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nexus9112 [7]
2 years ago
14

Question attached below

Mathematics
1 answer:
kap26 [50]2 years ago
3 0
It would be 0.21 because that is what is under 6 on the table
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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

6 0
3 years ago
Mr. Rawlings had 60 cookies he wanted to give each of his 16 grandchildren the same number of cookies what is the greatest numbe
Solnce55 [7]
He could give each grandchild 3 cookies each. He would then have 12 cookies remaining.

You would divide 60 by 16 which would be 3 with a remainder of 12. The remainder is the number of cookies left after giving each grandchild the same amount of cookies each.

I hope this helps!
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Y=3x- 15 ordered pair
astraxan [27]
Three ordered pairs would be
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Answer:13

Step-by-step explanation:none

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Paha777 [63]

Answer:

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.

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