Find the temperature u(x.1) from the heat equation in a laterally insulated copper bar 80cm cm long with c=1.158 cm/sec. If the initial temperature is represented by the below graph and the ends are kept at 0PC. 1/2 2 +x 3/2 1/2

The slope of the tangent line to the graph of y =; I+1 when x = 1 is %3D %3D - 4 3/4 O 1 4. 1/2

Suppose that a particle moves along a straight line with velocity cos(t/2) , sin(t/3), te [0, 7], t E (T, 37], v(t) = %3D in meters/second. What is the total distance traveled from t = 0 up to t = 3T seconds ? (You only need to input %3| Type your answer..

The height of a buoy on a lake is changing during a storm. The height's rate of change can be modeled by r(t) = 0.5 cos(0.2t) feet per second where t is measured in seconds. Is the buoy's height increasing or decreasing at time t = 10 seconds? Why?