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2 years ago

The equation of a circle is given below.

Mathematics

1 answer:

hram777 [196]2 years ago

8 0

Answer:

The center of the circle is (2/3, 0) and radius is ±6units

Step-by-step explanation:

Given the equation of a circle given as shown;

(x-2/3)²+y² = 36

To get the radius and centre of the circle, we will compare the equation with the general equation of a circle given as;

(x-a)²+(y-b)² = r² where (a, b) is the centre of the circle and r is the radius.

Comparing with the given equation,

we will see that;

a = 2/3, b = 0 and r² = 36

If r² = 36

r = ±√36

r = ±6

This shows that the center of the circle (a, b) = (2/3, 0) and radius is ±6

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2 years ago

The population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. A) Estimate how lo

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Answer:

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B) 100.42 years.

Step-by-step explanation:

We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.

A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.

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$7.1 \times 2=7.1(1.011)^{t}$

$\frac{7.1 \times 2}{7.1} =(1.011)^{t}$

$2 =(1.011)^{t}$

Now let us solve for t using logarithm.

$ln(2) =ln (1.011)^{t}$

$ln(2) =t \cdot ln(1.011)$

$0.6931471805599453 =t \cdot 0.0109399400383344$

$t=\frac{0.6931471805599453}{0.0109399400383344}$

$t=63.3593217267282743049\approx 63.36$

Therefore, it will take 63.36 years the population to be double.

B) Now we will find the number of years it will take the population to be triple of its size.

$7.1 \times 3=7.1(1.011)^{t}$

$\frac{7.1 \times 3}{7.1} =(1.011)^{t}$

$3 =(1.011)^{t}$

Now let us solve for t using logarithm.

$ln(3) =ln (1.011)^{t}$

$ln(3) =t \cdot ln(1.011)$

$1.0986122886681097 =t \cdot 0.0109399400383344$

$t=\frac{1.0986122886681097}{0.0109399400383344}$

$t=100.4221490079915311298\approx 100.42$

Therefore, it will take 100.42 years the population to triple of its size.

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