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3 years ago

If a sequence is defined recursively by (0)=3 and (n+1)=-f(n)+5 for n≥0, Then f(2) is equal to

Mathematics

1 answer:

lana66690 [7]3 years ago

6 0

Answer:

f(2) = 3

Step-by-step explanation:

We are given:

f(0) = 3

and

f(n+1) = -f(n) + 5

We have to find the value of f(2). In order to find f(2) we first have to find f(1)

f(n + 1) = - f(n) + 5

Using n = 0, we get:

f(0 + 1) = - f(0) + 5

f(1) = -f(0) + 5 Using the value of f(0), we get

f(1) = -3 + 5 = 2

Now using n = 1 in the function, we get:

f(1 + 1) = - f(1) + 5 Using the value of f(1), we get

f(2) = -2+ 5

f(2) = 3

Thus the value of f(2) will be 3

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Square root of -30 over square root of -10

Nuetrik [128]

Answer: The answer is: " √3 " .

_______________________________________

→ The simplified expression is: " √3 " .

_______________________________________

Step-by-step explanation:

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We are given:

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→ $\frac{\sqrt{-30}}{\sqrt{-10}}$ ;

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Note the "imaginary number" — " √(-1) " —

which is represented by the symbol: " *i* " .

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So, let us factor out Both the numerator And the denominator:

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Start with the "numerator" ; as follows:

The numerator is: √(-30) ; which factors into:

→ √-1 * √30 ;

_____________________________________

Note that: " √-1 " ; is an imaginary number; which is represented

by the symbol: " *i* " .

As such, we can rewrite the numerator as:

→ *i* √30 .

______________________________________

The denominator is: √(-10) ; which factors into:

→ √-1 * √10 ;

______________________________________

As noted above:

→ " √-1 " ; is an imaginary number; which is represented

by the symbol: " *i* " .

As such, we can rewrite the denominator as:

→ *i* √10 .

______________________________________

Now, let us rewrite the entire expression:

______________________________________

( *i* √30)

____________

( *i* √10)

______________________________________

Note: The *i* symbols "cancel out" to: " 1 " ;

→ { since: any "non-zero value" ; divided by "that same value" ;

is equal to: "1 " .} ;

→ { i.e., in our case: [ *i* ÷ *i* ] ; that is; " [*i* / *i* ], equals : " 1 " .}.

______________________________________

And we are left with:

______________________________________

→ " $\frac{\sqrt{30}}{\sqrt{10}}$ " .

______________________________________

Note that both the numerator and the denominator are "square roots" —

and furthermore — are square roots of a "positive number".

Specifically, the "numerator" is: " √30 " ;

And the "denominator is: " √10 " .

______________________________________

→ Note that the numerator: " √30 " ;

→ can be factored into: "√10 * √3 " ;

→ And that the "denominator" ; which is: " √10 " ; is one of the aforementioned 'factors' of the "numerator" .

_____________________________________

Let us rewrite the expression — and further simplify:

→ $\frac{\sqrt{30}}{\sqrt{10}}$ ;

_____________________________________

= $\frac{(\sqrt{10} *\sqrt{3})}{\sqrt{10}}$ ;

_____________________________________

Note: The "(√10)" values, "cancel out" to: "1" ;

→ {since: any "non-zero value" ; divided by "that same value" ;

is equal to: "1 " .} ;

→ { i.e., in our case: [" √10 ÷ √10 " ] ;

→ that is; [ " $\frac{\sqrt{10}}{\sqrt{10}}$ " ]" ;

→ equals : " 1 " .}.

_____________________________________

→ and we are left with: " (√3) / 1 " ;

→ which equals: " √3 " ;

→ which is our answer.

_____________________________________

Hope this is helpful to you.

Best wishes in your academic endeavors

— and within the "Brainly" community!

_____________________________________

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