Find the general solution by separating the variables then integrating:
dy / dx = cosx℮^(y + sinx)
dy / dx = cosx℮ʸ℮^(sinx)
℮^(-y) dy = cosx℮^(sinx) dx
∫ ℮^(-y) dy = ∫ cosx℮^(sinx) dx
-℮^(-y) = ℮^(sinx) + C
℮^(-y) = C - ℮^(sinx)
-y = ln[C - ℮^(sinx)]
y = -ln[C - ℮^(sinx)]
Find the particular solution by solving for the constant:
When x = 0, y = 0
-ln(C - 1) = 0
ln(C - 1) = 0
C - 1 = 1
C = 2
<span>y = -ln[2 - ℮^(sinx)]
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Answer:
first you divide the larger number into its separate parts. Here, 23 becomes 20 and 3.
Next, you multiply each separate part — 20 x 7 and 3 x 7.
Finally, you add all the products together. 140 + 21 equals 161, the product of 23 x 7.
Step-by-step explanation:
Answer:
<h3>63/3=21</h3><h3>21/3=7</h3><h3>7/3=7</h3><h2> -</h2>
<h3> 3</h3>
I have not done this in advance. I'm just going to write it down
and see what I can do with it:
[ 1/(x+3)² - 1/x² ] / 3
Multiply the top and bottom by (x+3)² :
[ 1 - (x+3)²/x² ] / 3 (x+3)²
Multiply the top and bottom by x² :
[ x² - (x+3)² ] / 3 x² (x+3)²
Now it's just a matter of expanding and cleaning things up,
and hope and pray that a lot of things cancel.
Eliminate the parentheses on top and bottom:
[ x² - x² - 6x -9 ] / 3 x² (x² + 6x + 9)
Combine the x² terms on top, and divide top and bottom by 3 :
[ - 2x - 3 ] / x² (x² + 6x + 9)
Finally, all I can make of this is:
- (2x + 3) / [ x(x+3) ]² .
That's not a whole lot prettier than the original form, but at least
we got rid of those fractions in the numerator of a fraction.
I hope this is some help to you.