If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81°?

1 answer:

mihalych1998 [28]3 years ago

4 0

Circumference of entire circle = 2 * PI * 10
circumference of entire circle = 62.832 feet
81 degrees is (9/40) of a circle
62.832 * (9/40) = 14.1372 

Source:
http://www.1728.org/radians.htm

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Find a vector parametrization for the line with the given description. Perpendicular to the yz-plane, passes through (0, 0, 8)

Brilliant_brown [7]

Answer:

$\left\{\begin{array}{l}x=t\\ \\y=0\\ \\z=8\end{array}\right.$

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Step-by-step explanation:

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If the line is perpendicular to this plane, then it is parallel to the normal vector, so the equation of this line is

$\dfrac{x-x_0}{1}=\dfrac{y-y_0}{0}=\dfrac{z-z_0}{0},$

where $(x_0,y_0,z_0)$ are coordinates of the point the line is passing through.

In your case, the line is passing through the point (0,0,8), so the canonical equation of the line is

$\dfrac{x-0}{1}=\dfrac{y-0}{0}=\dfrac{z-8}{0}$

Write a vector parametrization for this line

$\left\{\begin{array}{l}\dfrac{x-0}{1}=t\\ \\\dfrac{y-0}{0}=t\\ \\\dfrac{z-8}{0}=t\end{array}\right.\Rightarrow \left\{\begin{array}{l}x=t\\ \\y=0\\ \\z=8\end{array}\right.$