Answer:
85x + 125 = y
Step-by-step explanation:
Let x = the amount of hours worked
Let y = the total cost to pay for this plumber
85 is the hourly pay so we multiply by the amount of hours worked to find the cost per hours. We then add that to the initial cost of 125 and we get the total cost.
Answer:
![\displaystyle f'(\frac{\pi}{4})=2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D2)
Step-by-step explanation:
<u>Trigonometric Derivatives</u>
We have the function
![\displaystyle f(x)=\sin x \csc x-\frac{1}{\tan x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%3D%5Csin%20x%20%5Ccsc%20x-%5Cfrac%7B1%7D%7B%5Ctan%20x%7D)
We must recall that the sine and the cosecant are reciprocal functions, i.e.:
![\displaystyle \sin x =\frac{1}{\csc x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%20x%20%3D%5Cfrac%7B1%7D%7B%5Ccsc%20x%7D)
Also, the reciprocal of the tangent is the cotangent:
![\displaystyle \cot x =\frac{1}{\tan x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccot%20x%20%3D%5Cfrac%7B1%7D%7B%5Ctan%20x%7D)
Thus:
![\displaystyle f(x)=1-\cot x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%3D1-%5Ccot%20x)
Now it's easier to take the derivative
![\displaystyle f'(x)=0+\csc^2 x= \csc^2 x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%3D0%2B%5Ccsc%5E2%20x%3D%20%5Ccsc%5E2%20x)
Evaluating for x=π/4:
![\displaystyle f'(\frac{\pi}{4})= \csc^2 \frac{\pi}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D%20%5Ccsc%5E2%20%5Cfrac%7B%5Cpi%7D%7B4%7D)
Since csc π/4=
:
![\displaystyle f'(\frac{\pi}{4})= \sqrt{2}^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D%20%5Csqrt%7B2%7D%5E2)
![\displaystyle f'(\frac{\pi}{4})=2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D2)
Ten is the value of the underlined digit
Answer:
A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2) * 180 / n.
Step-by-step explanation:
There ya go.. :)