answer:The quotient is calculated by dividing each term of the polynomial frac{33 x^5}{5} - frac{18 x^4}{5} - frac{31 x^3}{5} + frac{6 x^2}{5} + frac{46 x}{5} - 3 by the linear term -frac{28 x^4}{5} of the divisor, treating the remaining terms as a constant. Dividing each term, we get: [ left(frac{33 x^5}{5}right) div left(-frac{28 x^4}{5}right) = -frac{33}{28}x, ] [ left(-frac{18 x^4}{5}right) div left(-frac{28 x^4}{5}right) = frac{18}{28} = frac{9}{14}, ] All other terms are of lower degree and will not contribute to the quotient. Hence, the quotient is -frac{33 x}{28} + frac{9}{14}. However, it seems there might be a mistake in the given answer. The simplified quotient should be -frac{33 x}{28} + frac{9}{14}, not -frac{33 x}{28} - frac{15}{28}.

answer:To differentiate the given function, we can use the sum/difference rule and the chain rule. The sum/difference rule states that the derivative of the sum or difference of two functions is equal to the sum or difference of the derivatives of the two functions. The chain rule states that the derivative of a function composed with another function is equal to the product of the derivative of the outer function and the derivative of the inner function. Using these rules, we can differentiate the given function as follows: f'(x) = frac{d}{dx}[cos (8 x+6)-tan (5-5 x)] f'(x) = frac{d}{dx}[cos (8 x+6)]-frac{d}{dx}[tan (5-5 x)] f'(x) = -8 sin (8 x+6)-5 sec ^2(5-5 x) Therefore, the derivative of the given function is -8 sin (8 x+6)-5 sec ^2(5-5 x). The answer is f'(x) = -8 sin (8 x+6)-5 sec ^2(5-5 x)

answer:To find the point on the line ( y = 3x + 2 ) closest to the origin, we can use the distance formula from the point ( (x, y) ) to the origin ( (0, 0) ), which is: [ d = sqrt{(x - 0)^2 + (y - 0)^2} ] Squaring both sides to eliminate the square root: [ d^2 = x^2 + y^2 ] Substitute ( y ) from the line equation: [ d^2 = x^2 + (3x + 2)^2 ] [ d^2 = x^2 + 9x^2 + 12x + 4 ] [ d^2 = 10x^2 + 12x + 4 ] To minimize ( d^2 ), we find the critical point by differentiating with respect to ( x ): [ frac{d}{dx}(d^2) = 20x + 12 ] Setting the derivative to zero: [ 0 = 20x + 12 ] [ x = -frac{3}{5} ] Now, substitute ( x ) back into the line equation to find ( y ): [ y = 3left(-frac{3}{5}right) + 2 ] [ y = -frac{9}{5} + frac{10}{5} ] [ y = frac{1}{5} ] Thus, the point nearest to the origin is ( left(-frac{3}{5}, frac{1}{5}right) ).

answer:Short-term goals: * To rally international support for the Allies in World War I. * To bring an end to the conflict. Long-term goals: * To prevent future wars by removing economic barriers to free trade. * To promote transparency in international relations by abolishing secret treaties. * To ensure national sovereignty and self-determination for all nations.