When he exercises after work, marcus runs an average mile in 8.3 minutes. at this average, how many miles will he run after 36 minutes, rounded to the nearest tenth

Marcus will run an average of 4.3 miles after 36 minutes.

Step-by-step explanation:

Given:

Marcus runs an average mile in 8.3 minutes.

1 miles = 8.3 minutes

We need to find miles he ran at same average in 36 minutes.

How many miles = 36 minutes

Using Unitary Method we will find miles he run at 36 mins by multiplying 1 mile with 36 minutes and the dividing it with 8.3 minutes we get;

An Average mile run after 36 min =

Rounding to nearest tenth we get ≈ 4.3 miles.

Hence, Marcus will run an average of 4.3 miles after 36 minutes.

  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.