The equation r = (sqrt A)/(pi) gives the radius r of circle with area A. What is the radius of a circle with the given area? Write your answer as a simplified radical and as a decimal rounded to the nearest hundredth.
a. 50 ft^2
by the way you wrote that wrong
pi r^2 = A
r^2 = (A/pi)
r = sqrt (A/pi)
which is
sqrt A/sqrt pi
r = sqrt(50) /sqrt pi = sqrt (25*2) /sqrt pi
= (5 sqrt 2) /sqrt pi
3.98 ft
That's exactly what it said in the textbook.
The formula.
It is incorrect then
The area of a circle is pi r^2
a = pi r^2
r^2 = a/pi
r = sqrt (a/pi) = sqrt a/srt pi
NOT
(sqrt a) / pi NO !
The text did NOT make that error, like no way. It is in your parentheses.
perhaps[is a computer]text/book may refer env of any 'even',en the slang of 'authored book'circle of publishers,factor geom address etc,informations!
To find the radius of a circle with a given area, we can use the equation r = sqrt(A) / pi. In this case, the given area A is 50 ft^2.
To find the radius, we need to substitute the value of A into the equation and simplify:
r = sqrt(50) / pi
First, let's simplify the radical:
sqrt(50) = sqrt(25 * 2) = sqrt(25) * sqrt(2) = 5 * sqrt(2)
Substituting back into the equation:
r = (5 * sqrt(2)) / pi
Now, let's calculate the decimal approximation rounded to the nearest hundredth.
Using the approximation value of pi as 3.14, we can calculate:
r ≈ (5 * sqrt(2)) / 3.14 ≈ 7.97 ft (rounded to the nearest hundredth)
Therefore, the radius of a circle with an area of 50 ft^2 is approximately 5 * sqrt(2) or 7.97 ft.