Miguel borrowed $1,800for 2 years and ended up paying $180 in simple interest . What was the interest rate

The number of players in a tennis tournament is reduced by half (50%) after every round. In round 1 there are 256 player, in rou

Aleks04 [339]

Answer:

$a_{n} = a_{1} (\frac{1}{2} )^{n - 1}$ where $a_{1} = 256$ .

The number of players compete in round 7 will be 4.

Step-by-step explanation:

The number of players in a tennis tournament is reduced by half (50%) after every round. In round 1 there are 256 players, in round 2 there are 128 players, and so on.

So, the number of players is multiplied by $\frac{1}{2}$ gives the number of players in the next round.

Therefore, the explicit function of number of players in nth round is given by

$a_{n} = a_{1} (\frac{1}{2} )^{n - 1}$ where $a_{1} = 256$ .

Therefore, the number of players compete in round 7 will be $a_{7} = 256 \times (\frac{1}{2} )^{(7 - 1)} = 4$ . (Answer)

8 0

2 years ago

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

dexar [7]

Answer:

The total revenue is $TR=580x-10x^2$ .

The marginal revenue is $MR=580-20x$ .

The fixed cost is $900.

The marginal cost function is $MC=50x+300$ .

Step-by-step explanation:

The Total Revenue ( $TR$ ) received from the sale of $x$ goods at price $p$ is given by

$TR=p\cdot x$

The Marginal Revenue ( $MR$ ) is the derivative of total revenue with respect to demand and is given by

$MR=\frac{d(TR)}{dx}$

From the information given we know that the price they can sell cakes is given by the function $p=580-10x$ , where $x$ is the number of cakes sold per day.

So, the total revenue is

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

And the marginal revenue is

$MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x$

The Fixed Cost ( $FC$ ) is the amount of money you have to spend regardless of how many items you produce.

The Marginal Cost ( $MC$ ) function is the derivative of the cost function and is given by

$MC=\frac{d(TC)}{dx}$

We know that the total cost function of the company is given by $C=(30+5x)^2$ , which it is equal to

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900$

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

And the marginal cost function is

$MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300$