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Blizzard [7]
1 year ago
12

Does the following series converge or diverge?

Mathematics
1 answer:
Alex777 [14]1 year ago
7 0

Answer:

converge

Step-by-step explanation:

the reason is : the individual terms of the series get smaller and smaller towards 0, and therefore the sum converges to a certain limit.

why do I know that the individual terms get smaller and smaller ?

because the terms are ultimately (with n getting very large the constant factors added constants become irrelevant)

n / (n^(3/2))

as sqrt(n³) = n^(3/2)

and n^(3/2) progresses much faster and stronger than n (or n¹), as 3/2 is larger than 1.

so, the denominator (bottom) of that fraction grows stronger than the numerator (top), and the terms go therefore against 0 with larger and larger n.

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How many solutions does this linear system have y= 1/2x+4 <br> x+2y=-8
lara [203]

Answer:

1 solution

Step-by-step explanation:

y = 1/2x + 4  

x + 2y = -8

Solve the second equation for y.

2y = -x - 8

y = -1/2x - 4

The two equations in slope-intercept form are:

y = 1/2x + 4

y = -1/2x - 4

The system consists of two lines with different slopes, so they intercept at a single point which is the solution.

Answer: 1 solution

4 0
3 years ago
Let f(x)=4x and g(x)=(4)x−1+2 . Which transformations are needed to transform the graph of f(x) to the graph of g(x) ? Select ea
Inessa05 [86]

Answer:

horizontal translation 1 unit right  and vertical translation 2 unit up

Step-by-step explanation:

we are given

f(x)=4^x

g(x)=4^{x-1}+2

We can see that in place x , we have x-1

So, it is shifted horizontally right side by 1 unit

We have +2 added to f(x)-value

It means 2 is added to y-value

So, it is shifted vertically upward by 2 units

So, horizontal translation 1 unit right  and vertical translation 2 unit up

5 0
3 years ago
Read 2 more answers
Find for x: 8 times 7=x
shepuryov [24]
8x7=56................
7 0
3 years ago
Read 2 more answers
Maisha has 3(x+2) hours reading a book 8x-5 hours sleeping and 2x hours playing.How many hours did she spend in all of these act
Mandarinka [93]
Add all the activities together

=3(x+2) + (8x-5) + 2x
multiply 3 by all in parentheses
=(3*x) + (3*2) + (8x-5) + 2x
=3x + 6 + 8x - 5 + 2x
combine like terms
=(3x + 8x + 2x) + (6 - 5)
=13x + 1

ANSWER: 13x + 1

Hope this helps! :)
6 0
3 years ago
Original: $458<br> Discount:<br> New: $137.40
Vanyuwa [196]

Answer:

Your answer would be 30% discount

Step-by-step explanation:

137.40 / 458 = .3

8 0
3 years ago
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