A 100-W (watt) light bulb has resistance R = 143 2 (ohms) when attached to household current, where voltage varies as V = Vo sin(27 ft), where Vo = 110 V, ƒ = 60 Hz. The power supplied to the bulb is P = J/s (joules per second) and the total energy expended over a time period [0, T] (in seconds) is T U = Р() dt Compute U if the bulb remains on for 7 hours. (Use decimal notation. Give your answer to one decimal place.) U = J

A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?

An object is suspended from the end of a spring. Its displacement, in cm, from the starting position is s(t) = 8 sin(10) where t is in seconds. Calculate the average rate of change in displacement of the object on the interval t = 1 second to t = 3 seconds. Include units. (a) (b) Estimate the instantaneous rate of change in displacement of the object att = 2 seconds. Include units.

A rocket has taken off and is rising vertically according to the position equation, s = 50t^2 (use this to find the “given” rate of change). It is being tracked by a device located 2000 ft from the point of lift-off. The angle θ (in radians) is the angle between the tracking line and the ground. Find the rate of change in the angle θ , 10 seconds after lift-off.(a) GIVEN: Use the position function to find the given rate of change at t = 10 sec.(b) FIND: Write the derivative you want to find.(c) Write an equation relating the variable θ and two sides of the triangle. Then, differentiate with respect to time. (d) Solve for the unknown derivative in (b) after substituting in known values. Note: first you will need to solve for both s and the length of the hypotenuse at t = 10 sec.. Use a calculator for your final computations.

cos x-sinxtanx=

What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

Solve: 2a[sinh(25/a)]=51

sin' COST %3D k/2

Calculate z=2x+y^2, Given x = 2.90 ± 0.43 , y = 7.50 ± 0.32, z=____+-_____