Step-by-step explanation:
3/4x + 5/8 = 4x/1
5/8 = 4x/1 - 3/4x
5/8 = 16x^2 - 3/4x
5/8 = 4x - 3/1
5/8 = 4x - 3
Cross multiply
8(4x - 3) = 5
32x - 24 = 5
32x = 5 + 24
32x = 29
X = 29/32
Answer:
x= 40
y= 38
Step-by-step explanation:
Answer:
X = - 4
Step-by-step explanation:
Given in problem
- x -4x - 7 = 5 -2x
Or, -5x - 7 = 5- 2x
Or, -5x + 2x = 5 + 7
Or, -3x = 12
Or, x = - 
∴ X = - 4 Answer
Answer:
the time taken for the radioactive element to decay to 1 g is 304.8 s.
Step-by-step explanation:
Given;
half-life of the given Dubnium = 34 s
initial mass of the given Dubnium, m₀ = 500 grams
final mass of the element, mf = 1 g
The time taken for the radioactive element to decay to its final mass is calculated as follows;
![1 = 500 (0.5)^{\frac{t}{34}} \\\\\frac{1}{500} = (0.5)^{\frac{t}{34}}\\\\log(\frac{1}{500}) = log [(0.5)^{\frac{t}{34}}]\\\\log(\frac{1}{500}) = \frac{t}{34} log(0.5)\\\\-2.699 = \frac{t}{34} (-0.301)\\\\t = \frac{2.699 \times 34}{0.301} \\\\t = 304.8 \ s](https://tex.z-dn.net/?f=1%20%3D%20500%20%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B34%7D%7D%20%5C%5C%5C%5C%5Cfrac%7B1%7D%7B500%7D%20%3D%20%20%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B34%7D%7D%5C%5C%5C%5Clog%28%5Cfrac%7B1%7D%7B500%7D%29%20%3D%20log%20%5B%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B34%7D%7D%5D%5C%5C%5C%5Clog%28%5Cfrac%7B1%7D%7B500%7D%29%20%20%3D%20%5Cfrac%7Bt%7D%7B34%7D%20log%280.5%29%5C%5C%5C%5C-2.699%20%3D%20%5Cfrac%7Bt%7D%7B34%7D%20%28-0.301%29%5C%5C%5C%5Ct%20%3D%20%5Cfrac%7B2.699%20%5Ctimes%2034%7D%7B0.301%7D%20%5C%5C%5C%5Ct%20%3D%20304.8%20%5C%20s)
Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.
3^(4x) = 3^(5 - x)
4x = 5 - x
4x + x = 5
5x = 5
x = 5/5 = 1
x = 1