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Diano4ka-milaya [45]
3 years ago
9

Please help me out!!!!

Mathematics
1 answer:
LuckyWell [14K]3 years ago
7 0

Answer:

the value for x is

11 \sqrt{3}

and the value for y is 11 on the triangle problem we use sin60 to find x and we use tan60 to find y

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A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per
HACTEHA [7]

Answer:

A) Revenue function = R(x) = (580x - 10x²)

Marginal Revenue function = (580 - 20x)

B) Fixed Cost = 900

Marginal Cost function = (300 + 50x)

C) Profit function = P(x) = (-35x² + 280x - 900)

D) The quantity that maximizes profit = 4

Step-by-step explanation:

Given,

The Price function for the cake = p = 580 - 10x

where x = number of cakes sold per day.

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

where x = number of cakes sold per day.

Please note that all the calculations and functions obtained are done on a per day basis.

A) Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity]

Revenue = R(x) = price × quantity = p × x

= (580 - 10x) × x = (580x - 10x²)

Marginal Revenue = (dR/dx)

= (d/dx) (580x - 10x²)

= (580 - 20x)

B) Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced]

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

The total cost function is a sum of the fixed cost and the variable cost.

The fixed cost is the unchanging part of the total cost function with changing levels of production (quantity produced), which is the term independent of x.

C(x) = 900 + 300x + 25x²

The only term independent of x is 900.

Hence, the fixed cost = 900

Marginal Cost function = (dC/dx)

= (d/dx) (900 + 300x + 25x²)

= (300 + 50x)

C) Find the profit function [Hint: profit is revenue minus total cost]

Profit = Revenue - Total Cost

Revenue = (580x - 10x²)

Total Cost = (900 + 300x + 25x²)

Profit = P(x)

= (580x - 10x²) - (900 + 300x + 25x²)

= 580x - 10x² - 900 - 300x - 25x²

= 280x - 35x² - 900

= (-35x² + 280x - 900)

D) Find the quantity that maximizes profit

To obtain this, we use differentiation analysis to obtain the maximum point of the Profit function.

At maximum point, (dP/dx) = 0 and (d²P/dx²) < 0

P(x) = (-35x² + 280x - 900)

(dP/dx) = -70x + 280 = 0

70x = 280

x = (280/70) = 4

(d²P/dx²) = -70 < 0

Hence, the point obtained truly corresponds to a maximum point of the profit function, P(x).

This quantity demanded obtained, is the quantity demanded that maximises the Profit function.

Hope this Helps!!!

8 0
3 years ago
Write an equation in standard form of a quadratic function that has x-intercepts -2 and 5 and k=-4
bulgar [2K]

Answer:

-2x + 5 = -4k

Step-by-step explanation:

8 0
3 years ago
Let f ( x ) = 2 x − 1 , g ( x ) = 3 x , and h ( x ) = x ^2 + 1 , what is h( h ( 5) ) ?
strojnjashka [21]
First you would solve for h(5) by plugging in 5 as your x, then solving it.

h(5) = 5^2 + 1
h(5) = 25 + 1
h(5) = 26

Next you would multiply the 26 by the individual h, which is basically h(1).

h(1) = 1^2 + 1
h(1) = 2

Lastly you multiply your h(1) value by the h(5) value to get your answer.

h(1) • h(5) = 26 • 2
h[h(5)] = 52
7 0
4 years ago
William just accepted a job at a new company where he will make an annual salary of
IRISSAK [1]

Answer:

Step-by-step explanation:

He gets a new job and it pays him $60k each year.

Amount per year: 60,000

He gets a raise of $5k

Amount per year: 65,000

After 5 years of working there you times 5 by your amount you get per year.

5 x 65,000 = 325,000

Therefore you get...

$325k every five years

To know how much it is in ten years multiply 325k by 2

325,000 x 2 = 650,000

Salary after 5 years: 325,000

Salary after 10 years: 650,000

<3 Enjoy,

    Dea

6 0
3 years ago
The amount of money in Joe’s savings account is increased by 8% each year. Given that he has £500 in 2016. Work out how much Joe
ololo11 [35]

Answer:

£700

Step-by-step explanation:

First we find the interest on this money.

Interest = Principal * Rate * Time

             =\frac{500 * 8 * 5}{100}

            =5 * 8 * 5

            =£200

Interest = £200

Now you add his actual money to the interest you just found to give you the total amount.

Amount = £500 + £200

             = £700

5 0
3 years ago
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