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elena55 [62]
1 year ago
10

Use the intermediate value theorem to prove that there is a positive number c such that c2 = 2.

Mathematics
1 answer:
schepotkina [342]1 year ago
6 0

So lets try to prove it,

So let's consider the function f(x) = x^2.

Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infinity).

Using the Intermediate Value Theorem,

it would be enough to show that at some point a f(x) is less than 2 and at some point b f(x) is greater than 2. For example, let a = 0 and b = 3.

Therefore, f(0) = 0, which is less than 2, and f(3) = 9, which is greater than 2. Applying IVT to f(x) = x^2 on the interval [0,3}.

Learn more about Intermediate Value Theorem on:

brainly.com/question/11377865

#SPJ4

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Evan invested $800 in an account that pays 3.25% interest compounded annually.
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Answer:

Evans would have $852.8

Step-by-step explanation:

Given

PV = \$800

r = 3.25\%

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Required

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This is calculated using:

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FV = 800 * (1 .0325)^2

FV = 852.845

FV = 852.8

FV =

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3 years ago
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Area of circle 1 = πr² 
Area of circle 1 = π (10)²
Area of circle 1 = 100π km²

Area of circle 2 = πr²
Area of circle 2 = π (5)²
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Number of times the bigger circle is greater than the smaller circle 
\dfrac{100 \pi }{25 \pi } = 4

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Answer: The big circle is 4 times greater than the small circle.
------------------------------------------------------------------------------------




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