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3 years ago

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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For the straight line defined by the points (2, 55) and (4, 91), determine the slope and y-intercept. do not round the answers.

mixas84 [53]

Hello : let A(2,55) B(4,91)<span>
the slope is : (YB - YA)/(XB -XA)
(91-55)/(4-2) = 36/2 =18
an equation is : y-55 = 18(x-2)</span>

<span> y-intercept when : x = 0 : y - 55 = 18(0-2)
y-55 = -36
y = 55-36 = 19</span>

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3 years ago

The population of rabbits on an island is growing exponentially. In the year 1991, the population of rabbits was 9100, and by 19

lisabon 2012 [21]

Answer:

$39,223\ rabbits$

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

$y=a(1+r)^x$

where

y is the population of rabbits

x is the number of years since 1991

a is the initial value

r is the rate of change

we have

$a=9,100$

substitute

$y=9,100(1+r)^x$

For the year 1998

the number of years is equal to

x=1998-1991=7 years

we have the ordered pair (7,18,000)

substitute in the exponential equation and solve for r

$18,000=9,100(1+r)^7$

$(18,000/9,100)=(1+r)^7$

elevated both sides to 1/7

$(1+r)=1.1023$

$r=0.1023$

therefore

$y=9,100(1+0.1023)^x$

$y=9,100(1.1023)^x$

Predict the population of rabbits in the year 2006

Find the value of x

x=2006-1991=15 years

substitute the value of x in the equation

$y=9,100(1.1023)^{15}$

$y=39,223\ rabbits$

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3 years ago

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Answer:

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Step-by-step explanation:

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Third has y-int at 2

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4 years ago

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