Consider the helix below:
![r(t)= (\cos(7t), \sin(7t), -t)](https://tex.z-dn.net/?f=r%28t%29%3D%20%28%5Ccos%287t%29%2C%20%5Csin%287t%29%2C%20-t%29)
We have to determine the value of helix at t = ![\frac{\pi}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%7D%7B6%7D)
So, ![r(\frac{\pi}{6})](https://tex.z-dn.net/?f=r%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29)
=![(\cos(\frac{7 \pi}{6}), \sin(\frac{7 \pi}{6}), -\frac{\pi}{6})](https://tex.z-dn.net/?f=%28%5Ccos%28%5Cfrac%7B7%20%5Cpi%7D%7B6%7D%29%2C%20%5Csin%28%5Cfrac%7B7%20%5Cpi%7D%7B6%7D%29%2C%20-%5Cfrac%7B%5Cpi%7D%7B6%7D%29)
Consider ![\cos(\frac{7 \pi}{6}) = \cos(\pi + \frac{\pi}{6}) = - \cos (\frac{\pi}{6}) = \frac{-\sqrt3}{2}](https://tex.z-dn.net/?f=%5Ccos%28%5Cfrac%7B7%20%5Cpi%7D%7B6%7D%29%20%3D%20%5Ccos%28%5Cpi%20%2B%20%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%3D%20-%20%5Ccos%20%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%3D%20%5Cfrac%7B-%5Csqrt3%7D%7B2%7D)
Consider ![\sin(\frac{7 \pi}{6}) = \sin(\pi + \frac{\pi}{6}) = - \sin (\frac{\pi}{6}) = \frac{-1}{2}](https://tex.z-dn.net/?f=%5Csin%28%5Cfrac%7B7%20%5Cpi%7D%7B6%7D%29%20%3D%20%5Csin%28%5Cpi%20%2B%20%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%3D%20-%20%5Csin%20%28%5Cfrac%7B%5Cpi%7D%7B6%7D%29%20%3D%20%5Cfrac%7B-1%7D%7B2%7D)
So, the value of helix
.
Answer: LN 40
Step-by-step explanation: Because thin of the answers and how to do it
Answer:
The area of a triangle is the space contained within its 3 sides. To find out the area of a triangle, we need to know the length of its three sides. The sides should be measured in feet (ft) for square footage calculations and if needed, converted to inches (in), yards (yd), centimetres (cm), millimetres (mm) and metres (m). The formula:
Square feet to square meters: multiply ft² by 0.092903 to get m²
Square yards to square feet: multiply yd² by 9 to get ft²
Square feet to square yards: multiply ft² by 0.11111 to get yd²
Square yards to square meters: multiply yd² by 0.8
Step-by-step explanation:
Answer: 8.4 inches.
Step-by-step explanation:
We know that the circumference of a circle can be calculated with this formula:
![C=2\pi r](https://tex.z-dn.net/?f=C%3D2%5Cpi%20r)
Where "r" is the radius of the circle.
We know that the circular cake (whose radius is 8 inches) is cut from the center into 6 equal pieces. Then, you need to divide the circumference of this circular cake by 6 to find the width of the outer edge of each piece of cake.
Therefore, this is (to the nearest tenth of an inch):
![C=\frac{2\pi (8in)}{6}\\\\C=8.4in](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B2%5Cpi%20%288in%29%7D%7B6%7D%5C%5C%5C%5CC%3D8.4in)