The formule is about area of a circle.
We need to solve the equation for x. Where x is the radius of the circle.
In order to solve it for x, we need isolate it for x on left side.
So, first we need to get rid pi from left side.
On dividing both sides by pi, we get
Taking square root on both sides, we get
A² + b² = c²
8² + x² = 16²
x² = 16² - 8²
x² = 192
x =√192
x =8√3
Answer:
<u>4 meters.</u>
Step-by-step explanation:
Benjamin has walked two legs of a right triangle, so you can connect her two movements with a line if you were sketching the situation.. The displacement is the objects overall change in position in relation to its origin, so in your case, Benjamin's apartment. While the total distance adds up regardless of her position.
So, the total distance Benjamin walked is 10m + 6m = 16m
Her displacement can be found by your best friends, the Pythagorean Theorem: 10m ^2 + 6m ^2 = delta x^2 (or displacement squared).. giving you a displacement of 11.66, or 12 m.
The difference between the distance she walked and her displacement is 4 meters.
I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!
This question can be solved primarily by L'Hospital Rule and the Product Rule.
I) Product Rule and L'Hospital Rule:
![y= \lim_{x \to 0} \frac{[2xcos(x)-x^2sin(x)]-2sin(x)cos(x)}{4x^3}](https://tex.z-dn.net/?f=y%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5B2xcos%28x%29-x%5E2sin%28x%29%5D-2sin%28x%29cos%28x%29%7D%7B4x%5E3%7D%20)
II) Product Rule and L'Hospital Rule:
![y= \lim_{x \to 0} \frac{[-2xsin(x)+2cos(x)]-[2xsin(x)+x^2cos(x)]-[2cos^2(x)-2sin^2(x)]}{12x^2} \\ y= \lim_{x \to 0} \frac{2cos(x)-4xsin(x)-x^2cos(x)-2cos^2(x)+2sin^2(x)}{12x^2}](https://tex.z-dn.net/?f=y%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5B-2xsin%28x%29%2B2cos%28x%29%5D-%5B2xsin%28x%29%2Bx%5E2cos%28x%29%5D-%5B2cos%5E2%28x%29-2sin%5E2%28x%29%5D%7D%7B12x%5E2%7D%20%5C%5C%20y%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B2cos%28x%29-4xsin%28x%29-x%5E2cos%28x%29-2cos%5E2%28x%29%2B2sin%5E2%28x%29%7D%7B12x%5E2%7D)
III) Product Rule and L'Hospital Rule:
![]y= \alpha + \beta \\ \\ \alpha =\lim_{x \to 0} \frac{-2sin(x)-[4sin(x)+4xcos(x)]-[2xcos(x)-x^2sin(x)]}{24x} \\ \beta = \lim_{x \to 0} \frac{4sin(x)cos(x)+4sin(x)cos(x)}{24x} \\ \\ y = \lim_{x \to 0} \frac{-6sin(x)-4xcos(x)-2xcos(x)+x^2sin(x)+8sin(x)cos(x)}{24x}](https://tex.z-dn.net/?f=%5Dy%3D%20%5Calpha%20%2B%20%5Cbeta%20%5C%5C%20%5C%5C%20%5Calpha%20%3D%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B-2sin%28x%29-%5B4sin%28x%29%2B4xcos%28x%29%5D-%5B2xcos%28x%29-x%5E2sin%28x%29%5D%7D%7B24x%7D%20%5C%5C%20%5Cbeta%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B4sin%28x%29cos%28x%29%2B4sin%28x%29cos%28x%29%7D%7B24x%7D%20%5C%5C%20%20%5C%5C%20y%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B-6sin%28x%29-4xcos%28x%29-2xcos%28x%29%2Bx%5E2sin%28x%29%2B8sin%28x%29cos%28x%29%7D%7B24x%7D)
IV) Product Rule and L'Hospital Rule:
![y = \phi + \varphi \\ \\ \phi = \lim_{x \to 0} \frac{-6cos(x)-[-4xsin(x)+4cos(x)]-[2cos(x)-2xsin(x)]}{24x} \\ \varphi = \lim_{x \to 0} \frac{[2xsin(x)+x^2cos(x)]+[8cos^2(x)-8sin(x)]}{24x}](https://tex.z-dn.net/?f=y%20%3D%20%5Cphi%20%2B%20%5Cvarphi%20%5C%5C%20%20%5C%5C%20%5Cphi%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%20%5Cfrac%7B-6cos%28x%29-%5B-4xsin%28x%29%2B4cos%28x%29%5D-%5B2cos%28x%29-2xsin%28x%29%5D%7D%7B24x%7D%20%20%5C%5C%20%5Cvarphi%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%20%5Cfrac%7B%5B2xsin%28x%29%2Bx%5E2cos%28x%29%5D%2B%5B8cos%5E2%28x%29-8sin%28x%29%5D%7D%7B24x%7D%20)
V) Using the Definition of Limit:
4,3,2,1,0,-1, -2, -3, -4,
