In Problems 1-6, refer to the footnote for the definitions of divisors, multiple, prime, even, and odd.* List the positive integers that are divisors of 20 . *An integer d is a divisor of an integer n (and n is a multiple of d ) if n = k d for some integer for some integer k . An integer n is even if 2 is a divisor of n ; otherwise, n is odd. An integer p > 1 is prime if its only positive divisors are 1 and p .
In Problems 1-6, refer to the footnote for the definitions of divisors, multiple, prime, even, and odd.* List the positive integers that are divisors of 20 . *An integer d is a divisor of an integer n (and n is a multiple of d ) if n = k d for some integer for some integer k . An integer n is even if 2 is a divisor of n ; otherwise, n is odd. An integer p > 1 is prime if its only positive divisors are 1 and p .
Solution Summary: The author explains that the list of positive integers that are divisors of 20 is left1,2,4,5,10,20right
In Problems 1-6, refer to the footnote for the definitions of divisors, multiple, prime, even, and odd.*
List the positive integers that are divisors of
20
.
*An integer
d
is a divisor of an integer
n
(and
n
is a multiple of
d
) if
n
=
k
d
for some integer for some integer
k
. An integer
n
is even if
2
is a divisor of
n
; otherwise,
n
is odd. An integer
p
>
1
is prime if its only positive divisors are
1
and
p
.
Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t
represents the number of minutes since the spill was first observed.
Radius (feet)
80
70
60
50
40
30
20
10
0
r
0 10 20 30 40 50 60 70 80 90
Time (minutes)
(a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π.
square feet
(b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a
function of the radius of the spill, r. Use a lower case k as the proportionality constant.
C(r) =
(c) Which of the following expressions could be used to represent the amount of time it took for the radius of the spill to
increase from 20 feet to 60 feet?
r(60) - r(20)
Or¹(80-30)
r(80) - r(30)
r-1(80) - r−1(30)
r-1(60) - r¹(20)
6. Graph the function f(x)=log3x. Label three points on the graph (one should be the intercept) with
corresponding ordered pairs and label the asymptote with its equation. Write the domain and range of the function
in interval notation. Make your graph big enough to see all important features.
Find the average value gave of the function g on the given interval.
gave =
g(x) = 8√√x, [8,64]
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY