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zmey [24]
3 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]3 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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<u>Answer-</u>

Figure 4 is the image of square LMNP after a translation of (x, y) → (x + 5, y – 3)

<u>Solution-</u>

The co-ordinates of the vertices are,

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M = (-1, 1)

N = (-1, -1)

P = (-3, -1)

A translation of (x, y) → (x + 5, y – 3) means, the point must be shifted 5 units right and then 3 units down.

After the transformation the new co-ordinates will be,

L = (-3+5, 1-3) = (2, -2)

M = (-1+5, 1-3) = (4, -2)

N = (-1+5, -1-3) = (4, -4)

P = (-3+5, -1-3) = (2, -4)

These are the co-ordinates of the figure no. 4

6 0
3 years ago
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Answer:

148.2

Step-by-step explanation:

LA= PH

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2 years ago
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Hey guys! I’m having a lot of trouble with this paper, would anyone mind explaining one of them to me?
lyudmila [28]

Answer: See Explanation

Step-by-step explanation:

This worksheet seems to be about "Special Right Triangles"

In this worksheet, it instructs you to find the missing side lengths.

Explaining number 1)

Step 1) Identifying the triangle and what it means

Since the triangle in number one is a 45-45-90 triangle with the given side length of "1" on one of the legs of the triangle, it can be concluded that the other leg also has a side length of "1" (due to the ratio of side on a 45-45-90 degree triangle), is also states the triangle has 45 degrees labeled on one of the angles, is can also be concluded that the other missing angle is 45 degrees.

Step 2) Answer

The answer to b is 1 and the answer to a is square root of 2, due to the properties of a 45 45 90 triangle (refer attachment)

*you can also use the following attachment to help you on this problem

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