Answer:
Option D.
Step-by-step explanation:
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Option D. is the correct answer.
AB is a diameter of the circle, CD is a chord equal to the radius of the circle. AC and BD when extented intersect at a point E.
Prove that angle AEB = 60°
1 answer:
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The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
What is the intermediate value theorem?
Intermediate value theorem is theorem about all possible y-value in between two known y-value.
x-intercepts
-x^2 + x + 2 = 0
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1, x = 2
y intercepts
f(0) = -x^2 + x + 2
f(0) = -0^2 + 0 + 2
f(0) = 2
(Graph attached)
From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3
For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.
<em>Your question is not complete, but most probably your full questions was</em>
<em>Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?</em>
Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
Learn more about intermediate value theorem here:
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Answer:
about 81 years
Step-by-step explanation:
A graphing calculator can give you the answer easily.
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You can solve the problem algebraically by putting in the given number and solving for t.
30000 = 32000/(1 +12.8e^(-.065t))
12.8e^(-.065t) = (32000/30000) -1 = 1/15
e^(-.065t) = 1/(15·12.8) = 1/192 . . . . . divide by 12.8
-0.065t = ln(1/192) ≈ -5.257 . . . . . . take the natural log
t = -5.257/-0.065 ≈ 80.88 . . . . . . . .divide by the coefficient of t
It will take about 81 years for the number of trees to reach 30,000.
