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).

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

Qrst is a parallelogram. determine the measure of ∠q pls

Given: lkm jkm, clmk prove: alkmajkm jmk. choose the word that completes the sentence correctly. proof: lkm jkm and lmk * umk are given. km km by the property of congruence. equivalence symmetric reflexive transitive