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Please be very careful with writing down all calculations step by step and also explain all conclusions and results thoroughlyin words using mathematical language:
1. All solutions to the differential equation y'-2y=0 should also be solutions to the differential equation y''-ay'+ay=0. Determine the constant a such that this is true.
2. Determine if the inverse applies for this value of a, that is, if all solutions to y''-ay'+ay=0 are solutions to y'-2y=0.
in 2006 75.9 of first-year college students responding to a national survey said they used the internet for research or
multiple choice question from probability and set language.choose the one alternative that best completes the statement
the sum of two numbers is less than 18. The first number is 6 more than the second. What are the possible values of the two numbers?
Through how many radians does a pulley with 10 cm diameter turn when 10 m of rope has been pulled through it without slippage? How many revolutions result?
Show a sketch of a region satisfying set of inequalities or system of inequalities
two truck drivers leave a cafe at the same time, traveling in different directions. one truck goes 8 mph faster thaan the other one. after 4 hr they are 408 miles apart. how fast is each truck going?
Find the absolute max and min values of f(x)=l+6x-3x^3 over the closed interval [0,4].
A baseball diamond is a square with side 90ft. A batter hits the ball and runs toward first base with a speed of 24ft/s. At what rate is her distance from second base decreasing when she is halfway to first base?
an open box is to be constructed from a square piece of metal by removing a square of side 3 inches form each corner and turning up the edges. if the box is to hold 108 cubic inches, what should be the dimensions of the metal.
The width of a rectangular garden is 2 feet shorter than one-half its length. If the perimeter of the garden is 32 ft., what are the dimensions of the garden?
Explain, in complete sentences, whether or not the expression x2 - 121 fits one of the special patterns and, if so, which one. Explain how the polynomial is factored.
An open-topped rectangular box must be made with a volume of 4500 ft3. If its bottom is a rectangle whose length is twice its width, what dimensions would minimize the total area of the bottom and four sides of the box?
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