Step-by-step explanation:
2-5^3+6x
2-125+6x
6x+2-125
6x-123
Answer:
about 315
Step-by-step explanation:
2,250×0.14
hope this helps!
Unfortunately your teacher is using x as both a variable and a multiplication sign. This is something that can be avoided by using something like the asterisk symbol to indicate multiplication.
Anyways, notice how the expression 
shows up twice. Once in the numerator (the entire numerator) and once again in the denominator (nearly the whole thing)
Let's replace that messy expression with the variable y. So we're letting 
This means,
At this point you can probably see how to get 
from here. The y terms cancel out when we divide leaving 1 up top and 3^x down below.
Answer:
a) k = 0.0001245 /year
b) The Shroud of Turin is 757.52 years old.
Step-by-step explanation:
a) dC/dt = - KC
dC/C = - kdt
Integrating the left hand side from C₀ to C₀/2 and the right hand side from 0 to t(1/2) (where t(1/2) is the radioactive isotope's half life)
In [(C₀/2)/C₀] = - k t(1/2)
In (1/2) = - k t(1/2)
- In 2 = - k t(1/2)
k = (In 2)/t₍₁,₂₎
t(1/2) is given in the question to be 5566 years
k = (In 2)/5566 = 0.0001245 /year
b) dC/C = - kdt
Integrating the left hand side from C₀ to C and the right hand side from 0 to t
In (C/C₀) = - kt
C/C₀ = e⁻ᵏᵗ
C = C₀ e⁻ᵏᵗ
When C = 91% of C₀ = 0.91 C₀, solve for t
0.91 C₀ = C₀ e⁻ᵏᵗ
0.91 = e⁻ᵏᵗ
e⁻ᵏᵗ = 0.91
- kt = In 0.91 = -0.00943
t = - 0.00943/(-0.0001245) = 757.52 years.
