Vector-Valued Function r(t) = (5 sin t, 4t, 5 cos t) O 5 Z 0 oy -5 1.0 0.5 0.0 0.0 -0.5 -1.0 Z 2 5 0.5 4 10 1.0 X X Find its length over the given interval. 3 Interval [0, π] O XO -5 2 yo N 0 -10 X 4 -2 -5 5 10 M 5 N

Construction and building inspectors ensure that construction meets local and national buillding codes and ordinances, zoning regulations, and contract specifications. They spend considerable time inspecting worksites, alone or as part of a team. Most work full time during regular business hours. Many states and local jurisdictions require some type of license or certification. The median annual wage was $56,040 in May 2014. SOURCE: Bureau of Labor and Statistics, U.S. Department of Labor, Occupational Outlook Handbook, 2016 - 2017 Edition E, Construction and Building Inspectors A wheelchalir ramp with a length of 614 Inches has a horizontal distance of 610 Inches. What is the ramp's vertical distance (height)? inches State your response to the nearest 0. 1 Construction laws are very specific when it comes to access ramps for the disabled. Every vertical rise of 1 inch requires a horizontal run of at least 12 inches. Does the ramp above satisfy the requirement? O Yes O No

Laplace transfoem

Integrate the trig identity 2 cos j x cos kx = cos(j + k )x + cos(j -k )x to show that cos j x is orthogonal to cos kx, provided j -/- k. What is the result when j = k?