0a two-inch-long grasshopper can jump a horizontal distance of 40 inches. an athlete, who is _ five feet nine, wants to cover a distance of one mile by jumping. if this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile?

a) nearest jump is JL = 1380 inches = 115ft

b) number of jumps in 1 mile N= 46 jumps

Step-by-step explanation:

Given that the jump length is proportional to the body length.

If 2 inch grasshopper can jump 40 inches.

JL = k(BL)

k = JL/BL

where JL = jump length = 40 inches

BL = Body length = 2 inches.

k = 40/2 = 20

The constant of proportionality is 20.

For the athlete :

BL = 5ft 9 inches = 5(12)+9 = 69 inches.

The jump length of the athlete is:

JL = k(BL) = 20(69)

JL = 1380 inches. = 115ft

The number of jumps in 1 mile is

1 mile = 63360 inches

N = 63360/1380

N = 45.9 = 46

N= 46

Therefore, 46 jumps would be needed.

answer: it's d

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4