f(x)=2x+5
first find inverse
write it without f(x)
y = 2x + 5
x = 2y + 5 swap the variables, now solve for y
- 5 -5
x - 5 = 2y
/2 /2 divide both sides by 2
(x-5)/2 = y
so f-1(x) = (x-5)/2
f-1(8) = (8-5)/2
= (3)/2
f-1(8) = 3/2
Answer:
The substance half-life is of 4.98 days.
Step-by-step explanation:
Equation for an amount of a decaying substance:
The equation for the amount of a substance that decay exponentially has the following format:
![A(t) = A(0)e^{-kt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-kt%7D)
In which k is the decay rate, as a decimal.
k-value of 0.1392.
This means that:
![A(t) = A(0)e^{-0.1392t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-0.1392t%7D)
Find the substance's half life, in days.
This is t for which
. So
![A(t) = A(0)e^{-0.1392t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-0.1392t%7D)
![0.5A(0) = A(0)e^{-0.1392t}](https://tex.z-dn.net/?f=0.5A%280%29%20%3D%20A%280%29e%5E%7B-0.1392t%7D)
![e^{-0.1392t} = 0.5](https://tex.z-dn.net/?f=e%5E%7B-0.1392t%7D%20%3D%200.5)
![\ln{e^{-0.1392t}} = \ln{0.5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-0.1392t%7D%7D%20%3D%20%5Cln%7B0.5%7D)
![-0.1392t = \ln{0.5}](https://tex.z-dn.net/?f=-0.1392t%20%3D%20%5Cln%7B0.5%7D)
![t = -\frac{\ln{0.5}}{0.1392}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7B%5Cln%7B0.5%7D%7D%7B0.1392%7D)
![t = 4.98](https://tex.z-dn.net/?f=t%20%3D%204.98)
The substance half-life is of 4.98 days.
D a theorem needs to be proven
Answer:
250π
1000π
Step-by-step explanation:
(refer to attached)
volume of cylinder is given by:
V = π r²h,
where r = radius of base and h = height of cylinder
Given r = 5 and h = 10, hence
V = π r²h
V = π (5)²(10)
V = π (25) (10)
V = 250π (answer)
For the second case, r = 10 cm
V = π r²h
V = π (10)²(10)
V = π (100) (10)
V = 1000π (answer)
Answer:
7:1
Step-by-step explanation:
There are two cubes, one with 14 cm and one with 2 cm. 14:2 is equal to 7:1.