Answer:
Radius, r = 61 cm
Step-by-step explanation:
According to the attached figure, we have,
Length of chord, AB = 22 cm
Such that, AP = PB = 11 cm
OP = 60 cm
It is required to find the radius of the circle. We know that radius of a circle is perpendicular to chord. So, APO forms a right angled triangle. Using Pythagoras theorem to find the radius of circle. Let it is r. So,
So, the radius of the circle is 61 cm.
The area is changing at an increasing rate because the values of A(0), A(5), and A(10) increases as t increases
<h3>Find the area at times t = 0, t = 5, and t = 10.</h3>The complete question is added as an attachment
The function is given as:
A(t) = 9 * (1.1)^t
Substitute t = 0, t = 5, and t = 10.
A(0) = 9 * (1.1)^0 = 9
A(5) = 9 * (1.1)^5 = 14.5
A(10) = 9 * (1.1)^10 = 23.3
The area is changing at an increasing rate because the values of A(0), A(5), and A(10) increases as t increases
<h3>Use the results of part a to find the radius of the culture at these three times</h3>The area of a circle is
A = πr^2
Make r the subject
r = √(A/π)
So, we have:
r = √(9/π) = 1.7
r = √(14.5/π) = 2.1
r = √(23.3/π) = 2.7
The radius is changing at an increasing rate
<h3>Write an equation for the composite function R(A(t)).</h3>In (b), we have:
r = √(A/π)
Express as a function
r(A(t)) = √(A/π)
Hence, the equation for the composite function is R(A(t)) = √(A/π)
<h3>The restriction for the function R * A</h3>We have:
r(A(t)) = √(A/π)
A(t) = 9 * (1.1)^t
This gives
r(A(t)) = √(9 * (1.1)^t/π)
The radius is 30.
So, we have:
√(9 * (1.1)^t/π) = 30
Square both sides
(9 * (1.1)^t/π)= 900
Divide by 9
(1.1)^t/π= 100
Multiply by π
(1.1)^t= 314
Take the logarithms of both sides
t * log(1.1) = log(314)
Solve for t
t = 60
Hence, the restriction on the domain is 0 <= t <= 60
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