Answer:
See Below.
Step-by-step explanation:
We are given that:
Where <em>I₀</em> and <em>k</em> are constants.
And we want to prove that:
From the original equation, take the derivative of both sides with respect to <em>t</em>. Hence:
![\displaystyle \frac{d}{dt}\left[I\right] = \frac{d}{dt}\left[I_0e^{-kt}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5BI%5Cright%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5BI_0e%5E%7B-kt%7D%5Cright%5D)
Differentiate. Since <em>I₀ </em>is a constant:
![\displaystyle \frac{dI}{dt} = I_0\left(\frac{d}{dt}\left[ e^{-kt}\right]\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdI%7D%7Bdt%7D%20%3D%20I_0%5Cleft%28%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5B%20e%5E%7B-kt%7D%5Cright%5D%5Cright%29)
Using the chain rule:
We have:
Substitute:
Distribute and simplify:
Hence proven.
Answer:
one
Step-by-step explanation: you cant simplify the equation so that both sides can be divided to get the same equation, if you graph it theres not a parabola so the only thing left is one.
Answer:
Charmaine earns $60.90 for 6h for mowing and 1h for babysitting.
Step-by-step explanation:
We must write the data problems.
Charmaine = $8.80/h mowing
Charmaine = $8.10/h babysitting
How much will Charmaine earn for 6 h mowing and 1 h babysitting?
1 h mowing ....................... $8.80
6 h mowing ....................... $x
x = 6 h mowing * $8.80
x = $52,8
To find the total earn of Charmaine, we have to gather the earns from mowing and babysitting.
$52,8 (from mowing) + $8.10 (from babysitting) = $60.90
Answer:
<P = 27°
Step-by-step explanation:
In a triangle, the sum of all three interior angles = 180
So triangle NOP, <N + <O + <P = 180
Plug in
9x - 1 + 3x - 2 + 2x + 1 = 180
14x = 2 = 180
14x = 182
x = 13
<P = 2x + 1
<P = 2(13) + 1
<P = 26 + 1
<P = 27
Answer:
<P = 27°
Use the information to form a ratio... 6:8 or 6/8. Now set it equal to a ratio per 100...
6/8 = x/100
Cross multiply
8x = 600
x = 600/8
x = 75
75% have moons
