answer:First, convert the angle from radians to degrees: [ frac{3pi}{2} = frac{180^circ}{pi} cdot left( frac{3pi}{2} right) = 270^circ. ] Then, calculate the sine of (270^circ): [ sin(270^circ) = -sin(90^circ) = -1. ] So, the solution is (boxed{-1}).

answer:First, let's find out how much water was initially in the container when it was 40% full. 40% of 40 liters is: 0.40 * 40 liters = 16 liters Now, let's find out how much water is in the container when it is 3/4 full. 3/4 of 40 liters is: (3/4) * 40 liters = 30 liters To find out how much water was added, we subtract the initial amount of water from the amount of water when the container is 3/4 full. 30 liters (3/4 full) - 16 liters (initially 40% full) = 14 liters So, boxed{14} liters of water were added to the container.

answer:When x=3, we have px^3+qx+3=27p+3q+3=2005, Therefore, 27p+3q=2002, Thus, when x=-3, px^3+qx+3=-27p-3q+3, =-(27p+3q)+3=-2002+3=-1999. Hence, the correct option is boxed{D}.

answer:1. **Identify and Understand the Given Information:** - Two identical cylindrical sheets are used to form a larger cylindrical sheet. - Each of the smaller cylinders encloses a volume of 100 cubic units. 2. **Examine the Relationship Between the Smaller and Larger Cylinders:** - When the smaller cylinders are laid flat and combined, their circumferences are doubled. - Since the circumference of a cylinder is (2pi r), doubling the circumference implies that the new radius (R) of the larger cylinder is twice the radius (r) of the smaller cylinders: [ R = 2r. ] 3. **Calculate the Area Ratio of Cross-sections:** - The cross-sectional area of a cylinder is (pi r^2). - Therefore, the area ratio of the cross-sections (smaller to larger) can be calculated as: [ frac{pi r^2}{pi (2r)^2} = frac{r^2}{4r^2} = frac{1}{4}. ] 4. **Exploit the Volume Relationship:** - Since the heights of all the cylinders are the same and the cross-sectional areas are in the ratio (1:4), - The volume ratio will also be (1:4). - Given that each smaller cylinder has a volume of 100 cubic units, the combined volume for the larger cylinder is: [ 4 times 100 = 400 text{ cubic units}. ] **Conclusion:** [ boxed{400} ]