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1. A spring exerts a force of 12 Newton's when it is stretched 2 meters beyond its natural length. What is the work done if this spring is stretched from its natural length to this point?
2. A crane is hauling up an object weighing 20 Newton's. The top of the crane is 10 meters above the ground. The cable weighs 2 Newton's/meter. How much work is done in hauling the object from the ground up to a height of 10 meters?
3. If two oppositely charged electric particles are separated by a distance of x meters, the force of attraction between them is given by: F = kq1q2/x2
where k, q1 and q2 are constants. If we start with a distance of a meters between the charges, calculate the work done if we move the charges apart until they are a distance of 2a meters apart.
4. The pressure P of a gas is related to its volume V by the formula P = k/v where k is a constant. A quantity of gas with an initial volume of 1 cubic meter and a pressure of 2.5 Newton's per square meter expands to a volume of 16 cubic meters. Find the work done by the gas.
The quantity of charge Q in coulombs (C) that has passed through a point in a wire up to time t. Find the current when t= 0.4s. Find the current when t= 1 s. At what time is the current the lowest?
A matrix A is said to be skew-symmetric if A^T = -A. Show that any square matrix can be represented as a sum of a symmetric matrix and a skew-symmetric matrix.
If the patient takes the medication, then he will have some side effects.
Define f(x) = x if x is rational and f(x)=0 if x is irrational. Compute the integration 1top0bottom f dx and integration 1top0bottom f dx. is f integrable on [0,1]?
Find each of the following for the given inner product defined in R^2 =3u(subscript 1)v(subscript 1) + u(subscript 2)v(subscript 2)
A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the to..
The marketing department at Bodnar Industries is developing a promotional campaign to introduce a new product. A listing of the various activities required, their immediate predecessors, and estimates of their times (in days) is given below.
The speed of a car traveling in a straight line reduced from 45 to 30 miles per hour in a distance of 264 feet. Find the distance in which the car can be brought to rest from 30 miles per hour, assuming the same constant deceleration.
a larger number is one more than twice the smaller. if ten more than the sum of the numbers is equal to four more
Evaluate the composite function
A rectangular parcel of land has an area of 5000 ft^2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, rounded to the nearest foot?
a consumer is considering purchasing a set of tires. she samples 30 companies and finds the average price of a set of
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