Differential Equations Answers

1.A woman is on a lake in a canoe 1km from the closest point P of a straight shoreline. She wants to get to a point Q, 10km along the shore from P. To do so, she paddles to a point R between P and Q and then walks the remaining distance to Q. She can paddle 3km/hour and walk 5km/hour. How should she pick the point R so that she gets to Q as quickly as possible?

solve the differential equation: dy/dx + y = (x+1)e^x

Dear Expert Dr math i have one problem please try to explain.Thank you
what is initial value problems and boundary vale problems.

Bacteria in a petrie dish double the area they cover everyday. If the dish is covered after 16 days, on what day was only one quarter of it covered?

(p + q)3

= (p + q)(p { + q)(p + q)
= (p + q)(p2 + 2pq + q2 )

= p3 + 2p2 q + pq2 + p2 q + 2pq2 + q3

= p3 + 3p2 q + 3pq2 + q3

I hope someone can help me with this question. Thank you very much.

"A woman 6ft tall walks away from a light 10ft above the ground. If her shadow lenghtens at the rate of 2ft/sec, how fast is she walking?"

Can anyone help me with this question? I've been trying to find ways to solve it but I have not found the correct way on how to. I hope you can help me with this question.

"Two points are moving horizontally in space at different heights above the earth. Show that the angle of elevation of the line joining them is greater when the distance between them is least."

Integrate W.R.T x:
e^x(1+1/x)
Explain with steps please

differentiate W.R.T x :
e rest to xlogx means e^xlogx (xlogx in power of e)

please explain with steps

Find the critical points and test for the maximun and minimum. y=x^3+3x^2+6x-4