You would also need to know the opposite segment of the given angle because sine is equal to opposite over hypotenuse.
Answer:
PartA
P = 4a
Part B
60 = P fence + 2a
60 = 6a
Part C
40
Step-by-step explanation:
We are building a fence so we are finding perimeter.
Adding the 3 sides
P = a+b+a
P = 2a+b
It is twice as long as it is wide
b= 2a
Replace in the equation for perimeter
P = 2a+(2a)
P = 4a
Part B
We know the perimeter is 60 for the entire backyard
The perimeter of the backyard is the fence plus the longer side
60 = P fence + b
Replacing b
60 = P fence + 2a
We know the equation for the perimeter of the fence is
60 = 4a + 2a
Combing like terms
60 = 6a
Part C
Solve for a and b
60 = 6a
Divide each side by 6
60/6 = 6a/6
10 =a
P fence = 4a
P = 4(10) = 40
Answer:
2d+18
Step-by-step explanation:
Distribute the 2 to the d and the 9
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:
<NLO and <OLN
Step-by-step explanation:
These two angle names are the same. the letters are simply reversed. it's like saying 1+2=3 and 2+1=3. the same. only reversed but still fluent in simplicity.
