The 40th parallel of north latitude runs across the United States through Philadelphia, Indianapolis, and Denver. At this latitude, Earth’s radius is about 3030 miles. The earth rotates with an angular velocity of LaTeX: \frac{\pi}{12} π 12 radians (or 15°) per hour toward the east. If a jet flies due west with the same angular velocity relative to the ground at the equinox, the Sun as viewed from the jet will stop in the sky. How fast in miles per hour would the jet have to travel west at the 40th parallel for this to happen? Show your work and explain your process.

793.25 mi/hr

Step-by-step explanation:

Given that:

The radius of the earth is = 3030 miles

The angular velocity =

If a jet flies due west with the same angular velocity relative to the ground at the equinox;

We are  to determine the How fast in miles per hour would the jet have to travel west at the 40th parallel for this to happen.

NOW;

Distance s is expressed by the relation

s = rθ

s = 793.25

The speed which depicts how fast in miles per hour the jet would have traveled is :

v = 793.25 mi/hr

Hence, the jet would have traveled 793.25 mi/hr due west at the  40th parallel for this to happen.

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.