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Lyrx [107]
2 years ago
15

If you’re given a number, subtract 1, then 2 from the result, then 3 from that result and so on until you reach 0 or a negative

number.
For example, if you’re given 15:

15 – 1 = 14
14 – 2 = 12
12 – 3 = 9
9 – 4 = 5
5 – 5 = 0

Which of these numbers will finish exactly at zero?

102 103 104 105 106
Mathematics
1 answer:
miskamm [114]2 years ago
8 0
105 will finish exactly at zero
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Answer:

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Step-by-step explanation:

A= 1/2 ( b*h )

A= 1/2 ( 7*5)

A= 1/2 ( 35)

A= 17.5

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Find the midpoint of the segment with the following endpoints.
sergij07 [2.7K]

Answer:

( 5.5 , 4 )

Step-by-step explanation:

Use mid point formula shown in image

first x= (X+X)/2

x=(4+7)/2

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4 0
2 years ago
Find integrate (1/(xsqrt(1+(lnx)^2)),1,e,x) ...?
prohojiy [21]
Note that x² + 2x + 3 = x² + x + 3 + x. So your integrand can be written as 

<span>(x² + x + 3 + x)/(x² + x + 3) = 1 + x/(x² + x + 3). </span>

<span>Next, complete the square. </span>

<span>x² + x + 3 = x² + x + 1/4 + 11/4 = (x + 1/2)² + (√(11)/2)² </span>

<span>Also, for the x in the numerator </span>

<span>x = x + 1/2 - 1/2. </span>

<span>So </span>

<span>(x² + 2x + 3)/(x² + x + 3) = 1 + (x + 1/2)/[(x + 1/2)² + (√(11)/2)²] - 1/2/[(x + 1/2)² + (√(11)/2)²]. </span>

<span>Integrate term by term to get </span>

<span>∫ (x² + 2x + 3)/(x² + x + 3) dx = x + (1/2) ln(x² + x + 3) - (1/√(11)) arctan(2(x + 1/2)/√(11)) + C </span>

<span>b) Use the fact that ln(x) = 2 ln√(x). Then put u = √(x), du = 1/[2√(x)] dx. </span>

<span>∫ ln(x)/√(x) dx = 4 ∫ ln u du = 4 u ln(u) - u + C = 4√(x) ln√(x) - √(x) + C </span>

<span>= 2 √(x) ln(x) - √(x) + C. </span>

<span>c) There are different approaches to this. One is to multiply and divide by e^x, then use u = e^x. </span>

<span>∫ 1/(e^(-x) + e^x) dx = ∫ e^x/(1 + e^(2x)) dx = ∫ du/(1 + u²) = arctan(u) + C </span>

<span>= arctan(e^x) + C.</span>
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Vedmedyk [2.9K]

Answer:

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Step-by-step explanation:

6 0
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