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nalin [4]
3 years ago
13

the revenue for the school play is given by: r=-50t^2 + 300t, where “t” is ticket price in dollars. The cost to produce the play

is given by: C=600-50t. Determine the ticket price that will allow Script & Cur to break even.
Mathematics
1 answer:
artcher [175]3 years ago
7 0

ANSWER

$3

Or

$4

EXPLANATION

The revenue function is

r =  - 50 {t}^{2}  + 300t

The cost function is,

C=600-50t

In order to break even, revenue must be equal to cost.

600 - 50t= -50 {t}^{2}  + 300t

Group every term on the LHS.

50 {t}^{2}  - 300t - 50t + 600 = 0

50{t}^{2}  - 350t + 600 = 0

Divide through by 50.

{t}^{2}  - 7t + 12= 0

Factor to obtain,

(t - 3)(t - 4) = 0

t = 3 \: or \: t = 4

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<h2>Answer:</h2><h3>A. Domain </h3>

The domain of a function is the x-values that the graph applies to. This means that the domain is whatever x-values the graph crosses. All vertical parabolas (like the one pictured) have a domain of all reals. This is because any x-value could be plugged into the function and provide a y-value. while it may not seem like it, that graph will cover every single x-value in existence.

  • Domain = All reals

<h3>B. Range</h3>

The range is similar to the domain but is for y-values. So, the range is whatever y-values the graph applies to and crosses. As you can see from the graph, there are no y-values above 1. This means the range is y≤1.

  • Range = y ≤ 1

<h3>C. Increasing Interval</h3>

A graph is increasing when the y-values are increasing. So, on the parent function of a parabola, the graph increases to the right and decreases to the left. However, this graph is inverted and shifted to the left, so the interval will also be flipped and shifted. In this case, the graph increases from -∞ to 2.

  • Increasing Interval = [-∞, 2]

<h3>D. Decreasing Interval</h3>

The decreasing interval is very similar to the increasing interval. This interval applies when the y-values are decreasing as the x-values increase. For a parabola, the increasing and decreasing intervals always meet at the x-value of the vertex, which is 2 on this graph. The y-values decrease during the interval 2 to ∞.

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The direction of a parabola is decided by the sign (+ or -) of the leading coefficient. Positive coefficients open up and negative opens down. As you can see from the graph, the sides of the parabola point downwards. This means that the leading coefficient must be negative.

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A parabola will always only have a min or a max, never both. If a graph opens up it has a min because there is one y-value which is the minimum possible y-value. Graphs that open downwards have a maximum because there is one y-value that is the largest possible. So, this graph has a maximum of 1 because that is the largest possible y-value.

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