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3 years ago

Find the area of a circle with a diameter of 56 millimeters.

Mathematics

1 answer:

ANEK [815]3 years ago

6 0

Answer: 784π mm²

Step-by-step explanation: To find the area of a circle, start with the formula for the area of a circle which is shown below.

Area = πr²

Notice that here, we're given the diameter instead of the radius.

Remember that the radius is equal to half of the diameter. So the radius of this circle will be equal to half 56 millimeters or 28 millimeters.

So plugging into the formula, we have (π)(28 mm)².

A common mistake is to plug 56 millimeters into the formula but remember that we must plug in the radius and not the diameter.

Multiplying, (28 mm)² is equal to (28 mm)(28 mm) or 784 mm².

So we have 784π mm².

So the area of the circle is 784π mm².

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Given that two fair dice are rolled 3 times and the sum of the numbers that come up is recorded.

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2 years ago

The point C(2,3) is translated along a vector that is parallel to the line y=3x-2. The translation vector has magnitude square r

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Step-by-step explanation:

The translation vector v can be resolved into its x and y components, where x² + y² = 10 (Pythagoras' Theorem) and y = 3x

(parallel to y = 3x - 2, slope = 3).

We have x² + (3x)² = 10,

=> x² + 9x² = 10, 10x² = 10, x = 1 or x = -1.

When x = 1, y = 3. When x = -1, y = -3.

Therefore 2 possible translation vectors

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Second new C'= (2 + (-1), 3 + (-3)) = (1, 0).

The possible images are (3, 6) and (1, 0).

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3 years ago