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Elenna [48]
2 years ago
15

Dan's goal is to raise more than $4000.00 in order to buy a car his senior year. If he has $2150 saved already and has a job tha

t pays $10 per hour, how many hours does he need to work between now and senior year in order to get his car?​
Mathematics
1 answer:
Neko [114]2 years ago
4 0

Answer:

185

Step-by-step explanation:

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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
Is 24 to 26equivalent ratios??
shtirl [24]
No it is not an equivalent ratio
8 0
3 years ago
Read 2 more answers
Evaluate: n + 8² if n = 2
Papessa [141]

Answer:

It would be 66

Step-by-step explanation:

6 0
3 years ago
An external sinusoidal force is applied to an oscillating system which can be modelled by a model spring and a damper. The gener
Anettt [7]

Answer:

The amplitude of the oscillation in this oscillating system, after reaching the steady-state, is 3.984.

Step-by-step explanation:

Assume you know a and b values, which you do not actually need to know to solve the question.

The given general solution of the equation is made up of three terms, namely:

  • A constant value (equal to 4),
  • a cosine term: 3.984cos(2nt-B)
  • a cosine, exponential term: 2.81exp(-8.58t)cos(at + o)

This means that, after a certain time (for large values of time "t"), when the system reaches its <u>steady-state</u>, the following will happen to these parts, respectively:

  • The constant value will remain as 4. It shall not cancel, but it shall not provide any oscillation either, and, in turn, no amplitude nor frequency.
  • The second term will always be a cosine, since it is a periodic function. Its amplitud is "3.984" and its frequency is "2n" radians/second. Its phase is actually "B".
  • This third term is not a periodic functon. It is made up of a periodic function multiplied by an exponential function, whose exponent is negative (for any positive value of time variable "t"). This exponential function approaches to zero when its exponent approaches to minus infinity. So, after a certain time -or, in other words, once the steady-state is eventually reached- the product will be a delimited function (cosine, whose absolute value is always than "1") multiplied by zero. That is, this third term, as a whole, approaches to zero for large, infinite values of time "t".

All in all, once the steady-state is reached, the solution shall remain as:

x = 4+ 3.984cos(2nt-B).

The only oscillation would be that of the cosine term, and its amplitude will be 3.984, an actual value given by the question itself.

4 0
3 years ago
What are the coordinates of the center of the circle (x-1)²+(y-2)²=2² and y=2x+2?
defon

Answer:

Compare the given equation of the circle (x - 1)² + (y -2)² = 2²

with standard form of circle: (x - h)² + (y - k)² = r²

Here, (h, k) is the center of the circle

and r is the radius of the circle.

Thus, The center of the circle is: (1, 2)

Also, for finding the point of intersections of (x - 1)² + (y -2)² = 2² and y = 2x + 2,

Substitute the value of y from equation of line in the equation of circle.

(x - 1)² + (2x + 2 - 2)² = 2²

⇒ (x - 1)² + (2x)² = 2²

⇒ x² + 1 - 2x + 4x² = 4

⇒ 5x² - 2x - 3 = 0

Applying Middle term splitting method

5x² - 5x + 3x - 3 = 0

⇒ 5x(x - 1) + 3(x - 1) = 0

⇒ (5x + 3)(x - 1) = 0

⇒ x = \frac{-3}{5} and x = 1

Thus, we get coordinates: (\frac{-3}{5} ,\frac{4}{5} ) and (1, 4)

6 0
3 years ago
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