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3 years ago

Provide reasons for the statements.(Thank you!)

Mathematics

1 answer:

Readme [11.4K]3 years ago

8 0

Answer:

That's great for you. I hope u got your answers

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QUESTION 3 [10 MARKS] A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the nu

Harman [31]

Answer:

(a)Revenue function, $R(x)=580x-x^2$

Marginal Revenue function, R'(x)=580-2x

(b)Fixed cost =900 .

Marginal Cost Function=300+50x

(c)Profit, $P(x)=-35x^2+280x-900$

(d)x=4

Step-by-step explanation:

Part A

Price Function $= 580 - 10x$

The revenue function

$R(x)=x\cdot (580-10x)\\R(x)=580x-x^2$

The marginal revenue function

$\dfrac{dR}{dx}= \dfrac{d}{dx}(R(x))=\dfrac{d}{dx}(580x-x^2)=580-2x\\R'(x)=580-2x$

Part B

(Fixed Cost)

The total cost function of the company is given by $c=(30+5x)^2$

We expand the expression

$(30+5x)^2=(30+5x)(30+5x)=900+300x+25x^2$

Therefore, the fixed cost is 900 .

Marginal Cost Function

If $c=900+300x+25x^2$

Marginal Cost Function, $\frac{dc}{dx}= (900+300x+25x^2)'=300+50x$

Part C

Profit Function

Profit=Revenue -Total cost

$580x-10x^2-(900+300x+25x^2)\\580x-10x^2-900-300x-25x^2\\$Profit,P(x)=-35x^2+280x-900$

Part D

To maximize profit, we find the derivative of the profit function, equate it to zero and solve for x.

$P(x)=-35x^2+280x-900\\P'(x)=-70x+280\\-70x+280=0\\-70x=-280\\$Divide both sides by -70\\x=4$

The number of cakes that maximizes profit is 4.

6 0

3 years ago

Betsy is shopping for a new rug, and she finds a square rug that she wants to purchase for her living room. Before purchasing th

Alika [10]

Options:

A.) square root

B.) exponential

C.) absolute value

D.) cube root

Answer : A) square root

We know area of square having side 's' = s* s = $s^2$

For example

Area of square = $16 cm^2$

To find side we take square root

Area = $(side)^2$

16 = $(side)^2$

Take square root on both sides

$\sqrt{16}= \sqrt{side^2}$

4= side

Betsy knows that the area of the rug is A square feet.

Area A = $(side)^2$

$\sqrt{A} = side$

So answer is square root.

6 0

3 years ago

Read 2 more answers

A car uses 1 gallon of gasoline for every 25 miles driven. At the start of a trip the tank was full of gasoline. After driving 5

dezoksy [38]

Answer:

d = 22 - x / 25

Step-by-step explanation:

The first thing is to calculate the tank capacity, we know that per gallon 25 miles are traveled and at 500 miles there were still two gallons, therefore:

500 miles / 25 miles / gallon = 20

and how there were still 2

20 + 2 = 22

the tank has a 22 gallon capacity

Therefore the equation would be:

d = 22 - x / 25

where x is the number of miles traveled.

for example, if they have traveled 500 miles it would be:

d = 22 - 500/25 = 22 - 20

d = 2 gallons

we can verify that it is correct because it is what the statement says

8 0

3 years ago

Please answer the question

Lunna [17]

A since 19 x 29= 551 and 551/375 is around 1.5

4 0

3 years ago

a camera sells for $100. this is $10 less than twice the price of the camera last year. what was the price of the camera last ye

Lesechka [4]

Answer:

55?

Step-by-step explanation:

110 would be the last year for two and then divide by two

8 0

3 years ago

Provide reasons for the statements.(Thank you!)​

Provide reasons for the statements.(Thank you!)