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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
What is Matrix addition and subtraction? Illustrate the procedure of Matrix addition and subtraction.
Show that 571 is a prime number. Ans: Let x=571⇒√x=√571 Now 571 lies between the perfect squares of (23)2 and (24)2 Prime numbers less than 24 are 2,3,5,7,11,13,17,1
Since we are going to be working almost exclusively along with systems of equations wherein the number of unknowns equals the number of equations we will confine our review to thes
What is the lesser of two consecutive positive integers whose product is 90? Let x = the lesser integer and let x + 1 = the greater integer. Because product is a key word for m
Differentiate following. Solution : It requires the product rule & each derivative in the product rule will need a chain rule application as well. T ′ ( x ) =1/1+(2x) 2
Two angles are supplementary. The evaluate of one is 30 more than twice the measure of the other. Determine the measure of the larger angle. a. 130° b. 20° c. 50° d. 70
The temperature at 6 P.M. was 31°F. Through midnight, it had dropped 40°F. What was the temperature at midnight? Visualize a number line. The drop from 31° to 0° is 31°. There
verify 4(sin^4 30^0+cos60^0 )-3(cos^2 ?45?^0-sin^2 90^0 )=2
(1)Derive, algebraically, the 2nd order (Simpson's Rule) integration formula using 3 equally spaced sample points, f 0 ,f 1 ,f 2 with an increment of h. (2) Using software such
Describe Square Roots? When a number is written inside a radical sign (√), the number is called the radicand, and we say that you are "taking the square root of" that number.
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