A flowerpot of mass 42N is hung above a window by three ropes, each making an angle of 20° with the vertical. What is the tension in each rope supporting the flowerpot?

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

What are the dimensions of the cross section that passes through the points a, f, g, and d?

Ice at 0.0∘c has a density of 917 kg/m3. a 3.00 cm3 ice cube is gently released inside a small container filled with oil and is observed to be neutrally buoyant. what is the density of the oil?