You and a friend want to know how much rope you need to climb a large rock. Your friend is 5.5 feet tall and casts a shadow that is 18 feet long. If the rock casts a shadow that is 209.5 feet long, calculate the height of the rock from the ground. Round your answer to the nearest foot. (Hint: make a drawing) a. 64 ft b. 18 ft c. 210 ft d. 219 ft

The value of x from the equation is 64 ft. Thus, they will be needing approximately 64 ft of rope.

Step-by-step explanation: The concept that is useful in order to answer this item is the concept of ratio and proportion. Let x be the height of the rock from the ground. We use the equation below to answer.

                                   5.5 ft / 18 ft = x ft / 209.5 ft

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

answer: he is 272195

step-by-step explanation: all you have to do is multiple 3535 and 77 and it equals 272195