A large water tower holds 3 million gallons of water, which has a mass of about 11 million kilograms. When the wind blows, this causes the steel structure to sway back and forth due to the force. An engineer studying the tower observes that a steady wind at a speed of 35 mph exerts a force of 1.45 million Newtons on the tower, causing it to lean 0.27 meters away from equilibrium. The engineer begins by assuming that the restoring force is proportional to the displacement F = –kx, so that the motion of the system can be modeled by the differential equation mx" + kx = 0. Here m is the mass of the tower, k is the spring constant, and x is the displacement of the tower away from its equilibrium position. (a) What is the spring constant k of the steel structure? Be sure to use the right units! (b) Write the general solution to the differential equation. (c) What is the angular frequency w at which the tower oscillates?

The salesclerk at TV-Rama says that the area of a 52 in. plasma screen is four times as large as the area of a 26 in. screen. Television screens are measured on the diagonal. Is the salesclerk correct? Explain.

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Solve linear eqaution by addition mehtod. X+y=5 X-y==11

(45 where & 2 a. a. The length of one side of a square tile is 1 feet. Determine the area of the tile in square feet (use A = s²). #H How many tiles would you need to cover a 9-foot by 10-foot bathroom floor, assuming no errors or waste?

Solve for m. The solution is m = | (Use integers or fractions for any numbers in the expression. Simplify your answer.) p= 3m + 3v Question Viewer Enter your answer in the answer box rch #メ A prt sc delete home %23 3. %24 4 & 7. backspace D F J. K pause alt ctrl

do all 6 questions please. questions 5, 6, 7, 8, 9, and 10.