Evaluate the function for x = 2: f(x) = 7x - 5
2 answers:
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Answer <u>(assuming it is allowed to be in point-slope format)</u>:
Step-by-step explanation:
1) First, determine the slope. We know it has to be perpendicular to the given equation, . That equation is already in slope-intercept form, or y = mx + b format, in which m represents the slope. Since
is in place of the m in the equation, that must be the slope of the given line.
Slopes that are perpendicular are opposite reciprocals of each other (they have different signs, and the denominators and numerators switch places). Thus, the slope of the new line must be .
2) Now, use the point-slope formula, to write the new equation with the given information. Substitute
,
, and
for real values.
The represents the slope, so substitute
in its place. The
and
represent the x and y values of a point the line intersects. Since the point crosses (1,4), substitute 1 for
and 4 for
. This gives the following equation and answer:
Answer:
31.76 ft and 58.64 ft
Step-by-step explanation:
The radius measures between 13 feet and 24 feet.
The wheel is able to turn 7π/9 radians before getting stuck.
We need to find the range of distances that the wheel could spin before getting stuck. That is, the length of arc.
Length of an arc is given as:
where θ = central angle = 7π/9 radians
r = radius of the circle
Therefore, for 13 feet:
For 24 feet:
The wheel could spin between 31.76 ft and 58.64 ft before getting stuck.