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Thepotemich [5.8K]
2 years ago
11

(d) Which athlete had a greater median distance? A or b

Mathematics
1 answer:
Lubov Fominskaja [6]2 years ago
4 0

Answer:

I think athlete B has the greater median distance

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use Taylor's Theorem with integral remainder and the mean-value theorem for integrals to deduce Taylor's Theorem with lagrange r
Vadim26 [7]

Answer:

As consequence of the Taylor theorem with integral remainder we have that

f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \int^a_x f^{(n+1)}(t)\frac{(x-t)^n}{n!}dt

If we ask that f has continuous (n+1)th derivative we can apply the mean value theorem for integrals. Then, there exists c between a and x such that

\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}dt = \frac{f^{(n+1)}(c)}{n!} \int^a_x (x-t)^n d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{n+1}}{n+1}\Big|_a^x

Hence,

\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{(n+1)}}{n+1} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1} .

Thus,

\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}

and the Taylor theorem with Lagrange remainder is

f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}.

Step-by-step explanation:

5 0
3 years ago
The student council has 10 members where 5 of the members are Seniors. They need to choose a President, Vice President, Secretar
natima [27]

Answer:

P=1/42.

Step-by-step explanation:

We know that the student council has 10 members where 5 of the members are Seniors. They need to choose a President, Vice President, Secretary and Treasurer. We calculate the probability that the President is a Senior:

We calculate the number of possible combinations:

C_4^{10}=\frac{10!}{4!(10-4)!}=210

Number of favorable combinations is 5.

Threfore, the probability is

P=5/210

P=1/42.

8 0
3 years ago
26s? + 33<br> Submit<br> Hzhjskapskdjsjababah
kipiarov [429]

Answer:

59

Step-by-step explanation:

just add the 2 and you should get 59

6 0
2 years ago
PLEASE HELP ITS DUE IN A FEW MINUTES
denis23 [38]
1. a+3a+4b=5b
2. a+3a=5b-4b
3. 4a=5b-4b
4. 4a=b
a=1/4b
(I think 1/4b is the answer) hope this helps :)
4 0
3 years ago
Read 2 more answers
Subtract 3 1/2 from 5 1/3
AleksAgata [21]

Answer:

11/6

Step-by-step explanation:

16/3 - 7/2 = 16/3 x 2/2 - 7/2 x 3/3 = 32/6 - 21/6 = 32-21/6 = 11/6

8 0
3 years ago
Read 2 more answers
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