Consider the curve (a helix) parametrized by r(t) = [hcost, sin t, at] where a > 0 is a positive constant. as a increases, does the curvature κ increase, decrease, or stay the same? justify your answer by describing what happens to the curve and interpreting the formula κ = dt ds , where s = s(t) is the reparametrization of r such that |r 0 (s)| = 1. you need not compute the curvature directly.

point a is the center of this circle.

the ratio of the lengths of (ef/bc) and (ad/ih) is 2: 1.

step-by-step explanation:

45

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).