A force vector has a magnitude of 592 newtons and points at an angle of 45° below the positive x axis. What are (a) the x scalar component and (b) the y scalar component of the vector? (a) Fx Number 419 Units N (b) Fy= Number i 419 Units N

What is the value of the following integral? 100/2 p7/2 I = xô (2 sin x – /2)dx s(2s IT

(b) Sphericals x=r sine coso y=r sine sino z=r cose Consider spherical coordinates as defined by their relationships to the Cartesian coordinates: x =r sin 8 cos p X2 =r sin 0 cos X3 =r cos 0 r2 = [xỉ + x3 + x e = tan-(x? + x3)x3 $ = tan-(x2/x1) or

For numeric entry in the Bb system the standard guidance applies: enter more digits than are signifi- cant in the answer field to ensure correct answers are marked as correct,convert to standard units if necessary unless otherwise stated but do not enter the unit in the answer field, if you choose to use scientific notation 2.0563 x 10-4 is entered as 2.0563E-4 (no spaces, the E must be capitalized). 1) Calculate the density of a block of unknown metal that has mass 234.00 g and is a cube that measures 9.000 cm on a side. 2) Calculate the volume of a 5.00 kg nugget of pure gold. 3) If the nugget in the previous problem were cast into a cube, what would the length of one of the sides be, measured in centimeters? 4) Calculate the mass of blood in the average human body, given the average volume of 5.0 L. 5) If a cylindrical rod of uranium is 25.00 cm long and has mass 9.874 kg, what is its radius?