Why does the formula for area of a circle make sense

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

4 0

Answer:

Step-by-step explanation:

The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pi times the radius. The animation above shows that a circle can be cut and rearranged to closely resemble a parallelogram (with height r and base pi times r) of area pi times the square of the radius. By dividing the circle into more than eight slices, the approximation obtained in this manner would be even better. By dividing the circle into more and more slices, the approximating parallelograms approximate the area of the circle arbitrarily close. This give a geometric justification that the area of a circle really is "pi r squared".

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X^2-10x+27 in the form (x-a)^2+B

Irina18 [472]

Answer:

(x-5)^2+2

Step-by-step explanation:

To convert between standard and vertex form, you have to complete the square (which, as a reminder, (a+b)^2 = a^2+2ab+b^2).

Since a^2 is x^2, and 2ab is -10x, then b must be -5, so b^2 is 25. Therefore, we add and subtract 25 from the expression:

(x-10x+25)+27-25

Then, we can make (x-10x+25) to (x-5)^2: