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} ? 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.

Twelve less than a number is at most 20

Find the value of x in the diagram below. select the best answer from the choices provided

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality