answer:The distance between a point and a plane can be calculated using the formula: {eq}pi equiv Ax + By + Cz + D = 0,;Sleft( {{x_0},{y_0},{z_0}} right) to dleft( {S,pi } right) = frac{{left| {A{x_0} + B{y_0} + C{z_0} + D} right|}}{{sqrt {{A^2} + {B^2} + {C^2}} }} {/eq} For the given point S(-4, 1, 9) and the plane -9x + 2y + 6z = 8, we have: {eq}pi equiv - 9x + 2y + 6z = 8 to - 9x + 2y + 6z - 8 = 0 Sleft( { - 4,1,9} right) dleft( {S,pi } right) = frac{{left| { - 9left( { - 4} right) + 2left( 1 right) + 6left( 9 right) - 8} right|}}{{sqrt {{{left( { - 4} right)}^2} + {1^2} + {9^2}} }} = frac{{left| {84} right|}}{{sqrt {98} }} = frac{{84}}{{7sqrt 2 }} = frac{{12}}{{sqrt 2 }} {/eq} Therefore, the distance between the point S(-4, 1, 9) and the plane -9x + 2y + 6z = 8 is {eq}frac{{12}}{{sqrt 2 }}.{/eq}

answer:To simplify the expression (9x + 5) - (4x + 3), follow these steps: 1. Distribute the negative sign to the terms inside the second parentheses: 9x + 5 - 4x - 3. 2. Combine like terms: (9x - 4x) + (5 - 3). 3. Simplify: 5x + 2. 4. The expression cannot be further simplified, so the final answer is 5x + 2.

answer:To differentiate the given function, we can use the product rule, which states that the derivative of a product of two functions is equal to the first function times the derivative of the second function plus the second function times the derivative of the first function. In this case, let (u = -sqrt{3 x^2-5}) and (v = cot (5 x+2)). Then, u' = -frac{1}{2sqrt{3 x^2-5}} (6 x) = -frac{3 x}{sqrt{3 x^2-5}} v' = -csc^2 (5 x+2) (5) = -5 csc^2 (5 x+2) So, by the product rule, f'(x) = u'v + uv' = -frac{3 x}{sqrt{3 x^2-5}} cot (5 x+2) - sqrt{3 x^2-5} (-5 csc^2 (5 x+2)) = frac{5 (3 x^2-5) csc^2 (5 x+2) - 3 x cot (5 x+2)}{sqrt{3 x^2-5}} The answer is f'(x) = frac{5 (3 x^2-5) csc^2 (5 x+2) - 3 x cot (5 x+2)}{sqrt{3 x^2-5}}

answer:Geography is the study of the Earth and its human and natural features. The two essential elements of geography are energy systems and human systems. Energy systems are the ways in which energy is produced, distributed, and used. They include the sources of energy, such as fossil fuels, renewable energy, and nuclear energy, as well as the ways in which energy is transported and used by humans. Human systems are the ways in which humans interact with their environment. They include the ways in which humans use land, water, and other resources, as well as the ways in which humans create and modify their environment. Both energy systems and human systems are essential to geography because they are the two main ways in which humans interact with the Earth. Energy systems provide the energy that humans need to survive and thrive, while human systems are the ways in which humans shape and adapt to their environment. Energy systems and human systems