Question

AME: points: ath 37: LAB Assignment #8 (5.1 Topics) early document your work in a professional way, answer questions in all their parts, press units correctly. When asked to explainy cle your final answers. Thank you our answer, do so in complete sentences 1. (5 pts.) Business: Manufacturing A manufacturer of modeling clay has determined which the clay hardens is related to the number, t, of minutes the clay has been in the open air after being taken out of its protective wrapping by the function H'(t). The hardness of the clay, H, is in the manufacturer's own hardness units. Interpret both the derivative H'(20) 0.3 and the integral H (20) 15.

Answer 1

H’(t) gives rate of hardening. So H’(20) gives rate of hardening at time t=20 minutes and it is equal to 0.3per minute.

H(20) the integral oh H’(t) gives total hardening of Clay for 20 minutes .this is equal to 15 .so till 20 minutes clay hardened by 15 units.

to understand the relationships consider velocity , displacement  relationships. Integral of velocity gives displacement . Here instead displacement we have hardening and instead of velocity we have H’(t)