3. Calculate: 14.83 – 6.32 (a) (b) 45-4.62)- 1065e15 (/13 + 5)? 4. Calculate: 24.5 + 64/3.52 + 8.3 - 12.5 76.4- 28/15 (b) (5.9² – 2.42)/3 +(08 1012890 (a) 5. Calculate: (a) cos(증). (b) sin 80°- (cos 14°sin 80°)2 V0.18 tan 6. Define the variable x as x-6.7, then evaluate: (a) 0.01x – 1.4x + 80x + 16.7 (b) + e* – 51/x 7. Define the variable t as t- 3.2, then evaluate: (a) 561-9815 (b) 14ealtsin(2rt) 8. Define the variables x and y as x= 5.1 and y = 4.2, then evaluate: (6) -- (b) (xy)²-+y_ x+y (x-y))2" 2x-y 9. Define the variables a, b, c, and d'as: a - 12, b - 5.6, c = За , and d- a-b) , then evaluate: (a) +-(d-b)? (b) -25. d+c 10. A sphere has a radius of 24 cm. A rectangular prism has sides of a, a/2, and a/4. (a) Determine a of a prism that has the same volume as the sphere. (b) Determine a of a prism that has the same surface area as the sphere. a/4 a/2

Entered Answer Preview Result 1000 1000 correct y"+100*y = 9*cos(10*t) y" + 100y = 9 cos(10t) correct correct correct (1/4)*[cos(8*t)-cos(10*t)] (cos(8t) – cos(10t)) incorrect 0.58 0.58 incorrect At least one of the answers above is NOT correct. A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass-spring system is disturbed from its rest state by the force F(t) = 90 cos(10t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. a. Determine the spring constant k. k = 1000 Newtons / meter b. Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y, y', y",t.) Differential equation: y"+100y=9cos(10t) help (equations) Initial conditions: y(0) = 0 and y'(0) help (numbers) c. Solve the initial…