An air traffic controller spots two planes at the same altitude flying toward each other. their flight paths form a right angle at point p. one plane is 150 miles from point p and is moving at 450 miles per hour. the other plane is 200 miles from point p and is moving at 450 miles per hour. 100 100 200 200 distance (in miles) distance (in miles) y s x p write the distance s between the planes as a function of time t.

Let the units of the problem be miles and hours. The first plane's distance from point p can be described by

... x = 150 -450t

The second plane's distance from point p can be described by

... y = 200 -450t

Since their flight paths are at right angles, the Pythagorean theorem can be used to describe the distance between them (s).

... s² = x² + y²

... s² = (150 -450t)² + (200 -450t)² = 22500 -135000t +202500t² +40000 -180000t +202500t²

... s² = 40500t² -315000t +62500 = 2500(162t² -126t +25)

... s = 50√(162t² -126t +25)

99

step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.