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vlabodo [156]
4 years ago
8

A pinecone drops from a tree branch that is 20 feet above the ground. The function h = –16t2 + 20 is used. If the height h of th

e pinecone is in feet after t seconds, at about what time does the pinecone hit the ground?
Mathematics
1 answer:
Svet_ta [14]4 years ago
4 0

Answer:

  t ≈ 1.118 . . . seconds

Step-by-step explanation:

Set h=0 and solve for t.

  0 = -16t^2 +20

  0 = t^2 -20/16 . . . . . . . . . . . . . . . divide by the coefficient of t^2

  t = √(5/4) = (1/2)√5 ≈ 1.118 . . . . . add 5/4 and take the square root

The pinecone hits the ground about 1.12 seconds after it drops.

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Urgent question in Mathematics. Solve this to get 15 points
Mnenie [13.5K]

Answer:

1.

Step-by-step explanation:

Note that 2^4 - 2^3 = 16 - 8 = 8 = 2^3

In a similar way 2^6 - 2^5 = 64 - 32 = 32 = 2^5.

So 2^99 - 2^98 = 2^98 ,  2^98 - 2^97 = 2^97 ,  2^97 - 2^96 = 2^96 and so on.

Therefore when we come to the last 2 terms we have 2^1 - 2^0 = 2 - 1

= 1 , so the answer is 1.

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3 years ago
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Does there exist a di↵erentiable function g : [0, 1] R such that g'(x) = f(x) for all x 2 [0, 1]? Justify your answer
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Answer:

No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Step-by-step explanation:

Assuming:  the function is f(x)=x^{2} in [0,1]

And rewriting it for the sake of clarity:

Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer

1) A function is considered to be differentiable if, and only if  both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:

g'(0)=g'(1)

2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]

The limit to the left

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g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)

3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Because this is the same as to calculate the limit from the left and right side, of g(x).

f'(c)=\lim_{x\rightarrow c}\left [\frac{f(b)-f(a)}{b-a} \right ]\\\\g'(0)=\lim_{x\rightarrow 0}\left [\frac{g(b)-g(a)}{b-a} \right ]\\\\g'(1)=\lim_{x\rightarrow 1}\left [\frac{g(b)-g(a)}{b-a} \right ]

This is what the Bilateral Theorem says:

\lim_{x\rightarrow c^{-}}f(x)=L\Leftrightarrow \lim_{x\rightarrow c^{+}}f(x)=L\:and\:\lim_{x\rightarrow c^{-}}f(x)=L

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When 'x' and 'y' are in direct proportion , then the relation between 'x' and 'y' is __________
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Step-by-step explanation:

If two quantities x and y vary (change) together in such a manner that the ratio of their corresponding values remains constant, then x and y are said to be in direct proportion.

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