Answer:
a) 21, 34.5, 54.75, 85.125
Step-by-step explanation:
All of the answer choices differ in the first term, so that is the only one you need to figure here. However, we will do them all, so you can see it done.
We note that x > 0 for all of the values of x that we need to use. That means the recursive relation is the one we're using for computation.
f(1) = 3/2·f(0) +3 = (3/2)(12) + 3 = 18 +3 = 21 . . . . . . matches choice (a)
f(2) = 3/2·f(1) +3 = (3/2)(21) +3 = 63/2 +3 = 69/2 = 34.5
f(3) = 3/2·f(2) +3 = (3/2)(34.5) +3 = 51.75 +3 = 54.75
f(4) = 3/2·f(3) +3 = (3/2)(54.75) +3 = 82.125 +3 = 85.125
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When you're computing for sequential input values, each depends on the previous value you computed.
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<em>Additional comment</em>
Using an exponential regression calculator (or spreadsheet), the explicit function can be found to be ...
f(x) = 18·1.5^x -6
1/7 + 2/7 ??
Would this be too easy of an answer??
Answer:
✑ Question :
- Is ( 11 , 9 ) , ( 11 , 5 ) , ( 9 , 3 ) a function ?
No , it's not a function.
✎ Reason :
This is not a function because one element 11 of set A is associated to elements 9 and 5 of set B.
♨ Explore about function :
↪ Function is a special type of relation. It is the refinement of relation. In a relation from A to B , every element of set A should have only one ( distinct ) image in B to be a function. In other words , if no two different ordered pairs have the same first component , then it is a function.
Hope I helped!
Have a wonderful day ! ツ
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1 pound of macadamia and 3 pounds of almonds
Answer:
- d, series and sequence diverge
- d, geometric/divergent
- c, e (geometric, |r|<1)
Step-by-step explanation:
<h3>1.</h3>
The sequence terms have a common difference of -5/8. That make it a non-trivial arithmetic sequence, so it diverges.
The series is the sum of terms of the sequence. Any non-trivial arithmetic series diverges.
(A "trivial" arithmetic series has a first term of 0 and a common difference of 0. It is the only kind of <em>arithmetic</em> series that doesn't diverge.)
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<h3>2.</h3>
The terms of the series have a common ratio of -2. That makes it a geometric series. The ratio magnitude is greater than 1, so the series diverges.
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<h3>3.</h3>
A sequence will converge only if the terms have a common difference of 0 or a common ratio with a magnitude less than 1. Of the offered choices, only C and E will converge:
c. geometric, r = 3/5
e. geometric, r = -1/6
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<em>Additional comment</em>
The convergence criteria stated for problem 3 applies only to arithmetic and geometric sequences. There are many other kinds of sequences that converge, but these are the kinds being considered in this problem set.
