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evablogger [386]
3 years ago
6

Kiran is about to start hiking on a trail that is 1.8 miles long. In his past hikes on the same trail, he had walked at a consta

nt rate of 2.4 miles an hour, which is 0.04 mile a minute. Function (F) represents Kiran's remaining distance on the trail, in miles, t, minutes after he starts walking. Write an equation to represent this function. Use function notation.
Mathematics
1 answer:
LenaWriter [7]3 years ago
5 0

Answer:

F(t) = 1.8 - 0.04t

Step-by-step explanation:

Given that :

Length of trail = 1.8m

Walking speed = 0.04 miles per minute

Distance left, t minutes after one statues walking :

Total distance covered after t minutes = speed * time = 0.04t

Distance left after t minutes :

Initial distance - distance covered

Hence,

F(t) = 1.8 - 0.04t

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Determine whether the statement is true or false. Justify your answers.
marusya05 [52]

Answer:

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis. ⇒ False

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis. ⇒ False

Step-by-step explanation:

<em>Let us explain the reflection about the axes</em>

  • If a graph is reflected about the x-axis, then the y-coordinates of all points on it will opposite in sign

Ex: if a point (2, -3) is on the graph of f(x), and f(x) is reflected about the x-axis, then the point will change to (2, 3)

  • That means reflection about the x-axis change the sign of y
  • y = f(x) → reflection about x-axis → y = -f(x)

  • If a graph is reflected about the y-axis, then the x-coordinates of all points on it will opposite in sign

Ex: if a point (-2, -5) is on the graph of f(x), and f(x) is reflected about the y-axis, then the point will change to (2, -5)

  • That means reflection about the y-axis change the sign of x
  • y = f(x) → reflection about y-axis → y = f(-x)

<em>Now let us answer our question</em>

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis.

It is False because reflection about x-axis change sign of y

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the x-axis

The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis.

It is False because reflection about y-axis change sign of x

The graph of y = f(-x) is a reflection of the graph of y = f(x) in the y-axis

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