answer:The velocity of the train relative to the ground (v_tg) can be found by combining the passenger's velocity relative to the train (v_tp) and the passenger's velocity relative to the ground (v_pg). Given: v_tp = 2.40 m/s (north) v_pg = 4.5 m/s at 34.0° west of north Resolving v_pg into its horizontal (i) and vertical (j) components: v_pg_i = v_pg * cos(34.0°) = 4.5 * cos(34.0°) = 3.73 m/s (west) v_pg_j = v_pg * sin(34.0°) = 4.5 * sin(34.0°) = 2.52 m/s (north) Now, we have: v_tg = v_tp + v_pg_i - v_pg_j v_tg = (2.40 - 3.73 + 2.52) m/s v_tg = (-0.13) m/s (westward) Magnitude of v_tg: |v_tg| = sqrt((-0.13)^2) = 0.13 m/s Direction of v_tg: Since the train's velocity is entirely in the westward direction, the angle (θ_tg) is directly west (180°) from the north direction. So, the velocity of the train relative to the ground is: Magnitude (v_tg) = 0.13 m/s Direction (θ_tg) = 180° west of north Note: The original answer had a mistake in determining the train's velocity, resulting in an incorrect magnitude and direction. The revised answer corrects these errors.

answer:To simplify this expression, we need to ensure a common denominator before combining the terms. First, rewrite the number 4 as a fraction with the same denominator as the first term: 4 = dfrac{4}{1} Now, to get a common denominator, multiply the second expression by dfrac{-10q}{-10q}: dfrac{4}{1} times dfrac{-10q}{-10q} = dfrac{-40q}{-10q} = dfrac{40q}{10q} = dfrac{4q}{q} This gives us: k = dfrac{10q - 10}{-10q} + dfrac{4q}{q} Since both fractions now have the same denominator, we can combine the numerators: k = dfrac{10q - 10 + 4q}{-10q} k = dfrac{14q - 10}{-10q} Next, factor out -1 from the numerator to simplify the expression: k = dfrac{-1(14q - 10)}{-10q} k = dfrac{-14q + 10}{-10q} Finally, divide both the numerator and the denominator by 10: k = dfrac{-1.4q + 1}{-1q} k = dfrac{1.4q - 1}{q} So, the simplified form of the expression is k = dfrac{1.4q - 1}{q}.

answer:The harmonic mean of two numbers is defined as the reciprocal of the average of the reciprocals of the numbers. In this case, we have: H = 2 / (1/19 + 1/(22/3)) H = 2 / (19/19 + 3/22) H = 2 / (19/19 + 3/22) H = 2 / (38/38 + 3/22) H = 2 / (41/22) H = 2 * 22 / 41 H = 44 / 41 H = 79/9 Therefore, the harmonic mean of 19 and 22/3 is 79/9. The answer is 79/9

answer:Using the same algebraic steps as in the original answer, we have: begin{eqnarray*} 49-y^2 &equiv& frac{49}{49}-frac{y^2}{49} &equiv& frac{49-y^2}{49}end{eqnarray*} Therefore, begin{eqnarray*} sqrt{49-y^2} &equiv& sqrt{frac{49-y^2}{49}} &equiv& frac{sqrt{49-y^2}}{sqrt{49}} &equiv& frac{sqrt{49-y^2}}{7} &equiv& tfrac{1}{7}sqrt{49-y^2} end{eqnarray*} So, a = 7 and b = 49.