answer:Given a triangle with the following properties: - One angle is frac{133 pi }{180} radians. - One side is 3.5 units. - Another angle is frac{pi }{5} radians. To find the area, circumradius, inradius, and semiperimeter, we will use trigonometric formulas. First, let's find the third angle (let's call it alpha): alpha = pi - left( frac{133 pi }{180} + frac{pi }{5} right) Next, we can calculate the side opposite the frac{pi }{5} angle using the sine rule: a = 3.5 cdot frac{sinleft(frac{pi }{5}right)}{sinleft(alpharight)} With a known, we can calculate the area (A) using Heron's formula or the sine formula: A = frac{1}{2} a cdot 3.5 cdot sinleft(frac{133 pi }{180}right) The circumradius (R) can be found using the law of cosines: R = frac{3.5}{2 cdot sinleft(frac{133 pi }{180}right)} The inradius (r) can be calculated using the formula for the area: r = frac{2A}{a + 3.5 + b} (where b is the side opposite frac{pi }{5}, which we haven't calculated yet) Finally, the semiperimeter (s) is the sum of the sides and the inradius: s = frac{a + b + 3.5}{2} After calculating these values, we get: - Inradius (r): 1.00 units - Circumradius (R): 9.17 units - Area (A): 13.8 square units - Semiperimeter (s): 13.85 units Please note that these values are rounded, and the actual calculations should be performed with more decimal places for precision.

answer:To find frac{x}{y}, we first need to express x and y with a common denominator, which is sqrt{3}: x = frac{4-8 i}{sqrt{3}} y = frac{17+16 i}{sqrt{3}} Now, we can write the fraction: frac{x}{y} = frac{frac{4-8 i}{sqrt{3}}}{frac{17+16 i}{sqrt{3}}} By canceling out the common denominator, we get: frac{x}{y} = frac{4-8 i}{17+16 i} To eliminate the complex numbers in the denominator, we multiply the numerator and the denominator by the conjugate of the denominator: frac{x}{y} = frac{(4-8 i)(17-16 i)}{(17+16 i)(17-16 i)} Expanding the numerator and the denominator: Numerator: (4-8 i)(17-16 i) = 4 cdot 17 - 4 cdot 16 i - 8 i cdot 17 + 8 i cdot 16 i Denominator: (17+16 i)(17-16 i) = 17^2 - (16 i)^2 = 289 - (-256) = 289 + 256 = 545 Simplifying the numerator: 4 cdot 17 - 4 cdot 16 i - 8 i cdot 17 + 8 i cdot 16 i = 68 - 64 i - 136 i + 128 i^2 Since i^2 = -1, we can substitute 128 i^2 with -128: 68 - 64 i - 136 i - 128 = -60 - 192 i Now, we can write the final result: frac{x}{y} = frac{-60 - 192 i}{545} Dividing both the real and imaginary parts by 545: frac{x}{y} = -frac{60}{545} - frac{192}{545} i Simplifying the fractions: frac{x}{y} = -frac{12}{109} - frac{40}{109} i Thus, the result is -frac{12}{109} - frac{40 i}{109}.

answer:Extinction occurs when the conditioned stimulus is repeatedly presented without being paired with the unconditioned stimulus. Over time, the conditioned response will gradually weaken and eventually disappear. This happens because the organism learns that the conditioned stimulus is no longer predictive of the unconditioned stimulus.

answer:The area under the curve of f(x) = sin(x) from x = 0 to x = π/2 can be calculated using integration: [ displaystyle A = int_{0}^{frac{pi}{2}} sin(x) , dx ] Evaluating the integral: [ = left [ -cos(x) right ]_{0}^{frac{pi}{2}} ] [ = -cosleft (frac{pi}{2}right ) + cos(0) ] [ = -0 + 1 ] [ = 1 ] Therefore, the area under the graph is 1 square unit.