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A boater rows across a straight river of constant width w, always heading (i.e., pointing the front of the boat) toward the position on the bank directly opposite the starting point. If the river flows with uniform speed v and if the speed with which the boater can row is also v, find the equation of the path of the boat. How far downstream does the boater finally land? (Hint: if x is the cross- stream position of the boat and y is its downstream position, find an expression for dy/dx. Then solve for y(x)).
The ice sculpture is a solid with base R. Cross sections of the sculpture perpendicular to the x-axis are right triangles with the hypotenuse of the triangle in the base. Find the volume of ice that is discarded when creating the sculpture.
Sketching the graph of Cosecant function and identifying its asymptotes
You have been given information that if a student is a resident and they enroll for more than 12 hours, then their tuition will equal $120 plus $10 per hour for every hour greater than 12.
In finding the average size of automobile tire that is purchased, the mean or median size might be a tire that does not exist. Therefore, one would want to know the size of tire bought most often.
Find the average rate of change from x=2 to x=5. Find the derivative f'(x) from first principles, by setting up the difference quotient, (f(x+h)-f(x))/(h) and finding lim h->0 (f(x+h)-f(x))/(h)
Find all subfields of Q ( sqrt2, sqrt 3) with proof that you have them all. What is the minimal polynomial of sqrt2+ sqrt3? Which subfields does it generate over Q?
The excursion boat Holiday travels 35 km upstream and then back again in 4 hours and 48 minutes. The speed of the Holiday in still water is 15 km/h, what is the speed of the current.
A rational number r = p/q, where p, q are in Z, is said to be properly reduced if p and q (q > 0) have no common integral factor other than +1 or -1. Define the function f as follows;
Need to provide a real world situation where the slope and intercept have some meaning in reality. The situation needs to describe what the dependent and independent variables are and what the slope and intercept means in terms of the real paramet..
If the bottom of the ladder slides away from the wall, how fast does x change with respect to theta when theta = pi/3
Find a linear model for the cost, of waste collection as a function of the number of kilograms.
The ratio of the number of Chinese boys to the number of Malay boys is 5:3.There are 178 more Chinese boys than Malay boys. How many girls are there in the hall?
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