alright whats your question ?
Answer:
31
Step-by-step explanation:
(3*22=66) / 6 + [28n - (4)2=20]
66 /6 = 11+ [20]
11+20= 31
Answer: Gear 14 or 14.3
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
![\dfrac{d}{dx} (\tan^3 x) = 3\sec^4 x - 3\sec^2 x](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20%28%5Ctan%5E3%20x%29%20%3D%203%5Csec%5E4%20x%20-%203%5Csec%5E2%20x)
Recall
![\dfrac{d}{dx}\tan x=\sec^2](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%5Ctan%20x%3D%5Csec%5E2)
Using the chain rule
![\dfrac{dy}{dx}= \dfrac{dy}{du} \dfrac{du}{dx}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cdfrac%7Bdy%7D%7Bdu%7D%20%5Cdfrac%7Bdu%7D%7Bdx%7D)
such that ![u = \tan x](https://tex.z-dn.net/?f=u%20%3D%20%5Ctan%20x)
we can get a general formulation for
![y = \tan^n x](https://tex.z-dn.net/?f=y%20%3D%20%5Ctan%5En%20x)
Considering the power rule
![\boxed{\dfrac{d}{dx} x^n = nx^{n-1}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdfrac%7Bd%7D%7Bdx%7D%20x%5En%20%3D%20nx%5E%7Bn-1%7D%7D)
we have
![\dfrac{dy}{dx} =n u^{n-1} \sec^2 x \implies \dfrac{dy}{dx} =n \tan^{n-1} \sec^2 x](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3Dn%20u%5E%7Bn-1%7D%20%5Csec%5E2%20x%20%5Cimplies%20%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3Dn%20%5Ctan%5E%7Bn-1%7D%20%5Csec%5E2%20x)
therefore,
![\dfrac{d}{dx}\tan^3 x=3\tan^2x \sec^2x](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%5Ctan%5E3%20x%3D3%5Ctan%5E2x%20%5Csec%5E2x)
Now, once
![\sec^2 x - 1= \tan^2x](https://tex.z-dn.net/?f=%5Csec%5E2%20x%20-%201%3D%20%5Ctan%5E2x)
we have
![3\tan^2x \sec^2x = 3(\sec^2 x - 1) \sec^2x = 3\sec^4x-3\sec^2x](https://tex.z-dn.net/?f=3%5Ctan%5E2x%20%5Csec%5E2x%20%3D%20%203%28%5Csec%5E2%20x%20-%201%29%20%5Csec%5E2x%20%3D%203%5Csec%5E4x-3%5Csec%5E2x)
Hence, we showed
![\dfrac{d}{dx} (\tan^3 x) = 3\sec^4 x - 3\sec^2 x](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%20%28%5Ctan%5E3%20x%29%20%3D%203%5Csec%5E4%20x%20-%203%5Csec%5E2%20x)
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For the integration,
![$\int \sec^4 x\, dx $](https://tex.z-dn.net/?f=%24%5Cint%20%5Csec%5E4%20x%5C%2C%20dx%20%24)
considering the previous part, we will use the identity
![\boxed{\sec^2 x - 1= \tan^2x}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csec%5E2%20x%20-%201%3D%20%5Ctan%5E2x%7D)
thus
![$\int\sec^4x\,dx=\int \sec^2 x(\tan^2x+1)\,dx = \int \sec^2 x \tan^2x+\sec^2 x\,dx$](https://tex.z-dn.net/?f=%24%5Cint%5Csec%5E4x%5C%2Cdx%3D%5Cint%20%5Csec%5E2%20x%28%5Ctan%5E2x%2B1%29%5C%2Cdx%20%3D%20%5Cint%20%5Csec%5E2%20x%20%5Ctan%5E2x%2B%5Csec%5E2%20x%5C%2Cdx%24)
and
![$\int \sec^2 x \tan^2x+\sec^2 x\,dx = \int \sec^2 x \tan^2x\,dx + \int \sec^2 x\,dx $](https://tex.z-dn.net/?f=%24%5Cint%20%5Csec%5E2%20x%20%5Ctan%5E2x%2B%5Csec%5E2%20x%5C%2Cdx%20%3D%20%5Cint%20%5Csec%5E2%20x%20%5Ctan%5E2x%5C%2Cdx%20%2B%20%5Cint%20%5Csec%5E2%20x%5C%2Cdx%20%24)
Considering ![u = \tan x](https://tex.z-dn.net/?f=u%20%3D%20%5Ctan%20x)
and then ![du=\sec^2x\ dx](https://tex.z-dn.net/?f=du%3D%5Csec%5E2x%5C%20dx)
we have
![$\int u^2 \, du = \dfrac{u^3}{3}+C$](https://tex.z-dn.net/?f=%24%5Cint%20u%5E2%20%5C%2C%20du%20%3D%20%5Cdfrac%7Bu%5E3%7D%7B3%7D%2BC%24)
Therefore,
![$\int \sec^2 x \tan^2x\,dx + \int \sec^2 x\,dx = \dfrac{\tan^3 x}{3}+\tan x + C$](https://tex.z-dn.net/?f=%24%5Cint%20%5Csec%5E2%20x%20%5Ctan%5E2x%5C%2Cdx%20%2B%20%5Cint%20%5Csec%5E2%20x%5C%2Cdx%20%3D%20%5Cdfrac%7B%5Ctan%5E3%20x%7D%7B3%7D%2B%5Ctan%20x%20%2B%20C%24)
![$\boxed{\int \sec^4 x\, dx = \dfrac{\tan^3 x}{3}+\tan x + C }$](https://tex.z-dn.net/?f=%24%5Cboxed%7B%5Cint%20%5Csec%5E4%20x%5C%2C%20dx%20%20%3D%20%5Cdfrac%7B%5Ctan%5E3%20x%7D%7B3%7D%2B%5Ctan%20x%20%2B%20C%20%7D%24)
Answer:
He did not control for lurking variables and their impacts on the results of his experiment. Amount of sunlight and water received are two outside variables(or confounding variables) that may impact the growth of his plants and influence the results. He needs to apply the same amount of sunlight and water to each plant within a different planting soil in order to rule out the influence of those two variables and test the sole effect of the soil brand on the plant growth. Otherwise, it would be hard to determine whether his plant growth was because of the soil brand or the different amounts of sunlight and water received