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Mademuasel [1]
3 years ago
15

A sequence is defined by the recursive function f(n 1) = f(n) – 2.if f(1) = 10, what is f(3)?16830

Mathematics
2 answers:
iogann1982 [59]3 years ago
5 0
Hello,

f(n+1)=f(n)-2
f(1)=10
f(2)=8
f(3)=6
...
artcher [175]3 years ago
3 0

Answer: f(3) =6

Step-by-step explanation:

Given: A sequence is defined by the recursive function

f(n+1)=f(n)-2

f(1)= 10

Then f(2) can be written as

f(2)=f(1+1)\\\\\Rightarrow f(2)=f(1)-2\\\\\Rightarrow f(2)=10-2\\\\\Rightarrow f(2)=8

Similarly, f(3) can be written as

f(3)=f(2+1)\\\\\Rightarrow f(3)=f(2)-2\\\\\Rightarrow f(3)=8-2\\\\\Rightarrow f(3)=6

Therefore, the value of f(3) =6.

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Which equation can you solve to find the potential solutions to the equation log2x log2(x – 6) = 4? x2 – 6x – 4 = 0 x2 – 6x – 8
sergeinik [125]

To solve the question we must know about Logarithm.

<h2>Logarithm</h2>

A log function is a way to find how much a number must be raised in order to get the desired number.

a^c =b

can be written as

\rm{log_ab=c

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

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The value of input can not be negative, the value of x is 8.

<h2>Given to us</h2>
  • \rm{ log_2x+log_2(x-6)= 4

<h2>Solution</h2>

\rm{ log_2x+log_2(x-6)= 4

  • Using log_ab + log_ac = log_a(bc),

        \rm{ log_2x(x-6)= 4

  • Taking antilog,

        x(x-6)= 2^4

  • Doing factorization

        x^2 -6x -16=0\\&#10;x^2 -8x +2x-16=0\\&#10;x(x-8)+2(x-8)=0\\&#10;(x+2)(x-8) = 0

Equating factors against 0,

1.    (x+2)=0\\&#10;x=-2

2.     (x-8)=0\\&#10;x=8

As the value of input can not be negative, the value of x is 8.

Hence, the value of x is 8.

Learn more about Logarithm:

brainly.com/question/3072484

8 0
2 years ago
(10 points): My sister Courtney is an assistant professor at a major university and a licensed psychologist. She
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Answer:

Courtney and her family traveled 14 miles in Mr. De Palma's cab from the airport to the hotel.  

Step-by-step explanation:

The total amount of the ride, including tip, was $42.00.  Since this amount represents exactly eight times the amount that was received as a tip, 42/8 is $5.25, which is the cost of the tip.  The other flat rates associated with the trip is the $3.15 for entry and $1.75 for each additional passenger (1.75 x 3=5.25).  Once you subtract these fees from the total amount, $42 - $5.25 (tip) - $5.25 (additional passengers) - $3.15 (entry) = $28.35.  Since Mr. De Palma charges $0.45 for every two-ninths of a mile, you take the revised total 28.35/.45 = 63.  Since 63 represents the amount for every two-ninths of a mile, you need to multiply this amount by 2/9 to get your total amount of miles, or 63 x 2/9 = 14.  

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The answer would be 1.4
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What is the best description of the data in the histogram
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You are assigned 32 math exercises for homework. You complete 87.5 of these before dinner. How many do you have left to do after
VARVARA [1.3K]

Answer:

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Step by step:

This is if the question is saying you completed 87.5% of the exercises. Otherwise, I don't know what it is asking.

87.5% of 32=28

32-28=4

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