Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter G, Problem 20PS
To determine
Find the distances of the Earth from the Sun when it is at aphelion and at perihelion.
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Jupiter orbits the Sun in an elliptical path with the Sun at one focus. At perihelion, Jupiter is closest to the Sun at 7.4052 × 108 km. If the eccentricity of the orbit is 0.0489, determine the distance at aphelion (farthest point between Jupiter and the Sun). Round to the nearest million km.
The moon’s orbit around the Earth is elliptical with the Earth at one focus and with eccentricity 0.0549. If the distance between the moon and Earth at the closest point is 363,300 km, determine the distance at the farthest point. Round to the nearest 100 km.
The distance from the planet Pluto to the Sun is 4.43 × 10° km at
perihelion and 7.37 x 10° km at aphelion. Find the eccentricity of Pluto's
orbit.
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- The number of cycles per second of a point in simple harmonic motion is its .arrow_forwardWhich A winch of radius 2 ft is used to lift heavy loads. If the winch makes 8 revolutions every 15 s, find the speed at which the load is rising.arrow_forwardA carousel with three rows of animals has an angular speed of six revolutions per minute The second row of animals is at a distance of 5 feet from the center. Find the linear speed of the second row of animals. Express your answer in terms of pie, and then round your answer to the nearest integer. arrow_forward
- A hamster runs in its wheel whose radius is 3 inches. The wheel completes 9.2 revolutions in 8 seconds. What is the linear velocity of the hamster's wheel?2. A wheel completes 5.6 revolutions in 8 seconds. What is the angular velocity of the wheel in radians per minute? Enter your answer, in exact form as a simplified fraction, in the box.arrow_forwardThe orbit of Mars around the sun is an ellipse with eccentricity 0.093 and semimajor axis 2.28 × 108 km. Find a polar equation for the orbit. (If you enter your answer in scientific notation, round the decimal value to two decimal places. Use equivalent rounding if you do not enter your answer in scientific notation.)arrow_forwardWith her arms fully expanded, a baseball player swings her bat. Using her shoulders as the center of rotation, the bat moves through 120o in only 0.2 seconds. What is the angular speed of the batter's swing in radians per second? Answer in terms of pi.arrow_forward
- If a bicycle wheel makes 7 rotations a second and has a diameter of 75 cm, what cosine function describes the height of a point on the end of the wheel? y = 75 cos(14πt) - 75 2 75 y = 75 cos(14πt) + 2 y = 75 cos(14πt) + 75 2 y = 75 cos(7πt) + 75 2 2arrow_forwardWith her arms fully expanded, a baseball player swings her bat. Using her shoulders as the center of rotation, the bat moves through 120o in only 0.2 seconds. What is the angular seed of the batter's swing in radians per second?arrow_forwardConsider a triangle A BC like the one below. Suppose that a= 56, c=63, and A= 40°. (The figure is not drawn to scale.) Solve the triangle. %3D Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or". В C = []•, B = [], 6 = ] No O or O %3D solution a C barrow_forward
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What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY