The cost of hiring a chainsaw is 10$ plus an amount that is proportional to the square of the number of hours for which the chainsaw is hired. If it costs $32.50 to hire the chainsaw for 3 hours, find to the nearest half hour, the length of time for which the chainsaw was hired if the cost of hire was $60.

Question

The cost of hiring a chainsaw is 10$ plus an amount that is proportional to the square of the number of hours for which the chainsaw is hired. If it costs $32.50 to hire the chainsaw for 3 hours, find to the nearest half hour, the length of time for which the chainsaw was hired if the cost of hire was $60.

Answer 1

Let's break down the information given.

The cost of hiring the chainsaw can be represented as:
Cost = $10 + k * (hours)^2

We know that it costs $32.50 to hire the chainsaw for 3 hours. Using this information, we can substitute these values into the equation:

32.50 = 10 + k * (3)^2
32.50 = 10 + 9k
22.50 = 9k
k ≈ 2.50

Now, we need to find the length of time for which the chainsaw was hired if the cost of hire was $60. Let's substitute these values into the equation:

60 = 10 + 2.50 * (hours)^2
50 = 2.50 * (hours)^2
20 = (hours)^2
hours ≈ √20
hours ≈ 4.47 hours

To the nearest half hour, the length of time for which the chainsaw was hired is approximately 4.5 hours.

Answer 2

To solve this problem, we need to set up an equation based on the information given.

Let's say "h" represents the number of hours for which the chainsaw is hired.

According to the given information, the cost "C" of hiring the chainsaw can be expressed as:

C = $10 + kh^2

Where "k" is a constant of proportionality.

We are given two points, (3, $32.50) and (h, $60), which we can use to solve for "k" and then determine the value of "h".

Let's start by plugging in the point (3, $32.50) into the equation to solve for "k":

$32.50 = $10 + k(3^2)
$32.50 = $10 + 9k
$22.50 = 9k
k = $22.50 / 9
k = $2.50

Now that we have the value of "k", we can use it in the equation along with the point (h, $60) to solve for "h":

$60 = $10 + ($2.50)(h^2)
$50 = $2.50h^2
20 = h^2
h = √20
h ≈ 4.47

Since the question asks for the length of time to the nearest half hour, we can round the value of "h" to the nearest half hour, which is 4.5 hours.

Therefore, the length of time for which the chainsaw was hired, given a cost of $60, is approximately 4.5 hours.

Answer 3

c=10+kh^2

Now you know that
10+9k=32.50
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