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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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A bird sees a worm on the ground 50 m. below. The bird dives for the worm at a speed of 6 m/sec. The function h\left( t \right)
iragen [17]

<u>Given</u>:

The height of the bird at time t is given by the function h(t)=-4.9t^2+6t+50

We need to determine the time it takes the worm to be eaten by the bird.

<u>Time taken:</u>

The time can be determined by substituting h(t) = 0 in the function.

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Switch sides, we get;

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Simplifying, we get;

t=\frac{-6 \pm \sqrt{36+980}}{-9.8}

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The values of t are given by

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Thus, the time taken by the bird to eat the worm is t=3.9 seconds.

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