17* pi = <span>53.4070 inches --> 4.4505 feet
600 divided by </span>4.4505 = about 134 rotations
Answer:
<u>11/12</u><u> </u><u>is</u><u> </u><u>the</u><u> </u><u>fraction</u><u> </u><u>that</u><u> </u><u>is</u><u> </u><u>closer</u><u> </u><u>to</u><u> </u><u>1</u><u>.</u>
Answer:
Please check the explanation.
Step-by-step explanation:
Given
f(x) = 3x + x³
Taking differentiate
![\frac{d}{dx}\left(3x+x^3\right)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%283x%2Bx%5E3%5Cright%29)
![\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3ASum%2FDifference%5C%3ARule%7D%3A%5Cquad%20%5Cleft%28f%5Cpm%20g%5Cright%29%27%3Df%5C%3A%27%5Cpm%20g%27)
![=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%283x%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5E3%5Cright%29)
solving
![\frac{d}{dx}\left(3x\right)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%283x%5Cright%29)
![\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'](https://tex.z-dn.net/?f=%5Cmathrm%7BTake%5C%3Athe%5C%3Aconstant%5C%3Aout%7D%3A%5Cquad%20%5Cleft%28a%5Ccdot%20f%5Cright%29%27%3Da%5Ccdot%20f%5C%3A%27)
![=3\frac{d}{dx}\left(x\right)](https://tex.z-dn.net/?f=%3D3%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5Cright%29)
![\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3Acommon%5C%3Aderivative%7D%3A%5Cquad%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5Cright%29%3D1)
![=3\cdot \:1](https://tex.z-dn.net/?f=%3D3%5Ccdot%20%5C%3A1)
![=3](https://tex.z-dn.net/?f=%3D3)
now solving
![\frac{d}{dx}\left(x^3\right)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5E3%5Cright%29)
![\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3APower%5C%3ARule%7D%3A%5Cquad%20%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5Ea%5Cright%29%3Da%5Ccdot%20x%5E%7Ba-1%7D)
![=3x^{3-1}](https://tex.z-dn.net/?f=%3D3x%5E%7B3-1%7D)
![=3x^2](https://tex.z-dn.net/?f=%3D3x%5E2)
Thus, the expression becomes
![\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%283x%2Bx%5E3%5Cright%29%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%283x%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28x%5E3%5Cright%29)
![=3+3x^2](https://tex.z-dn.net/?f=%3D3%2B3x%5E2)
Thus,
f'(x) = 3 + 3x²
Given that f'(x) = 15
substituting the value f'(x) = 15 in f'(x) = 3 + 3x²
f'(x) = 3 + 3x²
15 = 3 + 3x²
switch sides
3 + 3x² = 15
3x² = 15-3
3x² = 12
Divide both sides by 3
x² = 4
![\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7Dx%5E2%3Df%5Cleft%28a%5Cright%29%5Cmathrm%7B%5C%3Athe%5C%3Asolutions%5C%3Aare%5C%3A%7Dx%3D%5Csqrt%7Bf%5Cleft%28a%5Cright%29%7D%2C%5C%3A%5C%3A-%5Csqrt%7Bf%5Cleft%28a%5Cright%29%7D)
![x=\sqrt{4},\:x=-\sqrt{4}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B4%7D%2C%5C%3Ax%3D-%5Csqrt%7B4%7D)
![x=2,\:x=-2](https://tex.z-dn.net/?f=x%3D2%2C%5C%3Ax%3D-2)
Thus, the value of x will be:
![x=2,\:x=-2](https://tex.z-dn.net/?f=x%3D2%2C%5C%3Ax%3D-2)
Answer:
umm why not ask the teacher for help they will help you
Step-by-step explanation:
You have to fill in 3 for x so it woul look like 3x3-3 and that would be 6.