What is the slope of the line represented by the equation ?

Mathematics

1 answer:

Rzqust [24]3 years ago

5 0

Answer:

I think is 10 because 2 negatives make a positive and 2 would make the answer -10

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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

How do you find the width of a number when you have the feet and total area

mart [117]

Area=legnth times width
so if you know the area then solve for width
area=legnth times width
divide both sdies by legnth
area/legnth=width

if you have the legnth then you can solve
area divided by legnth=width

7 0

3 years ago

Read 2 more answers

What is the value of Tan θ?

abruzzese [7]

Answer:

I believe the answer is -4/3

Step-by-step explanation:

4 0

3 years ago

One question please help a friend out thanks you guys :-)

Dahasolnce [82]