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zmey [24]
2 years ago
6

Suppose that you have two different algorithms for solving a problem of size n. The first algorithm uses exactly n(log n) operat

ions and the second algorithm uses exactly n 3/2 operations. As n grows, determine which algorithm uses fewer operations?
Mathematics
1 answer:
Mumz [18]2 years ago
5 0

Answer:

Algorithm 1 uses:

n*log(n) operations.

While algorithm 2 uses:

n^(3/2) operations.

We want to see, as n grows, which algorithm uses fewer operations.

So we would want to first solve:

n*log(n) = n^(3/2)

This will give us the exact value of n such that the number of operations is the same in both algorithms.

dividing both sides by n we get:

log(n) = n^(3/2)/n = n^(3/2 - 1) = n^(1/2)

where we can use:

log(n) = ln(n)/ln(10)

ln(n) = ln(10)*n^(1/2)

This equation actually has no solutions.

This happens because the right side is always larger than the left side.

Then, the same thing happens for our two initial equations:

n^(3/2) is always larger than n*log(n), as you can see in the graph below, where n^(3/2)  is represented with the orange graph:

So we can conclude that the fist algorithm uses less operations as n grows.

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<h2><em><u>Answer:</u></em></h2>

Total Surface Area = 375 ft^2

<h2><em><u>Step-by-step explanation:</u></em></h2>

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<u>Area of the ceiling:</u>

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<u>Area of floor:</u>

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f = 67.5

<u>Area of the two trapezoids:</u>

t = 2(h * \frac{a + b}{2})

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t = 2(7.5 * \frac{6.5 + 7.5}{2})

t = 2(7.5 * \frac{14}{2})

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8 0
3 years ago
A straight angle is split in the ratio 3:1:4. Find the measure of each angle.
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Step-by-step explanation:

It should be noted that a straight angle is always equal to 180°.

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b. 1/8 × 180° = 22.5°

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Answer:

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2) 2x+2>4

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Hope this helped!! Have an amazing day :3

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