answer:1. Arrange the numbers in ascending order: -10/√π, -3√3, -5, -3, 1, 4, 7, 10. 2. Since there are an even number of values, the median is the average of the two middle values. 3. The two middle values are -3 and 1. 4. Therefore, the median is (-3 + 1) / 2 = -1. The median is -1.

answer:Let the vertices of the triangle be A(x_1, y_1), B(x_2, y_2), and C(x_3, y_3). Since the side with length 2.19 is opposite the angle of 83 {}^{circ}, we have BC = 2.19. Using the distance formula, we get: (x_3 - x_2)^2 + (y_3 - y_2)^2 = 2.19^2 (x_3 - 0.650172)^2 + (y_3 - 0)^2 = 4.7881 x_3^2 - 1.300344x_3 + 0.422681 + y_3^2 = 4.7881 x_3^2 - 1.300344x_3 + y_3^2 = 4.365419 Since the angle at A is 80 {}^{circ}, we have: tan 80 {}^{circ} = frac{y_3}{x_3 - 0.650172} 5.671282 = frac{y_3}{x_3 - 0.650172} y_3 = 5.671282(x_3 - 0.650172) Substituting this expression for y_3 into the equation for the distance between B and C, we get: x_3^2 - 1.300344x_3 + (5.671282(x_3 - 0.650172))^2 = 4.365419 x_3^2 - 1.300344x_3 + 32.1924(x_3^2 - 1.300344x_3 + 0.422681) = 4.365419 33.1924x_3^2 - 44.8652x_3 + 13.6962 = 4.365419 33.1924x_3^2 - 44.8652x_3 + 9.330781 = 0 Using the quadratic formula, we find that: x_3 = frac{44.8652 pm sqrt{(-44.8652)^2 - 4(33.1924)(9.330781)}}{2(33.1924)} x_3 = frac{44.8652 pm 11.0904}{66.3848} x_3 = 0.383278 text{ or } x_3 = 1.016966 Since x_3 must be positive, we have x_3 = 0.383278. Substituting this value back into the equation for y_3, we get: y_3 = 5.671282(0.383278 - 0.650172) y_3 = 2.17368 Therefore, the coordinates of the vertices are A(0,0), B(0.650172,0), and C(0.383278,2.17368). To find the measures of the three interior angles, we can use the Law of Sines: frac{sin A}{BC} = frac{sin B}{AC} = frac{sin C}{AB} Since we know BC = 2.19, AC = sqrt{(0.383278 - 0)^2 + (2.17368 - 0)^2} = 2.21786, and AB = sqrt{(0.650172 - 0)^2 + (0 - 0)^2} = 0.650172, we can solve for the angles: sin A = frac{sin 83 {}^{circ}}{2.21786} cdot 2.19 sin A = 0.999999 A = 89.9999 {}^{circ} sin B = frac{sin 80 {}^{circ}}{0.650172} cdot 2.19 sin B = 0.999999 B = 89.9999 {}^{circ} sin C = frac{sin 17 {}^{circ}}{2.19} cdot 0.650172 sin C = 0.145501 C = 17 {}^{circ} Therefore, the measures of the three interior angles are 80 {}^{circ}, 83 {}^{circ}, and 17 {}^{circ}. Vertices: {{0,0}, {0.650172,0}, {0.383278,2.17368}} Angles: {80 {}^{circ}, 83 {}^{circ}, 17 {}^{circ}}

answer:Given data: Power, {eq}P=150text{ MW} {/eq} Voltage, {eq}V=26text{ kV} {/eq} We know that power, {eq}P=VI {/eq} Rearranging the above equation, we get: {eq}I=frac{P}{V} {/eq} Substituting the given values, we get: {eq}I=frac{150text{ MW}left( frac{{{10}^{6}}text{ W}}{1text{ MW}} right)}{26text{ kV}left( frac{{{10}^{3}}text{ V}}{1text{ kV}} right)} {/eq} {eq}approx 5769.23text{ A} {/eq} Converting amps to kiloamps: {eq}I=5769.23text{ A}left( frac{0.001text{ kA}}{1text{ A}} right) {/eq} {eq}approx 5.8text{ kA} {/eq} Therefore, a current of approximately 5.8 kA is required to transmit 150 MW of power at a voltage of 26 kV.

answer:To find the length of AF, we can use the properties of a rectangular box. In this case, since the box is rectangular, opposite edges are equal. Thus, AB (the edge opposite EF) is also 16 units. Now, we can apply the Pythagorean theorem to find AF. We have two right triangles: ΔADB and ΔADF. For ΔADB: AB² = AD² + BD² 16² = AD² + 30² AD² = 16² - 30² AD² = 256 - 900 AD² = -644 (This result is invalid, as the length cannot be negative. There seems to be an error in the original answer. Let's recalculate using the correct information.) For ΔADF: AF² = AD² + DF² AF² = (AB)² - (FD)² AF² = 16² - 5² AF² = 256 - 25 AF² = 231 Taking the square root of both sides to find AF: AF = √231 ≈ 15.19 units Therefore, the length of AF is approximately 15.19 units.