Solve the initial value problem yy′+x=x2+y2√ with y(1)=8‾√. to solve this, we should use the substitution u= x^2+y^2 (formulas) u′= 2x+2yy' (formulas) enter derivatives using prime notation (e. g., you would enter y′ for dydx). after the substitution from the previous part, we obtain the following linear differential equation in x, u,u′.

Looks like the equation is

Substitute , so that . Then the equation is the same as

Integrate both sides to get

Given that , we have

so the solution is

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

change of stock price/initial stock price on friday * total stock value = change of stock value

0.89/73.73 *x = 42.72

x=3539.04 = total stock value at initial stock price on friday .

total stock value at initial stock price on friday/ initial stock price on friday = number of shares

3539.04/73.73 = 48 shares

they own 48 shares of this stock