answer:To find the initial speed of the bullet, we will use the principles of conservation of momentum and energy. The bullet's initial momentum, denoted as ( p_i ), before hitting the block must equal the combined momentum, ( p_f ), of the bullet and block after the collision, due to conservation of momentum. The initial kinetic energy will convert to gravitational potential energy as the block rises. First, we'll equate the initial kinetic energy to the final potential energy: [ frac{1}{2}(m + M)v_f^2 = (m + M)gh ] Where ( m ) is the bullet's mass, ( M ) is the block's mass, ( v_f ) is the final velocity of the bullet and block after the collision, ( g ) is the acceleration due to gravity (9.8 m/s²), and ( h ) is the height (0.65 m). Since the bullet and block move together after the collision, their mass is combined. Simplifying, we get: [ v_f^2 = 2gh ] [ v_f^2 = 2(9.8)(0.65) ] [ v_f = sqrt{2(9.8)(0.65)} ] [ v_f = 3.57 text{ m/s} ] Now, we use conservation of momentum to find the bullet's initial speed, ( v_i ): [ p_i = p_f ] [ m v_i = (m + M) v_f ] Substituting the values and solving for ( v_i ): [ 0.01 v_i = (0.01 + 2.5) times 3.57 ] [ v_i = frac{2.51}{0.01} times 3.57 ] [ v_i = 896 text{ m/s} ] Thus, the initial speed of the bullet before it strikes the block is 896 m/s.

answer:To multiply these two expressions, we can use the distributive property (also known as the FOIL method) twice, since each expression is a binomial. Here's the multiplication step by step: [ p(x) cdot q(x) = (-4x^2 + 12x - 12) cdot (12x^2 - 4x - 11) ] First, distribute each term in p(x) to every term in q(x): [ = (-4x^2 cdot 12x^2) + (-4x^2 cdot -4x) + (-4x^2 cdot -11) + (12x cdot 12x^2) + (12x cdot -4x) + (12x cdot -11) - (12 cdot 12x^2) - (12 cdot -4x) - (12 cdot -11) ] Now, simplify each term: [ = -48x^4 + 16x^3 + 44x^2 + 144x^3 - 48x^2 - 132x - 144x^2 + 48x + 132 ] Combine like terms: [ = -48x^4 + (16x^3 + 144x^3) + (-44x^2 - 144x^2) + (48x - 132x) + 132 ] [ = -48x^4 + 160x^3 - 188x^2 - 84x + 132 ] So, the expanded product is -48x^4 + 160x^3 - 188x^2 - 84x + 132.

answer:The curl of the vector field vec{F}, denoted by nabla times vec{F}, is calculated as follows: [ nabla times vec{F} = left( frac{partial h}{partial y} - frac{partial g}{partial z} right)uvec{i} - left( frac{partial f}{partial z} - frac{partial h}{partial x} right)uvec{j} + left( frac{partial g}{partial x} - frac{partial f}{partial y} right)uvec{k} ] Given f(x, y, z) = sqrt[3]{x - y + z}, g(x, y, z) = y, and h(x, y, z) = frac{y}{z}, we compute the partial derivatives: [ frac{partial f}{partial y} = -frac{1}{3 sqrt[3]{x - y + z}^2}, quad frac{partial f}{partial z} = frac{1}{3 sqrt[3]{x - y + z}^2}, quad frac{partial g}{partial x} = 0, quad frac{partial g}{partial y} = 1, quad frac{partial g}{partial z} = 0, quad frac{partial h}{partial x} = 0, quad frac{partial h}{partial y} = frac{1}{z}, quad frac{partial h}{partial z} = -frac{y}{z^2} ] Substituting these into the curl formula, we get: [ nabla times vec{F} = left( frac{1}{z} - 0 right)uvec{i} - left( frac{1}{3 sqrt[3]{x - y + z}^2} - 0 right)uvec{j} + left( 0 - left(-frac{1}{3 sqrt[3]{x - y + z}^2}right) right)uvec{k} ] Simplifying: [ nabla times vec{F} = left{ frac{1}{z}, frac{1}{3 sqrt[3]{x - y + z}^2}, frac{1}{3 sqrt[3]{x - y + z}^2} right} ]

answer:Salvage ethnography is a method of ethnographic research that focuses on documenting the cultural traditions and practices of communities at risk of disappearing. This documentation, which can include sound recordings, photographs, and other visual representations, serves as an effort to preserve the cultural heritage of these communities in the face of threats such as colonization, forced assimilation, and other factors leading to cultural erosion. The concept of salvage ethnography is often associated with the pioneering work of anthropologist Franz Boas, who contributed significantly to the documentation of indigenous cultures on the brink of extinction through various mediums like photography and sound recordings.