question 1: irrational,real
question 2: rational,real
Answer:
K is either 9 or 1
Step-by-step explanation:
Sqrt((0 - 3)² + (k - 5)²) = 5
Square both sides
(0 - 3)² + (k - 5)² = 5²
(0 - 3)² + (k - 5)² = 25
-3² + (k - 5)² = 25
9 + (k-5)(k-5) = 25
9 + k² - 5k - 5k + 25 - 25 = 0
k² - 10k +9 = 0
k² - 9k - k + 9 = 0
k(k - 9) - 1(k - 9) = 0
k - 1 = 0 ; k = 1
k - 9 = 9; k = 1
K = 9 or k = 1
K is either 9 or 1
The answer below (I need 20 characters to respond so just ignore the words between the parenthesis on this response)
Answer:
P = 309.35 + 2.31t
Step-by-step explanation:
The relation between the population of the USA and the time in years after 2010 will be linear as the increase in population is constant for every year since 2010 which is 2.31 million.
So, we can model the population P in million as a function of time(t) in years since 2010 as
P = 309.35 + 2.31t ....... (1)
Now, for t = 0 i.e. in the year 2010, the population will be obtained from equation (1) to be 309.35 million.
(Answer)
This equation uses two properties of logarithms:


So you could take the ln from left and right hand side in the equation, and get:
(2-x)ln 3 = x ln 5
then
2 ln 3 - x ln 3 - x ln 5 = 0 =>
x(ln 3 + ln 5) = 2 ln 3
so x = 2 ln 3 / (ln3 + ln5)
Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15
so x= ln9 / ln15