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siniylev [52]
2 years ago
5

The number obtained on rationalizing the denominator of 1/(√7--2) is

Mathematics
2 answers:
Studentka2010 [4]2 years ago
8 0

Given that:

1/(√7 - 2)

The denominator is (√7-2).

We know

The rationalising factor of (√a-b) is (√a+b)

Therefore, the rationalising factor of √7-2 is √7+2.

On rationalising the denominator them

⇛[1/(√7-2)]×[(√7+2)/(√7+2)]

⇛[1(√7+2)]/[(√7-2)(√7+2)]

Since, (a-b)(a+b) = a²-b²

Where, a = √7 and b = √2.

⇛[1(√7+2)]/[(√7)²-(2)²]

⇛[1(√7+2)]/[(√7*7)-(2*2)]

⇛[1(√7+2)]/[7-4]

⇛[1(√7+2)]/3

⇛(√7+2)/3

Hence, the denominator is rationalised.

<u>also</u><u> read</u><u> similar</u><u> questions</u><u>:</u>

Slav-nsk [51]2 years ago
3 0

\frac{1}{ \sqrt{7}  -(- 2)}  \\ rationalizing \:  \:  \: the \:  \:  \: denominator \:  \:  \: we \:  \:  \: have \\  =  \frac{1}{ \sqrt{7} + 2 }  \times  \frac{ \sqrt{7}  - 2}{ \sqrt{7}  - 2}  \\  =  \frac{ \sqrt{7}  - 2}{ {( \sqrt{7} )}^{2} -  {(2)}^{2}  }  \\  =  \frac{ \sqrt{7} - 2 }{7 - 4}  \\  =  \frac{ \sqrt{7}   - 2}{3}

Hope you could get an idea from here.

Doubt clarification - use comment section.

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Thirteen people on a softball team show up for a game. a)How many ways are there to choose 10 players to take the field? b)How m
marishachu [46]

Answer:

a) 286

b) 1,037,836,800

c) 285

Step-by-step explanation:

a) Since order is not important, the total possible number of ways to choose 10 players out of 13 is the following combination:

C(13,10)=\frac{13!}{(13-10)!10! } \\C(13,10)=\frac{13*12*11*10!}{(3*2*1)10! }\\C(13,10) = 286

b) The total number of possibilities to assign positions by the selecting 10 players is the permutation of 13 players for 10 positions:

P(13,10) = \frac{13!}{(13-10)!}\\P(13,10) = 13*12*11*10*9*8*7*6*5*4\\P(13,10) =1,037,836,800

c) The number of ways to pick 10 players including at least one woman is equal to the total number of ways to pick 10 players (found in item a) minus the the number of ways to pick 10 players without picking a single woman.

Since there 10 male players for 10 positions, there is only one possible way to pick a team without women, therefore:

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6 0
3 years ago
Each lap around a park is 1 1⁄5 miles. Kellyn plans to jog at least 7 1⁄2 miles at the park without doing partial laps. How many
Nitella [24]
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Let X be the number of laps Kellyn wants to jog to meet her 7 1/2 mile goal:
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6 0
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Read 2 more answers
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Nastasia [14]

Answer:

The given expression can't be expressed in polynomial form. Hence, it is not a polynomial.

Step-by-step explanation:

P(x,n) is a polynomial of nth degree if it is of the form,

P(x,n) = a_{0} + a_{1}x + a_{2}x^{2} + a_{3}x^{3} + ......... +a_{n}x^{n}

where n is a finite positive integer and n ∈ N

and 'a_{i}'s are fixed but otherwise arbitrary constants ∀  i = 0(1)n .

Now, the given expression is,

9x^{3} + \frac {1}{2x^{2}} + 3x^{-1}

which  doesn't fit in the above form. Hence, it is not a polynomial.

4 0
3 years ago
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