860jay
15.01.2020 •
Mathematics
Inctions (pp. 498-504)
exercises
13. graph the relation and connect the points. then
graph and write the inverse.
e
х
-1
y 1 1
0
0.2
1 2 3
0.04 0.008 0.001
otion of a series decreased
inverse
Solved
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Ответ:
a rational.
b. irrational.
step-by-step explanation:
a. the 2 numbers are rational so we can write them as a/b and c/d where a, b c and d are integers (not = 0.)
a/b * c/d = ac / bd.
by the closure property of integers , the product of 2 integers must also be an integer so we can write ac/bd = e/f where e and f are integers so the product is rational.
thus the product of 2 rational numbers is rational,
b. the product of a nonzero rational and an irrational is irrational.
let a/b be the rational number and x the irrational.
let us assume that a rational times an irrational number gives a rational number.
so we assume multiplying a/b * x = m/n where m and n are integers.
making x the subject my multiplying both sides by b/a we get:
x = mb/an which is rational. because m, b , a and n are integers
but we assumed x is irrational but we have proved it rational. so that is our contradiction.
so our assumption was wrong and rational * irrational must be irrational.
c. the rational cannot be zero because when we multiply by zero the answer is zero. it gives a different result to b.