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scoundrel [369]
3 years ago
6

A circle with radius 9 has a sector with a central angle of 120°.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
8 0

120º is 1/3 of a complete revolution of 360º. So the area of this sector should be 1/3 the area of the complete circle.

A circle with radius 9 has area 9^2 π = 81π.

So the sector has area 81π/3.

Put another way: The area <em>A</em> of a circular sector and its central angle <em>θ</em> (in degrees) occur in the same ratio as the area of the entire circle with radius <em>r</em> according to

<em>A</em> / <em>θ </em>º = (π <em>r </em>^2) / 360º

==>  <em>A</em> = π/360 <em>θ r</em> ^2

In this case, <em>r</em> = 9 and <em>θ</em> = 120º, so

<em>A</em> = π/360 * 120 * 81 = 81π/3

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A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plate
yulyashka [42]

Answer:

25

Step-by-step explanation:

From the given information;

Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.

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\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}

cost per hour = 125

If each plate costs $20 to make, then the total number of plate will equal to 40x

∴

The total cost can be computed as:

C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)

C'(x) = (-\dfrac{12500}{x^2})  + 20  --- (2)

At C'(x) = 0

\dfrac{12500}{x^2} = 20

\dfrac{12500}{20} = x^2

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x = \sqrt{625}

x = 25

C'' (x) = -12500 \times \dfrac{-2}{x^3} +0

C'' (x) = \dfrac{25000}{x^3}

where; x = 25

C'' (x) = \dfrac{25000}{25^3}

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As such, to minimize the cost, the printer needs to make 25 metal plates.

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What is the correct symbol?
Nadusha1986 [10]

Answer:

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Step 1: Solve the fraction

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100/81 = 1.2345678901.....

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