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Marina CMI [18]
3 years ago
6

What is the solution or solutions to the the equation x+2=2^x

Mathematics
1 answer:
Rainbow [258]3 years ago
3 0

Answer:

x=2

Step-by-step explanation:

2^2=4

2+2=4

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A coin is tossed 3 times. what is the probability of obtaning two heads out of the 3 tosses
Nataly [62]
I answered a similar problem yesterday.
In three coin tosses there are 8 possible outcomes:
H H H
H H T
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T H H
T T H
T H T
H T T
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Of those results, four out of the eight have at least 2 tails and so the probability is (4/8) or50%

If you need the probability of getting EXACTLY 2 tails then the probability is (3/8) or .375


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3 years ago
Verify by direct substitution that the given power series is a solution of the indicated differential equation. [Hint: For a pow
shepuryov [24]

Answer:

The given power series y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}} is a solution of the differential equation (1+x^2)y' + 2xy = 0

Step-by-step explanation:

This is a very trivial exercise, follow the steps below for the solution:

Step 1: Since n = 0, 1, 2, 3, 4, ........, Substitute the values of n into equation (1) below.

y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}.....................(1)

y = 1 - x^2 + x^4 - x^6 + x^8.........

Step 2: Find the derivative of y, i.e. y'

y' = -2x + 4x^3 - 6x^5 + 8x^7 .............

Step 3: Substitute y and y' into equation (2) below:

(1+x^2)y' + 2xy = 0\\\\(1+x^2)(-2x + 4x^3 - 6x^5 + 8x^7......) + 2x(1 - x^2 + x^4 - x^6 + x^8.......) = 0\\\\-2x+ 4x^3 - 6x^5 + 8x^7........ - 2x^3 +4x^5 - 6x^7 + 8x^9 ......+ 2x - 2x^3 + 2x^5 - 2x^7 + 2x^9...... = 0\\\\0 = 0

(Verified)

Since the LHS = RHS = 0, the given power series y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}} is a solution of the differential equation (1+x^2)y' + 2xy = 0

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Allushta [10]

Answer:

I think it is D. Because x=x and there's infinite possibilities.

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Use long division to write the fraction 1/12 as a decimal
timofeeve [1]
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