Form a differential equation if y=axe^x

We can differentiate this to form a differential equation. We get:

(assuming A is a constant):

y' = Ae^x + Axe^x.  [ Do not forget the product rule, buddy]

Now note that when you solve this ODE you get a family of solutions i.e, y=Axe^x + C which contains your y for the case C=0; The only way I know to avoid it is also give an initial condition and make it an IVP problem for the sake of completeness. Since this is a 1st order linear ODE, it has one parameter of solutions, and it needs one initial initial condition y(x0) = y0

I'd say y(1) = Ae is a good initial condition.

Hope this helps :)

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).