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Differentiate (assume k is a constant)
y=1/(p + ke^p)
y =
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- A 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 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 window has the shape of a square surmounted by a semicircle. The base of the window is measured as having width 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.
- Show detailed process using Newton's Law of Coolingline integralA 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.)