The length of a microtubule can be measured as L(t)=sqrt(t^2+0.1(sin(y))^2+0.1(cos (y))^2), where y(t) is the rotational angle along the microtubule, as it grows. Use implicit differentiation to show that (for L(t)≠0) L′(t) satisfies a simple formula L′(t)=t/L(t).

Exclude leap years from the following calculations. (a) compute the probability that a randomly selected person does not have a birthday on october 4. (type an integer or a decimal rounded to three decimal places as needed.) (b) compute the probability that a randomly selected person does not have a birthday on the 1st day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (c) compute the probability that a randomly selected person does not have a birthday on the 30th day of a month. (type an integer or a decimal rounded to three decimal places as needed.) (d) compute the probability that a randomly selected person was not born in january. (type an integer or a decimal rounded to three decimal places as needed.)