6.) Please answer #6 on this sheet and clearly explain how the answer was found.
ID: 2863144 • Letter: 6
Question
6.) Please answer #6 on this sheet and clearly explain how the answer was found.
Set up the integral for finding the volume above the cone z = Squareroot x^2 + y^2 and below the sphere x^2 + y^2 + z^2 = 18 A lamina occupies the disk x^2 + y^2 lessthanorequalto 4. Find its mass, if the density at any point is proportional to its distance from the origin, where the proportionality constant Find integral_C (y + e^Squareroot x)dx + (2x + cos y^2)dy where C is the boundary of the region bounded by the parabola y=x^2 and the lines y=0 and x=1 Find the vector projection of onto Find the tangential component a_t of the acceleration vector a at t=1 for the curve r(t) = The three sides A, B, and C of a rectangular box are changing with time. At a certain instant, A=1m, B=2m, C=2m while A and B are increasing at 2m/s and C is decreasing at 3m/s. How fast is the volume of the box changing at that instant?Explanation / Answer
volume of box V =ABC
differentiate with respect to time
dV/dt =((dA/dt)BC)+((dB/dt)AC)+((dC/dt)AB)
given A=1,B=2,C=2 ,dA/dt=2,dB/dt =2,dC/dt=-3(negative since its decreasing)
dV/dt =(2*2*2)+(2*1*2)+((-3)*1*2)
dV/dt =8+4-6
dV/dt =6
volume increasing at 6m3/s
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