answer:To calculate the tip percentage, we first need to determine the amount of the tip. This can be done by subtracting the cost of the meal from the total bill: ``` Tip = Total Bill - Cost of Meal Tip = 270 - 200 Tip = 70 ``` Now that we know the tip amount, we can calculate the tip percentage by dividing the tip by the cost of the meal and multiplying by 100: ``` Tip Percentage = (Tip / Cost of Meal) x 100 Tip Percentage = (70 / 200) x 100 Tip Percentage = 0.35 x 100 Tip Percentage = 35% ``` Therefore, the tip percentage is 35%.

answer:To find the volume, we apply the shell method. The volume of an elemental shell with radius r = x and height h = y is: {eq}begin{align*} dV &= 2pi , r , h , dx &= 2pi , x , y , dx &= 2pi , x left( x^{-frac{1}{3}} right) , dx &= 2pi , left( x^{-frac{1}{3} + 1} right) , dx &= 2pi , left( x^{frac{2}{3}} right) , dx end{align*}{/eq} Integrating this elemental volume from x = 1 to x = 4 gives us the total volume: {eq}begin{align*} V &= 2pi int_1^4 left( x^{frac{2}{3}} right) , dx &= 2pi left[ frac{x^{frac{2}{3} + 1}}{frac{2}{3} + 1} right]_1^4 &= 2pi left[ frac{x^{frac{5}{3}}}{frac{5}{3}} right]_1^4 &= 2pi times frac{3}{5} left[ x^{frac{5}{3}} right]_1^4 &= 2pi times frac{3}{5} left[ 4^{frac{5}{3}} - 1^{frac{5}{3}} right] &= 2pi times frac{3}{5} left[ 4^{frac{5}{3}} - 1 right] &= 34.228 , text{cubic units} end{align*}{/eq} Therefore, the volume of the solid formed by revolving the region around the y-axis is 34.228 cubic units.

answer:The harmonic mean of a set of numbers is calculated as the reciprocal of the average of their reciprocals. Let's denote the numbers as a = frac{44}{3}, b = frac{49}{3}, and c = frac{25}{3}. The harmonic mean H can be computed as follows: H = frac{3}{left(frac{1}{a} + frac{1}{b} + frac{1}{c}right)} Now, let's calculate the reciprocals and then their sum: frac{1}{a} = frac{3}{44}, frac{1}{b} = frac{3}{49}, frac{1}{c} = frac{3}{25} sumleft(frac{1}{a}, frac{1}{b}, frac{1}{c}right) = frac{3}{44} + frac{3}{49} + frac{3}{25} After adding these, we find the harmonic mean: H = frac{3}{left(frac{3}{44} + frac{3}{49} + frac{3}{25}right)} approx frac{3}{left(0.0681818 + 0.0612245 + 0.12}right)} approx frac{3}{0.2494063} approx 12.0059 Rounded to the nearest thousandth, the harmonic mean is frac{53900}{4481} approx 12.006. So, the harmonic mean of frac{44}{3}, frac{49}{3}, and frac{25}{3} is approximately 12.006.

answer:To evaluate the function f(x) = -tan(4 - 8x) at x = -48, substitute -48 for x: [ f(-48) = -tan(4 - 8(-48)) = -tan(4 + 384) = -tan(388) ] The tangent of 388^circ is approximately 75.142. Therefore, [ f(-48) = -75.142 ]