Take the horse to overtake the

Mathematics

1 answer:

S_A_V [24]3 years ago

6 0

Answer:

120 km/h

Step-by-step explanation:

Speed in one direction = 40 km/h
Speed on return = x
Average speed = 60 km/h

Let the distance be d

Average speed

2d/(d/40 + d/x) = 60
d/40 + d/x = 2d/60
1/40 + 1/x = 1/30
1/x = 1/30 - 1/40
1/x = (4-3)/120
1/x = 1/120
x = 120 km/h

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Answer:

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3 years ago

How is the series 5+11+17…+251 represented in summation notation?

NISA [10]

Answer:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

Step-by-step explanation:

Given:

Series 5+11+17+...+251

To find:

Summation notation of the given series

Summation Notation:

$\displaystyle \large{\sum_{k=1}^n a_k}$

Where n is the number of terms and $\displaystyle \large{a_k}$ is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

11-5 = 6
17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

Arithmetic Sequence

$\displaystyle \large{a_n=a_1+(n-1)d}$

Where $\displaystyle \large{a_n}$ is the nth term, $\displaystyle \large{a_1}$ is the first term and $\displaystyle \large{d}$ is the common difference: