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harkovskaia [24]
3 years ago
13

Determine whether the series converges: sum(k=1 -> infinity) [1/(1+lnk)]

Mathematics
1 answer:
fgiga [73]3 years ago
3 0
Series is strictly decreasing so apply Integral test.
Limit test is also applicable, it implies it may converge.
Integrate 1/(1+lnx) you may need product rule.
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A sector has angle 2.5 radians and perimeter of 18cm. find the radius of the sector
babunello [35]

Answer:

4 cm

Step-by-step explanation:

Perimeter = 18cm

θ = 2.5 radian

s = rθ, s = Arc length

Perimeter of Sector, P = arc length, s + 2r

Perimeter = rθ + 2r

r = Radius

18cm = r(2.5) + 2r

18cm = 2.5r + 2r

18cm = 4.5r

r = 18 /4.5

r = 4

8 0
3 years ago
The sum of two consecutive odd integers is 84. Find the two integers.
Rudik [331]

Answer: n + (n + 2) = 84

Step-by-step explanation:

If n is the smallest integer, the other integer must be two more than that, because it has to be odd. The two numbers add up to 84, so the other side of the equation is 84.

5 0
3 years ago
Read 2 more answers
Directions in picture.
densk [106]
Use PEMDAS, the answer that I got is 19.
8 0
3 years ago
Read 2 more answers
Find the area of following rhombuses. Round your answers to the nearest tenth if<br> necessary.
polet [3.4K]

Answer:

Area =55.4ft^2

Step-by-step explanation:

Given

The attached rhombus

Required

The area

First, calculate the length of half the vertical diagonal (x).

Length x is represented as the adjacent to 60 degrees

So, we have:

\tan(60) = \frac{4\sqrt 3}{x}

Solve for x

x = \frac{4\sqrt 3}{\tan(60)}

\tan(60) = \sqrt 3

So:

x = \frac{4\sqrt 3}{\sqrt 3}

x = 4

At this point, we have established that the rhombus is made up 4 triangles of the following dimensions

Base = 4\sqrt 3

Height = 4

So, the area of the rhombus is 4 times the area of 1 triangle

Area = 4 * \frac{1}{2} * Base * Height

Area = 4 * \frac{1}{2} * 4\sqrt 3 * 4

Area =2 * 4\sqrt 3 * 4

Area =55.4ft^2

7 0
3 years ago
Determine whether the relation describe c as a function of w.
Delicious77 [7]

Answer:

Function:

c = f(w) = 0.49, 0 < w ≤ 1

            = 0.70,  1 < w ≤ 2

            = 0.91, 2 < w ≤ 3

Step-by-step explanation:

Yes, the relation described can be interpreted as a function.

Here, c is the cost of a mail letter. c depends upon w, which is the weights of the mail letter.

As described in the question, the relation can be expressed as a function.

c can be expressed as a function of w in the following manner:

c(cost of mail) = f(w), where w is the independent variable and c is the dependent variable

c = f(w) = 0.49, 0 < w ≤ 1

            = 0.70,  1 < w ≤ 2

            = 0.91, 2 < w ≤ 3

where, c is in dollars and w is in ounces.

5 0
4 years ago
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