Given that AC is a diameter of the circle above and that mŁABD= 649, find m2DBC.

Mathematics

1 answer:

zlopas [31]4 years ago

5 0

Answer: D

Step-by-step explanation:

You can visually see that they are equal to each other, since the dimater goes directly through the center

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An old-fashioned bicycle has two differently sized wheels. The circumference of the front wheel is 9 feet larger than the circum

Lady_Fox [76]

So, the bicycle looks like the one in the picture below.

now, the circumference of the smaller wheel, will just be C = 2πr, with a radius of "r".

we also know that the large wheel has a circumference that is 9 feet larger than the small one, so, since the small one has a circumference of 2πr, then the large one will have a circumference of 2πr + 9.

after Thomas cycled for a while, the large did 500 revolutions, or times around, whilst the small one did 1400, since it's smaller. On that time, they covered however, the same amount of ground, since they're on the same bike.

The amount covered by the small one in 1400 cycles, is 1400(2πr), that's how much ground it covered.

The amount covered by the large one in 500 cycles, is 500(2πr + 9).

And we know that ground covered, is the same for both, therefore, we also know that 1400(2πr) = 500(2πr + 9).

$\bf \stackrel{small~wheel}{1400(2\pi r)}~~=~~\stackrel{large~wheel}{500(2\pi r+9)}\implies 14(2\pi r)=5(2\pi r+9)
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28\pi r=10\pi r+45\implies 18\pi r=45\implies r=\cfrac{45}{18\pi }
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so, how much ground did they cover anyway?

well, we could use either, since we know what the radius is, hmmmm let's use say the small wheel's circumference,

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14+2x=4x: divide 2x on each side

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if a rectangle has a greater perimeter than another rectangle, does it also have a greater area? Explain.

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No.

The maximum possible area given a constant amount of material for a quadrilateral will always be a square.

For example if the material for the perimeter is 64 we can form a rectangle that is 22 by 10 which will have an area of 220 u^2.

However a square using the same amount of material will have sides of 64/4=16 and an area of 16^2=250 u^2

So in general the area is maximize the closer the sides are to being equal and minimized as the difference between the sides becomes greater. In the case of comparing the material, perimeter, of a rectangle to a square for the same amount of material the square will use less material than the rectangle.

A square can have a smaller perimeter and a greater area that a rectangle.

In the example above the rectangle had a perimeter of 64 u and an area of 220 u^2. If we made a square with just 60 u, it would have an area of 225 u^2.

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