In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus.
Answer:
Step-by-step explanation:
According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one <em>c</em> within (a, b) such that f'(c) = 0.
We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a <em>c</em> in (5, 8) such that g'(c) = 0.
So, differentiate the function. We can take the derivative of both sides with respect to <em>x: </em>
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Differentiate:
Let g'(x) = 0:
Solve for <em>x</em>. First, divide everything by negative seven:
Factor:
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Zero Product Property:
Solve for each case. Hence:
Since the first solution is not within our interval, we can ignore it.
Therefore:
Answer:
see below
Step-by-step explanation:
Except for the stretch factor, your work is completely correct. Multiplying only the x-coordinate by a factor of 2 results in a horizontal stretch by that factor.
Your coordinates and graph are correct.
In the comparison, you just need to say what happened.
Answer:
$2560
Step-by-step explanation:
if 10%=256
then 10 times the amount 100% is 2560