Tutor profile: Brian A.

A 41 meter guide wire is attached to the top of a 34.6 meter antenna and to a point on the ground. What angle, in degrees, does the guide wire make with the ground?

We draw our triangle with the antenna being the vertical line, the ground our horizontal one, creating a right angle, and the guide wire connecting the two ends completing the triangle. The vertical one is 34.6 m and the hypotenuse or guide wire is 41 m. We are looking for the angle between the ground/horizontal line and guide wire/hypotenuse. This means we need to use sine because the lengths we know are opposite of the angle and the hypotenuse of the triangle. sin(a) = 34.6 / 41 => a = 57.6 deg

The circumference of a circle is 30 (pi). What is its area?

The circumference (C) of a circle is given by the formula C = 2(pi)r, where r is the radius of the circle. We know C, so we can find r. 30 (pi) = 2 (pi) r r = 15 Therefore, the radius of the circle is 15. now we use this to find the area of the circle. The area of a circle is given by the formula A= (pi) r^2. Substitute the length of the radius into this formula and calculate the area. A =(pi)(15)^2 = 225(pi)

An airplane starts at rest and accelerates down a runway at 3.20 m/s^2 for 32.8 s until it finally lifts off the ground. Determine the distance traveled before takeoff.

We know the following: initial velocity (vi) is 0 m/s because it starts from rest acceleration (a) is 3.2 m/s^2 (stated) time (t) is 32.8 s (stated) We are looking for the following: distance (d) Based on our 4 kinematics equations, we are looking one that has vi, a, t, and d, which means we will use the following equation: d = vi*t + 0.5*a*t^2 We plug everything in: d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)^2 Our answer: d = 1720 m