A10-foot ladder placed on level ground leans against the side of a house. the ladder reaches a point that is 9.2 feet up on the side of the house. the occupational safety and health administration (osha) sets standards for a variety of occupations to prevent accidents and other safety hazards. osha’s standard for the angle formed by a ladder and level ground is 75° . the same 10-foot long ladder is placed against the building according to osha’s safety standard. what is the distance between the foot of the ladder and the foot of the building? round your answer to the nearest tenth. show your work.

A. x = sin-1()

x = 66.9 ≈ 67

x = 67°

B. x = 10 × cos(75)

x = 2.6

Hope this helps!

a) Sin θ = 9.2/10

Θ = Sin-1 0.92

66.92608193 ~ 67 degrees

b) Sin 75 = x/10

10 sin 75 =x

10 (0.96592583) = x

X= 9.7 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}