Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist. (enter your answer using interval notation.) t(t − 9)y' + y = 0, y(1) = 1

If either or , the ODE has the trivial solution , but . So any solution to the ODE that satisfies the initial condition can only exist on the interval .

look a the sides they are perpendicular

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).