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melomori [17]
3 years ago
11

A 210∘ arc has a length of 42π. Find the radius of the circle.

Mathematics
1 answer:
Phantasy [73]3 years ago
4 0

Answer:

20

Step-by-step explanation:

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A box is being created out of a 15 inch by 10 inch sheet of metal. Equal-sized squares are cutout of the corners, then the sides
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Answer:

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

Step-by-step explanation:

Given that,

A box is being created out of a 15 inches by 10 inches sheet of metal.

The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.

The length of the metal box be = (15-2x) inches.

The width of the metal box be =(10-2x) inches

The height of the metal box be =x inches

Then, the volume of the metal box= length×width×height

                                                         =(15-2x)(10-2x)x cubic inches

                                                         =(150x-50x²+4x³) cubic inches

∴ V= 4x³-50x²+15x

Differentiating with respect to x

V'=12x²-100x+15

Again differentiating with respect to x

V''=24x-100

For maximum or minimum value, V'=0

12x²-100x+15=0

Apply quadratic formula x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}, here a=12, b= -100 and c=15

x=\frac{-(-100)\pm\sqrt{(-100)^2-4.12.15}}{2.12}

\Rightarrow x=\frac{100\pm\sqrt{9280}}{2.12}

\Rightarrow x=0.1528,8.18

For x= 8.18, The value of (15-2x) and (10-2x) will negative.

∴x=0.1528 .

Now, V''|_{x=0.1528}=24(0.1528)-100

∴At x=0.1528 inch, the volume of the metal box will be maximum.

Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box  has largest volume.

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What is the mode of the following set of numbers: 10, 20, 30, 20, 30, 10, 30, 20, 30, 15 *
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Answer:

A. 30

Step-by-step explanation:

Because it showed up the most

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Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. S
Georgia [21]

Answer:

Step-by-step explanation:

Total number of boxes of cookies that Kendal bought to bring to the party is x.

Each box contains 12 cookies. This means that total number of cookies in x boxes would be

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She decides to keep two boxes for herself. This means that the total number of cookies that she kept for herself would be

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The equation that can be used to find the number of boxes, x, Kendal bought would be

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Divide 304 by 8, then multiply the answer by 5

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