Inverse Laplace of [ 0.9s / (s^2 + 0.1s -0.02)]
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![Inverse Laplace of [ 0.9s / (s^2 + 0.1s - 0.02)]
Select the correct response:
O none of the choices
O - 0.1 e^(0.1t) + 0.2 e^ (-0.2t)
O - e^(0.1 t) + 0.2 e^ (-0.21)
O 0.3 e^(0.1t) + 0.6 e (-0.2t)
O - 0.3 e^(0.1t) + 0.5 e^ (-0.2t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1543865-f18d-4ce4-a1d9-6cdaad95dc15%2Ffab6b758-c776-4a42-80e3-522a9e253b35%2F7g86rjc_processed.jpeg&w=3840&q=75)
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- A spaceship is moving in a straight line at 36,000 miles per socond. Suddenly it accelerates at a(t) = 18t miles per second squared. Assume that the speed of light is 186,000 miles per second and that relativistic effects do not influence the velocity of the spaceship. How long does it take the ship to reach the speed of light and how far does it travel during that time?A mass of 1 kgkg is attached to the end of a spring whose restoring force is 180 NmNm. The mass is in a medium that exerts a viscous resistance of 156 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object. Suppose the spring is stretched 0.07 mm beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 7sin(3t)7sin(3t) NN at time tt seconds. Find an function to express the steady-state component of the object's displacement from the spring's natural position, in mm after tt seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.)Water flows through a circular pipe of cross-sectional area 6.16cm2 at a uniform speed of 10 cm per second. At 6 a.m, water starts flowing through the pipe into an empty rectangular tank of base area 3 m2. a) what is the depth of water in the tank at 8.30 a.m ? b) If the tank is 1.2 m high and has a hole at the bottom through which water leaks at the rate of 11.6cm3 per second, determine the time at which the tank will be filled.
- Use a linear approximation (or differentials) to estimate the given number. Consider the linear approximation at a = 1000 1/1002integral arctan4t dtA water container with a square base, whose cross section is 4ft2 and whose height is 9 ft is fully filled with an unknown fluid. It has a hole at the base of radius 1 inch. When will the container be empty? Use application of First Order ODE Orifice.
- 20. Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.08 cm thick to a spherical ball with a radius of 90 cm. 17. A 5m ladder is leaning against a wall. Its upper end is sliding down the wall at a rate of 2m/s. Find how fast the bottom end of the ladder is moving at the point 3m from the wall.Integral of arcsin(t) (dt) using trig substitutionA window has the shape of a square surmounted by semi-circle. The base of the window has a width of 60 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum error possible in computing the area of the window.
- A topographer wants to determine the area of a certain field. She measures two adjacent sides of the terrain obtaining measurements of 400m and 800m, with a maximum error of half a meter in each measurement. She determines that the angle between the two sides is 40° with a maximum error of 0.2°. If the field is triangular, use differentials to estimate the maximum error in the terrain area.How does Riemann integral work geometrically, the process of finding the area under a curve?If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt. Then, suppose oil spills from a ruptured tanker and spreads in a cricular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 30 m? *Please use handwriting not type script, i understand it better that way. thank you. Also, please label your known and knowns and draw a diagram*
