Difference between a bowling ball and a baseball
2 answers:
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He must type the remainder of the report by rate 32 words per minute to finish it in 25 minutes
Step-by-step explanation:
The given is:
- Henry has been typing a book report that contains 1250 words
- He has been typing for 1/4 hour at a rate of 30 words per minutes
- He must type the remainder of the report in 25 more minutes
We need to find his rate to finish the remaining report in 25 minutes
∵ Henry has been typing for 1/4 hour at a rate of 30 words per minute
- We must to change hour to minutes
∵ 1 hour = 60 minutes
∴ hour =
hour × 60 = 15 minutes
∴ He has been typing for 15 minutes at a rate of 30 words per minute
∵ The number of words has been typed = his rate × time
∴ The number of words has been typed = 30 × 15 = 450 words
∵ The book report that contains 1250 words
- Subtract the number of words has been typed from the total
words to find the remaining word in the book
∴ The remaining words = 1250 - 450 = 800 words
∵ He plans to finish them in 25 minutes
- Substitute the number of the remaining words and the time
in the rule above to find his rate
∵ 800 = his rate × 25
- Divide both sides by 25
∴ His rate = 32 words per minute
He must type the remainder of the report by rate 32 words per minute to finish it in 25 minutes
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Answer:
621 and 82 are relatively prime.
Step-by-step explanation:
Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one).
The greatest common divisor of two integers <em>a</em> and <em>b</em> is the largest integer that divides them both.
The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.
The Euclidean algorithm solves the problem:
<em>Given integers a, b find </em><em />
The Euclidean algorithm provides a fast way to determine <em>d</em> without knowing the prime factors of <em>a</em> or <em>b</em>. Here is an outline of the steps:
- Let
,
- Given <em>x</em>, <em>y</em>, use the division algorithm to write
.
- If r = 0, stop and output <em>y</em>; this is the gcd of a, b.
- If
, replace (<em>x, y</em>) by (<em>y, r</em>). Go to step 2.
The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.
Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:
Step 1: Subtract D from N repeatedly until we get a result that lies between 0 (inclusive) and D (exclusive) and is the smallest non-negative number obtained by repeated subtraction.
Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.
Applying the above steps,
The gcd(621, 82) is 1. Therefore, 621 and 82 are relatively prime.