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Veseljchak [2.6K]
3 years ago
7

Determine if the sequence converges: [ln(n)]^2 /n

Mathematics
1 answer:
Finger [1]3 years ago
8 0
We will use l´Hopital´s rule for calculating limits involving indeterminate form (in this case: ∞ / ∞ ) using the derivative of the numerator and denominator:\lim_{n \to \infty}  \frac{ln^{2}n }{n}  =  \lim_{n \to \infty} \frac{2ln(n)* \frac{1}{n} }{1} =  \lim_{n \to \infty}  \frac{2ln(n)}{n} This is still form ∞/∞ and we will use the derivative again:\lim_{n \to \infty}  \frac{2ln(n)}{n}  =  \lim_{n \to \infty}  \frac{ \frac{1}{n} }{1} = \lim_{n \to \infty}  \frac{1}{n}=1/∞ = 0
The sequence converges.
 
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A cone has a volume of 24 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?
ivann1987 [24]

Answer:

8 cubic inches

Step-by-step explanation: I just know

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3 years ago
Find UW.<br><br>(Please explain how you got UW so I know how to do the other ones!)
Aleonysh [2.5K]

Answer:

X = 6

Step-by-step explanation:

DU = DU .....(1)

DV =DW ......(2)

angle VDU = angle WDU .......(3)

so triangle VDU and triangle WDU are Congruent Triangles

thus VU = WU

we solve : 9x + 1 = 7x + 13 , x = 6

7 0
3 years ago
Write the equation described in each case.
Lapatulllka [165]

Answer:

The Answer is: y = -1/4x + 6

Step-by-step explanation:

Given point: (4, 5)

Given equation: y = -1/4x - 11

Slope: m = -1/4, a parallel line will have the same slope.

Start with the point slope form and solve for y:

y - y1 = m(x - x1)

y - 5 = -1/4(x - 4)

y - 5 = -1/4x + 1

y = -1/4x + 1 + 5

y = -1/4x + 6

Proof:

f(x) = -1/4x + 6

f(4) = -1/4(4) + 6

= -1 + 6 = 5, giving (4, 5)

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4 0
3 years ago
Help help help help me pleaseeeeeeeee
kobusy [5.1K]

The ticket price which will maximize the student's council is: C. $3.10.

<h3>What is price?</h3>

Price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.

Based on the information provided about Valley High School student council, we can logically deduce the following data:

  • Total number of students = 420 students.
  • Lowest ticket price = $2.00.
  • Increase in ticket price = $0.20.
  • Attendance = 20 fewer students

<h3>How to determine the ticket price?</h3>

Mathematically, the equation which model the profit is given by:

Profit = price × number of tickets sold

P(x) = (2 + 0.2x)(420 - 20x)

P(x) = 840 + 84x - 40x - 4x²

P(x) = -4x² + 44x + 840.

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -44/2(-4)

Xmax = -44/-8.

Xmax = 5.5

Ticket price for maximum profit is given by:

Ticket price = 2 + 0.2x

Ticket price = 2 + 0.2(5.5)

Ticket price = $3.10.

Read more on maximized profit here: brainly.com/question/13800671

#SPJ1

8 0
2 years ago
What is the volume of a rectangular prism with a height of 22 1/2 centimeters and a base area of 562 1/2 square centimeters?
umka2103 [35]

The correct answer is D. You can solve this by multiplying the values.

7 0
3 years ago
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