A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole. The angle of depression from the top if the pole is 43 degrees. What is the length of the wire?

Step-by-step explanation:

Refer the given figure.

The length of wire is CB.

Given that AB = 20 feet

∠ACB = 47°

We have

Length of wire = 27.35 feet

Step-by-step explanation:

angle of depression, θ = 43°

distance between the pole and the wire on the ground, d = 20 ft.

Let the length of the wire is L.

According to the diagram,

Cosθ = d / L

Cos 43 = 20 / L

0.73 = 20 / L

L = 27.35 ft

Thus, the length of the wire is 27.35 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}

circumference divided by 3.141592654 then timesthe radius twice

step-by-step explanation:

circumference divided by 3.141592654 then timesthe radius twice