find the value of x.​

Answer:

Consider,

[tex]\sf \:\ ^nC_{r} + \ ^nC_{r - 1} \\ \\ [/tex]

We know,

[tex]\boxed{ \sf{ \:\ ^nC_{r} \: = \: \frac{n!}{r!(n - r)!} \: }} \\ \\ [/tex]

So, using this result, we get

[tex]\sf \: = \: \dfrac{n!}{r!(n - r)!} + \dfrac{n!}{(r - 1)!(n - r + 1)!} \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{n!}{r(r - 1)!(n - r)!} + \dfrac{n!}{(r - 1)!(n - r + 1)(n - r)!} \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{n!}{(r - 1)!(n - r)!}\left(\dfrac{1}{r} + \dfrac{1}{n - r + 1} \right) \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{n!}{(r - 1)!(n - r)!}\left( \dfrac{n - r + 1 + r}{r(n - r + 1)} \right) \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{n!}{(r - 1)!(n - r)!}\left( \dfrac{n+ 1}{r(n - r + 1)} \right) \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{(n + 1)n!}{r(r - 1)!(n - r + 1)(n - r)!} \\ \\ [/tex]

[tex]\sf \: = \: \dfrac{(n + 1)!}{r!(n + 1 - r)!} \\ \\ [/tex]

[tex]\sf \: = \: \ ^{n + 1}C_{r} \\ \\ [/tex]

Hence,

[tex]\sf\implies \bf \: \ ^nC_{r} + \ ^nC_{r - 1}= \: \ ^{n + 1}C_{r} \\ \\ [/tex]

or

[tex]\sf\implies \: \binom{n}{r} + \binom{n}{r - 1} = \binom{n + 1}{r} \\ \\ [/tex]

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Answer: In order to information an opinion , we should have adequate information on a particular issue . In adequate or lack of information can make people doubt the honesty of the government .

Explanation:

Answer:

In order to information an opinion, we should have

adequate information on a particular issue. In adequate or

lack of information can make people doubt the honesty of

the government.

Explanation:

IF U FIND THE ANSWER USEFUL THEN PLZ MARK THE AMSWER AS BRAINLIEST...AND DON'T FORGET TO FOLLOW

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Class 10

>>Maths

>>Pair of Linear Equations in Two Variables

>>Algebraic Methods of Solving a Pair of Linear Equations

>>A boat goes 15km upstream and 22km down

Question

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A boat goes 15km upstream and 22km down stream in 15 hours. In 14 hours it can go 45 upstream and 55km down stream. The speed of the boat in still water in km/hr is

Medium

Solution

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Correct option is D)

Let speed of boat in still water(in km/hr) =x and speed of stream(in km/hr) =y

Time required by the boat to travel d kilometers upstream is

x−y

d

.

Time required by the boat to travel d kilometers downstream is

x+y

d

.

According to the given condition,

x+y

22

+

x−y

15

=5

And

x+y

55

+

x−y

45

=14

Here only x is to be found so option method cannot be used using substitution method

Let

x+y

1

=u,

x−y

1

=v

22u+15v−5=0

55u+45v−14=0

Then, by cross multiplication

−15×14−(45)×−5

u

=

−5×55−22×(−14)

v

=

22×45−55(15)

1

−210+225

u

=

−275+308

v

=

990−825

1

15

u

=

33

v

=

165

1

u=

11

1

,v=

5

1

x+y=11, x−y=5

Add both the equations.

⇒ 2x=16

⟹x=8

Explanation: