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1. a) Suppose that a is a natural number and that a2 is divisible by 3, show that a is divisible by 3. (Hint: show that if a is not divisible by 3, then neither is a2.)
b.) Show that sqrt(3) is not rational.
the perimeter of a rectangle is 54 feet. describe the possible lengths of a side if the area of the rectangle is not to exceed 152 square feet.
Write the definite integral that represents the arc length of one period of the curve y=sin2x (do not evaluate the integral)
Your first rational expression is 5m2 + m7m
To form an open box, squares of side 4cm are cut from each corner of a square piece of tin and then the sides of the tin are turned up. If the volume of the box is to be 400cm^3, what should be the area of the original piece of tin be?
How many small screen televisions must be produced in a month in order to minimize the company's average cost? Show all steps and justify your answer.
Write a goal equation that represents the fluctuations in the production level from May to June, June to July, and July to August.
Evaluate the triple integral 0∫1 0∫20∫x z dz dy dx. Evaluate∫∫∫T z dV where T is the solid bounded by z = 0, and z = √(9-x2-y2)
How to solve a problem with Property Tax in a position in Pennsylvania earning 50,000 per year. You found a duplex that you can purchase with an assessed value of $75,000.
Let G be a group and let φ: S3 → G be a non-trivial homomorphism. Suppose φ is not injective. Find the kernel of φ. If φ is surjective, what is G
Determine the least squares regression line
A rectangular box has a height of 4 feet to within an accuracy of 1 in and a square base with width 2 feet to within an accuracy of 1 in. Find the volume V and the approximate error dV in the volume of the can.
Villages A , B , C and D are connected by overhead telephone lines joining AB , AC , BC , BD and CD . As a result of severe gales, there is a probability p (the same for each link) that any particular link is broken. Show that the probability that..
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