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ASHA 777 [7]
3 years ago
15

The ticket office at Orchestra Center estimates that if it charges x dollars for box seats for a concert, it will sell 50 - x bo

x seats. The function S = 50x - x2 gives the estimated income from the sale of box seats. Graph the function, and use the graph to find the price for box seats that will give the greatest income.

Mathematics
2 answers:
Rasek [7]3 years ago
5 0

Answer:  

Here, the given function,

S(x) = 50 x - x ^2 ----- (1)

For the maximum value of s(x),

s'(x) = 0

Where s'(x) is the first derivative of S(x)

By differetiating equation (1) with respect to x,

We get,

S'(x)= 50 - 2x

⇒ For maximum value of S(x), s'(x) = 0

⇒  50 - 2x = 0

⇒ 2x = 50

⇒ x = $ 25



Dmitriy789 [7]3 years ago
4 0
To estimate the price of box seats for the ticket office to have the greatest income, we derive the equation and equate the derivative to zero. 
                                    S = 50x - x²
Deriving,
                                dS = 50 - 2x = 0
The value of zero from the generated equation is 25. Thus, the company should sell tickets at approximately $25. 
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3 years ago
the total weight of 6 pieces of butter and a bag of sugar is 3.8 Ib. if the weight of the bag of sugar is 1.4 Ib, what is the we
baherus [9]

0.4 lbs each.

<h3>Further explanation</h3>

<u>Given: </u>

  • The total weight of 6 pieces of butter and a bag of sugar is 3.8 Ib.
  • The weight of the bag of sugar is 1.4 Ib

<u>Question: </u>

What is the weight of each piece of butter?

<u>The Process: </u>

The two steps for obtaining the weight of each piece of butter are as follows:

<u>Step-1:</u> the total amount of butter is the total bag of butter and sugar subtracted by the weight of the bag of sugar.

\boxed{ \ 3.8 \ lbs - 1.4 \ lbs = 2.4 \ lbs \ }

<u>Step-2:</u> the total amount of butter divided by the number of pieces of butter is the the weight of each piece of butter.

\boxed{ \ 2.4 \ lbs \div 6 \ pieces = \boxed{ \ 0.4 \ lbs/piece \ } \ }

Let's also consider the following quick steps.

<u>Quick steps: </u>

\boxed{ \ \frac{(3.8 - 1.4) \ lbs}{6 \ pieces} = \boxed{ \ 0.4 \ lbs/piece \ } \ }

Therefore, the weight of each piece of butter is 0.4 lbs.

<h3>Learn more </h3>
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Keyword: the total weight, 6 pieces of butter, a bag of sugar is 3.8 Ib, if the weight of the bag of sugar is 1.4 Ib, each piece, subtracted, divide

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3 years ago
How do you get an equation to solve for all 3 sides of a triangle?
slavikrds [6]

In your solving toolbox (along with your pen, paper and calculator) you have these 3 equations:

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When there is an angle opposite a side, this equation comes to the rescue.

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3. Law of Cosines (the Cosine Rule):

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This is the hardest to use (and remember) but it is sometimes needed  

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It is an enhanced version of the Pythagoras Theorem that works  

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There are SIX different types of puzzles you may need to solve. Get familiar with them:

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2. AAS

This mean we are given two angles of a triangle and one side, which is not the side adjacent to the two given angles.

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Such a triangle can be solved by using Angles of a Triangle to find the other angle, and The Law of Sines to find each of the other two sides. See Solving "AAS" Triangles.

 

3. ASA

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4. SAS

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In this case, use The Law of Sines first to find either one of the other two angles, then use Angles of a Triangle to find the third angle, then The Law of Sines again to find the final side. See Solving "SSA" Triangles .

 

6. SSS

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In this case, we have no choice. We must use The Law of Cosines first to find any one of the three angles, then we can use The Law of Sines (or use The Law of Cosines again) to find a second angle, and finally Angles of a Triangle to find the third angle.

7 0
3 years ago
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ryzh [129]
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