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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.
a tire placed on a balancing machine in a service station starts from rest an d turns through 4.7 revolutions in 1.2 seconds before reaching its final angular speed Calculate its a
The price of heating oil rose from $1.10 per gallon to $1.43 per gallon. What is the percent of increase? The price of heating oil rose $0.33 ($1.43 - $1.10 = $0.33). To ?nd ou
Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event B. Likewise for independent
whta are the formulas needed for proving in trignometry .
Now we have to look at rational expressions. A rational expression is a fraction wherein the numerator and/or the denominator are polynomials. Here are some examples of rational e
Let a and b be fixed real numbers such that a The open interval (a, b): We define an open interval (a, b) with end points a and b as a set of all r
Owner of a computer repair shop has daily revenue with mean $7200 and SD $1200 Daily revenue for next 30 days will be monitored. What is probability that daily revenue for those 30
Fundamental Theorem of Calculus, Part II Assume f ( x ) is a continuous function on [a,b] and also assume that F ( x ) is any anti- derivative for f ( x ) . Then,
If secA= x+1/4x, prove that secA+tanA=2x or 1/2x. Ans: Sec? = x + 1/4x ⇒ Sec 2 ? =( x + 1/4x) 2 (Sec 2 ?= 1 + Tan 2 ?) Tan 2 ? = ( x +
Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon
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