Given: (2xsinycosy-x+2x2eyx^2)dy=(y-sin2y-4xyeyx^2)dx Show the complete and detailed solution of the following: Test for exactness Solve DE Continue solution Final answer

Show complete solution

x²dx 3 2 3 (5-x') 2.

Solve (2xy-2xy- = 0 4xy² +2x) dx + (3x2y + 4y) dy %3D

A mouse on a tightrope is moving such that its position relative to some fixed point is given by x(t)=−2/3t^3+9t^2−36t+18 where x is measured in centimeters and tt is measured in seconds.Write an expression for the mouse's velocity. v(t)=v(t)=  What is the mouse's velocity when t=4t=4? cm/s Write an expression for the mouse's acceleration. a(t)=a(t)=   What is the mouse's acceleration when t=4t=4? cm/s2

S -00 Hiw:- Evalute x sinx dx x²+2x+2

x Vr2 Vx² + 1 dx 0.

The windchill index announced during the winter by the weather bureau measures how cold it "feels" for a given temperature t (in degrees Fahrenheit) and wind speed w (in miles per hour). It is calculated by the formula C(t, w) = 35.74 + 0.6215t - 35.75w 0.16 + 0.4275tw0.16 + '.+ If the temperature is 31 degrees and the wind speed is 10 miles per hour, estimate the change in the windchill temperature if the wind speed increases by 4 miles per hour and the temperature drops by 5 degrees. (Round your answer to two decimal places.)