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3 years ago

PLEASE HELP QUICKLY!! I WILL MARK BRAINLIEST!!Find the value of x:

Mathematics

1 answer:

Arlecino [84]3 years ago

5 0

6x+2x= 180
8x=180
x=22.5

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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

Beth is going to the State Fair which costs $10 to get in. Each ride costs $5.50. If he has $45 to spend at the Fair, what is th

Jet001 [13]

Answer:same2434..[-

Step-by-step explanation:25790=/,svxy

5 0

2 years ago

Read 2 more answers

a tree casts a shadow that is 20 ft long. the angle of elevation of the sun is 29°. how tall is the tree?

mars1129 [50]

You can use the trig ratios. Draw a diagram to see which one is appropriate.
Tan would be used.
Tan29=x/20
20Tan29=x
Put this into your calculator and see what you get

3 0

2 years ago

2(x-5)=3(x+7) Show the process, please.

chubhunter [2.5K]

Answer:

-31

Step-by-step explanation:

(2×x) - (2×5) = (3×x) + (3×7)

2x-10 = 3x+21

2x-3x = 21+10

-x = 31

therefore, x = -31

5 0

3 years ago

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Area of a rectangle is 36 what is x if the width is x and length is x+5

Reika [66]

If the length is x+5, the width would be x(x+5)=36

5 0

3 years ago