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A body of mass 6 kg moves in a (counterclockwise) circular path of radius 7 meters, making one revolution every 8 seconds. You may assume the circle is in the xy-plane, and so you may ignore the third component.
A. Compute the centripetal force acting on the body.
B. Compute the magnitude of that force.
Explain the main differences among integers, rational numbers, real numbers, and irrational numbers. How are these used in everyday life? How would you explain the use of each to someone who did not know about the differences?
The perimeter of a rectangle is twice the length plus twice the width. The area of a rectangle is the product of its length and width. Suppose we let l represent the length and w represent the width of a rectangle.
Give an example of an exponential function. Find this exponential function's inverse, which will be a logarithmic function. Plot the graph of both the functions.
Find the largest possible product of such numbers.
where cosh(x)=(e^x+e^-x)/2 is the hyperbolic cosine, which is an important function in physics and engineering.
A survey of 100 mayonnaise purchasers showed 65 were loyal to one brand. For a survey of 100 bath soap purchasers showed only 53 were loyal to one brand.
Dividing a complex number with another number.
Another worker (worker 2) produces at an average rate of 65 per day with a standard deviation of 21. What is the productivity that during one week (5 working days) worker 1 will produce more than worker 2?
Find the area of the shaded region. The hexagon is regular. Round to the nearest hundredth.
Probability questions
What is the difference between intersecting and perpendicular lines? Can two lines exist that are not intersecting or parallel? Explain your answer.
a piece of cardboard is twice as it is wide. It is to be made into a box with an open top by cutting 2-in squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard.
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