1) is:
![P=\frac{2}{L} [\frac{X}{2} - \frac{Sin(2\pi x/L)}{4\pi /L}]|_{x_{1}}^{x_{2}}](https://tex.z-dn.net/?f=%20P%3D%5Cfrac%7B2%7D%7BL%7D%20%5B%5Cfrac%7BX%7D%7B2%7D%20-%20%5Cfrac%7BSin%282%5Cpi%20x%2FL%29%7D%7B4%5Cpi%20%2FL%7D%5D%7C_%7Bx_%7B1%7D%7D%5E%7Bx_%7B2%7D%7D%20)
(a) The probability to find the particle between x = 4.95 nm and 5.05 nm is:
![P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{4.95}^{5.05} = 4.98 \cdot 10^{-5}](https://tex.z-dn.net/?f=%20P%3D%5Cfrac%7B2%7D%7B100%7D%20%5B%5Cfrac%7BX%7D%7B2%7D%20-%20%5Cfrac%7BSin%282%5Cpi%20x%2F100%29%7D%7B4%5Cpi%20%2F100%7D%5D%7C_%7B4.95%7D%5E%7B5.05%7D%20%3D%204.98%20%5Ccdot%2010%5E%7B-5%7D%20)
(b) The probability to find the particle between x = 1.95 nm and 2.05 nm is:
![P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{1.95}^{2.05} = 7.89 \cdot 10^{-6}](https://tex.z-dn.net/?f=%20P%3D%5Cfrac%7B2%7D%7B100%7D%20%5B%5Cfrac%7BX%7D%7B2%7D%20-%20%5Cfrac%7BSin%282%5Cpi%20x%2F100%29%7D%7B4%5Cpi%20%2F100%7D%5D%7C_%7B1.95%7D%5E%7B2.05%7D%20%3D%207.89%20%5Ccdot%2010%5E%7B-6%7D%20)
(c) The probability to find the particle between x = 9.90 nm and 10.00 nm is:
![P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{9.90}^{10.00} = 1.89 \cdot 10^{-4}](https://tex.z-dn.net/?f=%20P%3D%5Cfrac%7B2%7D%7B100%7D%20%5B%5Cfrac%7BX%7D%7B2%7D%20-%20%5Cfrac%7BSin%282%5Cpi%20x%2F100%29%7D%7B4%5Cpi%20%2F100%7D%5D%7C_%7B9.90%7D%5E%7B10.00%7D%20%3D%201.89%20%5Ccdot%2010%5E%7B-4%7D%20)
(d) The probability to find the particle in the right half of the box, that is to say, between x = 0 nm and 50 nm is:
![P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{0}^{50.00} = 0.5](https://tex.z-dn.net/?f=%20P%3D%5Cfrac%7B2%7D%7B100%7D%20%5B%5Cfrac%7BX%7D%7B2%7D%20-%20%5Cfrac%7BSin%282%5Cpi%20x%2F100%29%7D%7B4%5Cpi%20%2F100%7D%5D%7C_%7B0%7D%5E%7B50.00%7D%20%3D%200.5%20)
(e) The probability to find the particle in the central third of the box, that is to say, between x = 0 nm and 100/6 nm is:
![P=\frac{2}{100} [\frac{X}{2} - \frac{Sin(2\pi x/100)}{4\pi /100}]|_{0}^{16.7} = 2.9 \cdot 10^{-2}](https://tex.z-dn.net/?f=%20P%3D%5Cfrac%7B2%7D%7B100%7D%20%5B%5Cfrac%7BX%7D%7B2%7D%20-%20%5Cfrac%7BSin%282%5Cpi%20x%2F100%29%7D%7B4%5Cpi%20%2F100%7D%5D%7C_%7B0%7D%5E%7B16.7%7D%20%3D%202.9%20%5Ccdot%2010%5E%7B-2%7D%20)
I hope it helps you!
Exact form: 94/5 decimal form : 18.8 mixed number form : 18 4/5
Answer:
6 < u < 8
Step-by-step explanation:
10 > 5u/4 > 15/2
To solve this, we need to isolate the variable u
10(4) > 5u/4(4) > 15/2(4)
40 > 5u > 30
40/5 > 5u/5 > 30/5
8 > u > 6
It probably wants you to write it in order so,
6 < u < 8
Your welcome, and if you have any questions, feel free to comment! :D
Answer:
straight line, C
Step-by-step explanation:
The graph of a linear function is a straight line. Graphically, where the line crosses the x -axis, is called a zero, or root. Algebraically, a zero is an x value at which the function of x is equal to 0 . Linear functions can have none, one, or infinitely many zeros.
I hope this helps.
Answer:
I'm not sure how you are asking this question because this is not exactly a question and I needed to know what the 49 was but I have an idea..
Step-by-step explanation:
49ft = 588 in
