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mars1129 [50]
3 years ago
12

Help with this please!

Mathematics
1 answer:
uranmaximum [27]3 years ago
4 0
Here. Remember to get the correct units. If you need extra help, I am more than willing to help!

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If f and g are continuous functions with f(0) = 2 and the following limit, find g(0). lim_(x->0)[2 f(x) - g(x)] = -3
ladessa [460]

We have by distributivity of limits over sums, and continuity of f(x) and g(x), that

\displaystyle \lim_{x\to0} \bigg(2f(x) - g(x)\bigg) = 2 \lim_{x\to0} f(x) - \lim_{x\to0} g(x) = 2 f(0) - g(0)

Given f(0)=2, it follows that

2^2 - g(0) = -3 \implies g(0) = \boxed{7}

5 0
1 year ago
Sam colors each tile in a 4 by 4 grid white or black. A coloring is called rotationally
DiKsa [7]

Answer:

  65,280

Step-by-step explanation:

Consider the 4×4 grid ...

  \left[\begin{array}{cc}a&b\\d&c\end{array}\right]

where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.

The same will be true of 270° rotational symmetry, for the same reason.

__

For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)

__

The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...

  65,536 -256 = 65,280 . . . . colorings not rotationally symmetric

8 0
3 years ago
What is the measure of angle 5 if the measure of angle 2 is 37 degrees and the measure of angle 3 is 72 degrees
ahrayia [7]

Answer:

160 is a whole angle so 37+72=109                             160-109=51

51 is your answer

Step-by-step explanation:

7 0
2 years ago
What is 3,000 more than 150?
Scrat [10]

Answer:

<h2>3,150</h2>

Step-by-step explanation:

We need to find a number that is 3,000 more than 150. To do this set up an equation and let x = the result.

x = 150 + 3,000

x = 3,150

Check

3,150 = 150 + 3,000

3,150 = 3,150 Correct :)

<em>PLEASE MARK BRAINLIEST</em>

5 0
3 years ago
Maleek rested a 15.5-foot ladder against a building. The base of the ladder is 8.2 feet from the building. How far up the buildi
oksian1 [2.3K]

Answer:

13.2 ft

Step-by-step explanation:

x^2 + 8.2^2 = 15.5^2

x = \sqrt{15.5^2 -8.2^2}

x = 13.2 ft

3 0
3 years ago
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