The circumference of a circle is 16π inches. Show how you can use this information to calculate the same circle’s area.
2 answers:
The equation used to find the area of a circle is 
×radius²=A
The equation used to find the circumference of a circle is×diameter=circumfrence
1) You will need your diameter and radius in order to find the area of the circle. In this case, working backward will help.
2) Set your circumference equation equal to 16 and solve for diameter by dividing by on the left and right sides.
3) From this, you will find that your diameter equals 16in.
4) Half of a circles diameter is the radius so divide 16in (diameter) by 2 to find the radius. This will come out to be 8in.
5) Now that you know the radius, you can plug in the radius to the area of a circle equation to find the area of the circle:×(8)²
6)×(8)²= 201.06in²=A
-E :)
The equation used to find the circumference of a circle is
1) You will need your diameter and radius in order to find the area of the circle. In this case, working backward will help.
2) Set your circumference equation equal to 16
3) From this, you will find that your diameter equals 16in.
4) Half of a circles diameter is the radius so divide 16in (diameter) by 2 to find the radius. This will come out to be 8in.
5) Now that you know the radius, you can plug in the radius to the area of a circle equation to find the area of the circle:
6)
-E :)
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Finding the discriminant:
The roots of a quadratic equation are real and distinct if the value of its discriminant is greater than 0.
If we observe the value of discriminant, it is a sum of two terms in this case. The first term is square of (5h), which will always be a positive term or zero if h is zero. The second term is 24k. The value of 24k will always be positive for positive values of k.
Thus for positive values of k, the discriminant of given equation is always positive and thus we can say the root of given equation will always be real and distinct for positive values of k.