An object is moving back and forth on the x-axis according to the equation x(t) = 3sin(20πt), t> 0, where x(t) is measured in cm and t in seconds. give decimal answers below. (a) how many complete back-and-forth motions (from the origin to the right, back to the origin, to the left and finally back to the origin) does the object make in one second? (b) what is t the first time that the object is at its farthest right? (c) at the time found in part (b), what is the object's velocity? (d) at the time found in part (b), what is the object's acceleration?

Imagine you are standing in the antarctic during the southern hemisphere summer. the sky is clear and blue. there are no clouds in the sky. your shadow is cast on the icy ground. what is the color of the shadow?

An architect plans to use solar energy to heat the next house he designs. what principle of absorption and infrared energy can be applied to the design of the new house? how could she apply to those principals?

Asteel tube (k=50 w/mk) of inner and outer diameter di = 20mm and do=26mm, respectively, is used to transfer heat from hot gases flowing over the tube (h-hot = 200w/m2k) to cold water flowing through the tube (h-cold = 8000 w/m2k). what is the cold-side overall heat transfer coefficient uc? to enhance heat transfer 16 straight fins of rectangular profile are installed longitudinally along the outer surface of the tube. the fins are equally spaced around the circumference of the tube, each having a thickness of 2mm and a length of 15mm. what is the corresponding overall heat transfer coefficient uc? *solve for uc in both cases*