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Answer:
Part A)
Part B)
Part C)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or
Let
x -----> the number of workers
y ----> the number of pieces made
In this problem
The relation between the variables x and y represent a direct variation (proportional variation)
so
For x=16, y=40
Find the value of the constant of proportionality k
substitute the values
The linear equation is equal to
Part A) How many workers are needed to make 20 pieces
For y=20 pieces
substitute in the linear equation
Part B) How many workers are needed to make 25 pieces
For y=25 pieces
substitute in the linear equation
Part C) How many workers are needed to make 100 pieces
For y=100 pieces
substitute in the linear equation
Answer: the height of the pole is 16.1 m.
Step-by-step explanation:
The scenario is illustrated in the attached photo.
x represents the height of the pole.
y represents the distance from the foot of one stabilizing wire to the foot of the pole.
30 - y represents the distance from the foot of the other stabilizing wire to the foot of the pole.
In solving the triangles, we would apply the tangent trigonometric ratio which is expressed as
Tan θ, = opposite side/adjacent side.
Considering triangle ACD,
Tan 60 = x/y
x = ytan60 = y × 1.732
x = 1.732y- - - - - - - - -1
Considering triangle BCD,
Tan 38 = x/(30 - y)
x = (30 - y)tan38 = 0.781(30 - y)
x = 23.43 - 0.781y- - - - - - - - -2
Substituting equation 1 into equation 2, it becomes
1.732y = 23.43 - 0.781y
1.732y + 0.781y = 23.43
2.513y = 23.43
y = 23.43/2.513
y = 9.3
x = 1.732y = 1.732 × 9.3
x = 16.1 m
