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A body of mass 5 kg is held in equilibrium under gravity by two inextensible light ropes. One rope is horizontal and the other is inclined at an angle ? to the horizontal, as shown in the diagram below. The tension in the rope inclined at ? to the horizontal is 72N. Find the angle ?, giving your answer to the nearest degree.
find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ. Use theta for θ.
Find the mean score
If the fencing costs $14 per linear foot to install and the farmer is not willing to spend more than $7000, find the dimensions for the plot that would enclose the most area.
In polar coordinates, write equations for the line x=1 and the circle of radius 2 centered at the origin. Write an integral in polar coordinates representing the area of the region to the right of x=1 and inside the circle.
Two weather tracking stations are on the equator 146 miles apart. A weather balloon is located on a bearing of N 35°E from the western station and on a bearing of N 23°E from the eastern station. How far is the balloon from the western station?
Calculate the MRS, then calculate MRS for the product combination (x,y)= (1,1). Calculate the implicit derivative first then the value for the given point.
Amy paid $81.11 for a pair of shoes during a 40% off sale. What was the original price?
The intersection of two open sets is compact iff it is empty. Can the intersection of an infinite collection of open sets be a non-empty compact set?
verifying some important results over real valued functions.prove or disprovelet fgh be real-valued functions and let
Assume z is a function of x and y, defined implicitly by the equation -4xyz + yx + z2 + z + 7. Calculate the indicated partial derivatives at the point (x,y,z) = (1,3,1).
Adams High School has 151 freshman, 198 sophomores, 221 juniors, and 242 seniors. If two students are selected at random without replacement, what is the probability of selecting a freshman on the first selection and a senior on the second selecti..
1. graph the following2. find the derivatives of the following3. evaluate the following4. suppose that the rate of
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