A small airplane flies 1015 miles with an average speed of 290 miles per hour. 1.75 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time; what was the average speed of the 747

The average speed of the 747 was of 580 miles per hour.

Step-by-step explanation:

We use the following relation to solve this question:

In which v is the velocity, d is the distance and t is the time.

A small airplane flies 1015 miles with an average speed of 290 miles per hour.

We have to find the time:

1.75 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time;

The time of the Boeing 747 is:

Distance of , the velocity is:

The average speed of the 747 was of 580 miles per hour.

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

300pi

step-by-step explanation: