(x^2) + (y^2) + (z^2) = 1 and (x^2) + (y^2) + (z^2) = 4
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- We have two vectors A=(6.0, 9.6) and B=(-8.6, 4.4). What angle does the sum of these vectors make with the x-axis in degrees?Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown. The monument is made from tens of thou- sands of small stone blocks of density = 800 kg/m3 . The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. (a) Choosing a coordinate system with x = 0 at the center of the pyramid, y = 0 at the base of the pyramid, and z = 0 at the face of the pyramid shown in the diagram, determine the coordinates of the center of mass of the pyramid in the x, y, and z directions. (b) How much work did laborers do on the blocks to put them in position while building the entire monument? Note: The gravitational potential energy of an object–Earth system is given by Ug = MgyCM, where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference level.The two vectors a→ and b→ in the figure have equal magnitudes of 10.2 m and the angles are θ1 = 30° and θ2 = 101°. Find (a) the x component and (b) the y component of their vector sum r→, (c) the magnitude of r→, and (d) the angle r→ makes with the positive direction of the x axis.
- In the figure, a force P acts on a block weighing 45.0 N. The block is initially at rest on a plane inclined at angle = 18.0° to the horizontal. The positive direction of the x axis is up the plane. The coefficients of friction between block and plane are μ = 0.540 and Uk = 0.340. In unit-vector notation, what is the frictional force on the block from the plane when Pis (a) (-5.30 N)î, (b) (-8.10 N)î, and (c) (-15.1 N)? (a) Number i (b) Number i (c) Number i i+ i+ i i i+ i j Units j Units j UnitsIf the vector B⃗B→ has a magnitude of 45 mm and makes an angle of 30 ∘∘ with the +x+x axis, the vector -B⃗B→ has the same direction as B⃗B→ but a magnitude of -45 mm. makes an angle of -30 ∘∘ with the +x+x axis. has a magnitude of 45 mm. has the opposite direction of B⃗B→ and a magnitude of -45 mm.Asap plzzzz