In the graph, each sinusoidal curve shows the shape of a vibrating string at a different moment. for which values of x does a node occur? (let k = an integer from -2 to +2.) k + 0.5 0.5k k 2k + 1.5

An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 127 ft at an angle of 31.0° above the horizontal. it then moves 127 ft at an angle of 46.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

Unpolarized light of intensity i_0=750w/m^2 is incident upon two polarizers. after passing through both polarizers the intensity is i_2=280w/m^2. (a) what is the intensity of the light after it passes through the first polarizer in w/m^2? (b) write an equation for the angle between the polarizers in terms of the initial (i_0) and final (i_2) intensities. (c) find the angle between the polarizers in degrees.

The mass of the sun is 1.99×1030kg and its distance to the earth is 1.50×1011m. what is the gravitational force of the sun on the earth?