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Law Incorporation [45]
3 years ago
6

The length of a rectangular state park is 2 miles longer than twice the width. The area of the park is 84 square miles. What is

the width of the park?

Mathematics
1 answer:
klasskru [66]3 years ago
8 0

Answer:

Step-by-step explanation:

hello : look this solution

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Suppose that f : [a, b] → [a, b] is continuous. Prove that f has a fixed point. That is, prove that there exists c ∈ [a, b] such
nikklg [1K]

Answer:

Step-by-step explanation:

define the function:

g(x) = f(x) -x

As both f(x) and x are continuous functions, g(x) will also be continuous.

Now, what can we say about g(a) = f(a) -a?

we know that a\leq f(a) \leq b, thus:

a-a\leq f(a)-a \leq b-a\\0 \leq g(a) \leq b-a

thus  g(a) is non-negative.

What about g(b) ? Again we have:

a\leq f(b) \leq b\\a-b \leq f(b) -b \leq  0\\a-b \leq g(b) \leq  0

That means that g(b) is not positive.

Now, we can imagine two cases, either one of g(a) or g(b) is equal to zero, or none of them is. If either of them is equal to zero, we have found a fixed point! In fact, any point c for which g(c)=0 is a fixed point, because:

g(c) = 0 \implies f(c) -c = 0 \implies f(c) = c

Now, if g(a) \neq  0 and g(b) \neq 0, then we have that

g(a) >0 and g(b) < 0. And by Bolzano's theorem we can assert that there must exist a point c between a and b for which g(c)=0. And as we have shown before that point would be a fixed point. This completes the proof.

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3 years ago
HELP ME ILL GIVE YALL BRAINLIESST
Hatshy [7]

Answer:

615.44 cm^2

Step-by-step explanation:

here r, radius is 14 cm and π as 3.14

area of circle = πr^{2}

3.14 * 14^2

3.14 * 14 * 14

615.44cm^2

8 0
2 years ago
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