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3 years ago

10

I need help with these three questions can you help me?

1 answer:

ololo11 [35]3 years ago

8 0

Answer:

#2- A

#3- D

#4-1

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:

<u>Part A </u>

Price Function $= 580 - 10x$

The revenue function

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

The marginal revenue function

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

<u>Part B </u>

<u>(Fixed Cost)</u>

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 .

<u> Marginal Cost Function</u>

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

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

<u>Part C </u>

<u>Profit Function </u>

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$

<u> Part D </u>

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

5 roommates share the cost of an apartment: rent,electricity, and gas. rent costs 1800 and gas costs 150 per month. each roommat

Naddik [55]

Answer:

Electricity bill is 175

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Step-by-step explanation:

Given

$Rent = 1800$

$Gas = 150$

$Each\ Roommate = 425$ monthly

$Number\ of\ Roommate = 5$

Required

Determine the electricity bill

If each roommate pays 425, then 5 roommates pay 5 * 425

$Total = 5 * 425$

$Total = 2125$

This implies that: the monthly cost of room, gas and electricity add up to 2125.

In other words,

$Gas + Rent + Electricity = 2125$

$150 + 1800+ Electricity = 2125$

$1950+ Electricity = 2125$

$Electricity = 2125 - 1950$

$Electricity = 175$

<em>Hence, the electricity bill is 175</em>

4 0

2 years ago

4b-4=3b+4<br> solve for b

damaskus [11]

Answer:

4b-3b=4+4

b=8

Step-by-step explanation:

Hence, the value of b is 8

#hope it helps

6 0

2 years ago

Read 2 more answers

mr. pollack's biology class observed the growth of pea plants. if 5 pea plants grew to 30 cm and 15 pea plants grew to 50 cm, wh

rodikova [14]

U do 5 times 30 and get 150 then take 15 times 50 and get 750 last take 750 plus 150 and u get 900 cm

7 0

3 years ago

The midpoint of AB is M (2,0). If the coordinates of A are, (-3, 3), what are the coordinates of B?

gregori [183]

Given:

M is the midpoint of AB.

M(2,0) and A(-3, 3).

To find:

The coordinates of point B.

Solution:

Midpoint formula:

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Let the coordinates of point B are (a,b). Then, using the midpoint formula, we get

$(2,0)=\left(\dfrac{-3+a}{2},\dfrac{3+b}{2}\right)$

On comparing both sides, we get

$\dfrac{-3+a}{2}=2$

$-3+a=2\times 2$

$a=4+3$

$a=7$

And,

$\dfrac{3+b}{2}=0$

$3+b=0$

$3+b-3=0-3$

$b=-3$

Therefore, the coordinates of point B are (7,-3).

5 0

2 years ago