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marishachu [46]
3 years ago
6

Write a function using function notation to describe each situation. Find a reasonably domain and range for each function. A new

spaper charges $3 per line for the first 4 lines plus a $20 fee to advertize.
Mathematics
1 answer:
uysha [10]3 years ago
8 0

Answer:

The answer is below

Step-by-step explanation:

The domain of a function is the set of all independent variables for the function while the range of a function is the set of all possible dependent variables.

Let x represent the number of newspaper lines and f(x) be the charges for advertisement. x is the independent variable and f(x) is the dependent variable.

Since the newspaper charges $3 per line for the first 4 lines plus a $20 fee to advertise, the function is given as:

f(x) = 3x + 20 for 0 < x < 4

But for more than four lines, the charges is given as:

f(x) = 12 + 20 = 32         4 < x < ∞

Therefore, the domain and range of the function is:

Domain = (0, ∞)

Range = (20, 32}

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A restaurant operator in Accra has found out that during the lockdown,if she sells a plate of her food for Ghc 20 each,she can s
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The demand equation illustrates the price of an item and how it relates to the demand of the item.

  • The slope of the demand function is -1/2
  • The equation of the demand function is: R(x) = (300 - 10x) \times (20 + 5x)
  • The price that maximizes her revenue is: Ghc 85

From the question, we have:

Plates = 300

Price = 20

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}

The slope (m) is calculated using:

m = \frac{y_2 - y_1}{x_2 - x_1}

So, we have:

m = \frac{25-20}{290-300}

m = \frac{5}{-10}

m = -\frac{1}{2}

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

R(x) = (300 - 10x) \times (20 + 5x)

Open the brackets to calculate the maximum revenue

R(x) =6000 + 1500x - 200x - 50x^2

R(x) =6000 + 1300x - 50x^2

Equate to 0

6000 + 1300x - 50x^2 =0

Differentiate with respect to x

1300 - 100x =0

Collect like terms

100x =1300

Divide by 100

x =13

So, the price at maximum revenue is:

Price= 20 + 5x

Price= 20 + 5 * 13

Price= 85

In conclusion:

  • The slope of the demand function is -1/2
  • The equation of the demand function is: R(x) = (300 - 10x) \times (20 + 5x)
  • The price that maximizes her revenue is: Ghc 85

Read more about demand equations at:

brainly.com/question/21586143

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Step-by-step explanation:

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In 2 mins., a conveyor belt moves 300 lbs. Of recycle aluminum from delivery truck to a storage area. A smaller belt moves the s
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Answer:

1.8 minutes or 108 seconds

Step-by-step explanation:

The question tells us that the larger belt moves 300 lbs in 2 mins. And this is equal to 150 lb per minute

The question also tells us that a smaller belt moves the same quantity of 300 lbs in 18 mins. And this is equal to an average of 16.667 lb per min.

Both belts will move at a rate of 166.667 lb per min.

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