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The center of a national park is located at (0,0). A special nature preserve is bounded by by straight lines connecting the points A at (3,2), B at (5,1), C at (8,4) and D at (6,5) in a parallelogram. The yearly rainfall at each point is given by RF(x,y) =x2-xy+y2 in inches. Transform this into a rectangle in v - r space using the Jacobian theory we studied and determine the following.
1. Find the average rainfall per year for the entire region.
2. Suppose that we desire to constract a weather station at a point in order to report a number on a regular basis that might represent the average rainfall for the entire preserve. Assuming we pick the center of "mass" of the rainfall density function for this point, find the location of the weather station in the (x,y) system
The frequency of oscillation of an object suspended on a spring depends on the stiffness k of the spring (called the spring constant) and the mass m of the object. If the spring is
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Find out the surface area of the solid acquired by rotating y = √ (9-x 2 ), - 2 x 2 about the x-axis. Solution The formula that we'll be using here is, S = ∫ 2Πyds
Example of Decimal to Fraction Conversion: Example: Convert 18.82 to a mixed number. Solution: Step 1: 18.82 is 18 and 82 hundredths. 18.82 = 18(8
Patio measures 24 meters square. Patio stone are 30 cm each side. How many stones are required to cover the patio?
Tangent, Normal and Binormal Vectors In this part we want to look at an application of derivatives for vector functions. In fact, there are a couple of applications, but they
X and Y are centers of circles of radius 9cm and 2cm and XY = 17cm. Z is the centre of a circle of radius 4 cm, which touches the above circles externally. Given that XZY=90 o , w
One integer is four times other. The sum of the integers is 5. What is the value of the lesser integer? Let x = the lesser integer and now let y = the greater integer. The ?rst
A company is setting up an assembly line to produce 100 units/hour. The table shown below identifies the work elements, times, and immediate predecessors. a) What cycle tim
Advantages and disadvantages of paasche indices
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