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2 years ago

Examine the diagram. It is not drawn to scale.

Mathematics

1 answer:

konstantin123 [22]2 years ago

8 0

Answer: I estimate that it is 119

Step-by-step explanation:

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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

2 years ago

What is the value of y?

RUDIKE [14]

Answer:

C. 55

Step-by-step explanation:

Since all angles in a triangle add up to 180°, we have:

40 + y + y + 30 = 180

2y + 70 = 180

2y = 110

y = 55

7 0

2 years ago

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∫ 5cos(x) - 2sec²(x) dx

daser333 [38]

$\bf \displaystyle \int [5cos(x) - 2sec^2(x)]dx\implies 5\int cos(x)dx~-~2\int sec^2(x)dx
\\\\\\
5sin(x)-2tan(x)+C$

5 0

2 years ago

Plz help me with my math

dsp73

If the area is 10 square meters than double that is area of a rectangle with height = 5m and base of 4m because height • base should produce 20m^2.

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2 years ago

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P- 6= -5 what is the answer (NEED HELP)

slega [8]

Answer:

P=1

Step-by-step explanation:

1-6=-5

3 0

2 years ago