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wariber [46]
3 years ago
9

What is the area of a circle with a radius of 6 ft? Use 3.14 for π. Round to the nearest tenth if necessary.

Mathematics
2 answers:
Ne4ueva [31]3 years ago
4 0

Step-by-step explanation:

write what you know

A = pi x r^2

r = 6ft

Annd plug and chug

Kamila [148]3 years ago
3 0

Answer:

\boxed {\boxed {\sf a \approx 113.0 \ ft^2}}

Step-by-step explanation:

The area of a circle is the space inside the shape. The formula is:

a= \pi r^2

We know the radius of the circle is 6 feet and we are using 3.14 for pi.

  • r= 6 ft
  • π= 3.14

Substitute the values into the formula.

a= (3.14) \times (6 \ ft)^2

Solve the exponent.

  • (6 ft)² = 6 ft * 6 ft = 36 ft²

a= (3.14) \times 36 \ ft^2

Multiply.

a=113.04 \ ft^2

Let's round to the nearest tenth. The 4 in the hundredth place tells us to leave the 0 in the tenths place.

a \approx 113.0 \ ft^2

The area of the circle is approximately <u>113.0 square feet.</u>

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myrzilka [38]

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

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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

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